Business Email Rubric
Subject Line
Subject line
clearly states the
main point of the
email
5points
Subject line is a
bit long (5+
words) or a bit
short (1 word) but
states the point of
the email
3points
Subject line does
not correspond to
the main point of
the email
2points
Subject line is
missing
0points
Greeting
Email includes a
professional
greeting that is
appropriate for the
audience; uses
the person's first
name
5points
Email includes a
professional
greeting that is
adequate for the
audience but uses
the person's first
and last name or
just the last name
3points
Email includes a
greeting but it is
not personalized
2points
Email lacks a
greeting
0points
Introductory
Comment
Email includes an
introductory
positive, relevant
comment
5points
it Email includes
an introductory,
positive comment
but may be very
general
3points
Email includes an
introduction only
2points
Email lacks an
introductory
comment
0points
Content
Purpose of the
email is clear, as
is the outcome;
content is succinct
and well organized
and does not
include
unnecessary
information
5points
Purpose of the
email is clear, as
is the outcome;
content could be
better organized
3points
Purpose of the
email is not clear
and/or content is
poorly organized;
it took more than
one reading to
understand what
the email is about
2points
Email seems to be
a collection of
unrelated
statements; it is
difficult to figure
out what the
purpose is
0points
Closing and
Signature
Email includes a
complementary
closing and
signature with all
required items
(name,
title/position,
company name,
phone number)
5points
Email includes a
complementary
closing and
signature but the
signature is
incomplete
3points
Email may be
missing either a
complementary
closing or
signature
2points
Email lacks a
closing and
signature
0points
Writing
Conventions
Email looks
professional and
does not have any
formatting or
writing errors
5points
Email is well
presented with
minimal (<3)
formatting or
writing errors
3points
Email includes
several (3+)
formatting or
writing errors
2points
Email is poorly
presented and has
an accumulation
of writing errors
that interfere with
readability
0points
BUS308 Week 3 Lecture 2
Examining Differences – ANOVA and Chi Square
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. Conducting hypothesis tests with the ANVOA and Chi Square tests
2. How to interpret the Analysis of Variance test output
3. How to interpret Determining significant differences between group means
4. The basics of the Chi Square Distribution.
Overview
This week we introduced the ANOVA test for multiple mean equality and the Chi Square
tests for distrib ...
Ashford 4: - Week 3 - Discussion 1
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
ANOVA
In many ways, comparing multiple sample means is simply an extension of what we covered last week. Just as we had 3 versions of the t-test (1 sample, 2 sample (with and without equal variance), and paired; we have several versions of ANOVA – single factor, factorial (called 2-factor with replication in Excel), and within-subjects (2-factor without replication in Excel). What examples (professional, personal, social) can you provide on when we might use each type? What would be the appropriate hypotheses statements for each example?
Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on why you agree or disagree with the statistical test that your peers have described as appropriate in this scenario.
Ashford 4: - Week 3 - Discussion 2
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
Effect Size
Several statistical tests have a way to measure effect size. What is this, and when might you want to use it in looking at results from these tests on job related data?
Ashford 4: - Week 3 - Assignment
Problem Set Week Three
Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations.
All statistical calculations will use the Employee Salary Data Set and the Week 3 assignment sheet.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
See comments at the right of the data set.
ID
Salary
Compa
Midpoint
Age
Performance Rating
Service
Gender
Raise
Degree
Gender1
Grade
8
23
1.000
23
32
90
9
1
5.8
0
F
A
The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
10
22
0.956
23
30
80
7
1
4.7
0
F
A
Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11
23
1.000
23
41
100
19
1
4.8
0
F
A
14
24
1.043
23
32
90
12
1
6
0
F
A
The column labels in the table mean:
15
24
1.043
23
32
80
8
1
4.9
0
F
A
ID – Employee sample number
Salary – Salary in thousands
23
23
1.000
23
36
65
6
1
3.3
1
F
A
Age – Age in years
Performance Rating – Appraisal rating (Employee evaluation score)
26
24
1.043
23
22
95
2
1
6.2
1
F
A
Service – Years of service (rounded)
Gender: ...
BUS 308 Week 3 Lecture 3 Setting up ANOVA and Chi Square .docxjasoninnes20
BUS 308 Week 3 Lecture 3
Setting up ANOVA and Chi Square
Expected Outcomes
After reading this lecture, the student should know how to:
1. Set-up the data for an ANOVA analysis.
2. Set-up and perform an ANOVA test.
3. Set-up a table of mean differences.
4. Set-up and perform a Chi Square test.
Overview
Setting up the ANOVA test is quite similar to how the t and F tests were set up. The Chi
Square set-up is a bit more complex, as it is not found in the Data Analysis list of tools.
ANOVA
The set-up of ANOVA within Excel is very similar to how we set up the F and T tests
last week; place the data set in appropriate groups and then use the ANOVA input box. One
difference this week is that the Fx (or Formulas) list does not include an option for ANOVA, so
we need to use the Data | Analysis tools.
Data Set-up
Single Factor. As with the t-test, ANOVA has a couple of versions to select between.
Each is used to answer slightly different questions, and these will be examined below. The most
significant difference lies in the data table used for each version.
We will be working primarily with the ANOAV Single Factor, which deals with
examining possible differences between the means of a single variable within different groups.
A question of whether or not the mean compa-ratios are equal across the grades is an example of
the kind of question answered with this approach.
Question 1. Week 3’s first question is about salary mean equality across the grades. Our
lecture example will deal with compa-ratio mean equality across the grades. The set-up for the
Single Factor ANOVA we just went through assumed this. The initial steps in the hypothesis
testing process are similar to what we have done before:
Step 1: Ho: All Compa-Ratio means are equal across the grades
Ha: At least one compa-ratio mean differs
Notice that these are the standard ANOVA – Single factor null and alternate hypothesis
statements that identify the specific variable (compa-ratio) and statistic (mean) that we
are testing, and merely say “no difference” and “at least one differs.”
Step 2: Alpha = 0.05
Step 3: F statistic and Single Factor ANOVA; used to test multiple means
Step 4: Decision Rule: Reject Ho if the p-value < 0.05
Step 5: Conduct the test – place the test function in cell K08.
As with the F and T tests, we need to group the data into distinct groups. For example, if
we are going to test the compa-ratio mean across grades, then the data must be set-up in a
table with grades across the top, as in the screen shot below. Note that as was done with
the T and F test input data, the raw or initial data was listed and then sorted. Values were
then copied into related groups; we used male and female groups for the F and t tests and
grade groups for this test.
Test Set-up. Go to the Data | Analysis and select ANOVA Single Factor gives us the
following input screen. This is completed for our compa-ratio ...
BUS 308 Week 3 Lecture 3 Setting up ANOVA and Chi Square .docxcurwenmichaela
BUS 308 Week 3 Lecture 3
Setting up ANOVA and Chi Square
Expected Outcomes
After reading this lecture, the student should know how to:
1. Set-up the data for an ANOVA analysis.
2. Set-up and perform an ANOVA test.
3. Set-up a table of mean differences.
4. Set-up and perform a Chi Square test.
Overview
Setting up the ANOVA test is quite similar to how the t and F tests were set up. The Chi
Square set-up is a bit more complex, as it is not found in the Data Analysis list of tools.
ANOVA
The set-up of ANOVA within Excel is very similar to how we set up the F and T tests
last week; place the data set in appropriate groups and then use the ANOVA input box. One
difference this week is that the Fx (or Formulas) list does not include an option for ANOVA, so
we need to use the Data | Analysis tools.
Data Set-up
Single Factor. As with the t-test, ANOVA has a couple of versions to select between.
Each is used to answer slightly different questions, and these will be examined below. The most
significant difference lies in the data table used for each version.
We will be working primarily with the ANOAV Single Factor, which deals with
examining possible differences between the means of a single variable within different groups.
A question of whether or not the mean compa-ratios are equal across the grades is an example of
the kind of question answered with this approach.
Question 1. Week 3’s first question is about salary mean equality across the grades. Our
lecture example will deal with compa-ratio mean equality across the grades. The set-up for the
Single Factor ANOVA we just went through assumed this. The initial steps in the hypothesis
testing process are similar to what we have done before:
Step 1: Ho: All Compa-Ratio means are equal across the grades
Ha: At least one compa-ratio mean differs
Notice that these are the standard ANOVA – Single factor null and alternate hypothesis
statements that identify the specific variable (compa-ratio) and statistic (mean) that we
are testing, and merely say “no difference” and “at least one differs.”
Step 2: Alpha = 0.05
Step 3: F statistic and Single Factor ANOVA; used to test multiple means
Step 4: Decision Rule: Reject Ho if the p-value < 0.05
Step 5: Conduct the test – place the test function in cell K08.
As with the F and T tests, we need to group the data into distinct groups. For example, if
we are going to test the compa-ratio mean across grades, then the data must be set-up in a
table with grades across the top, as in the screen shot below. Note that as was done with
the T and F test input data, the raw or initial data was listed and then sorted. Values were
then copied into related groups; we used male and female groups for the F and t tests and
grade groups for this test.
Test Set-up. Go to the Data | Analysis and select ANOVA Single Factor gives us the
following input screen. This is completed for our compa-ratio.
Week 3 Lecture 9 Effect Size When we reject the null h.docxcockekeshia
Week 3 Lecture 9
Effect Size
When we reject the null hypothesis with an ANOVA test, we have two questions that
arise. The first, which pair of means differs significantly, we have dealt with already. The
second question, similar to what we asked with the t-test null hypothesis rejection is; what
caused the rejection, the sample size or the variable interactions? This question is again
answered using an effect size measure.
Recall that the effect size measure shows how likely the variable interaction caused the
null hypothesis rejection. Large values lead us to say the variables caused the outcome, while
small values lead us to say the outcome has little to no practical significance as the sample size
was the most likely cause of the rejection of the null.
With the single factor ANOVA, the effect size measure is eta squared, and equals the
SS(between)/SS(total) (Tanner & Youssef-Morgan, 2013). For our salary example in Lecture 8,
eta squared equals 17686.02 (SS(between) / 18066 (SS(total) = 0.979 (rounded). Eta squared
effect size measures have different interpretation values than Cohen’s d (from the t-
test). According to Nandy (2012), a small eta squared effect size has a value of 0.01, a medium
of 0.06, and a large value of 0.14 or more. This means we have a large effect size, and the
variables of salary and grade interaction are the most likely cause of our rejecting the null
hypothesis rather than the sample size.
Side note: Eta squared can also be interpreted as the percent of “differences between
group scores that can be explained by the independent variable” (Tanner & Youssef-Morgan,
2013, p. 123). This is consistent with our saying the variable interactions caused the outcome.
Different Forms of ANOVA
Just as the t-test has several forms, so does the ANOVA test. Excel has three versions
available. While we will focus only on the single factor test, a brief description of the other two
versions will be presented.
ANOVA: Two factor without replication
The ANOVA – two factor without replication tests mean differences from two different
variables at the same time. If we are interested in knowing if the mean salary differs by grade
and also by gender, we can perform one two-factor test rather than two separate tests. As
mentioned in lecture two for this week, this is more efficient and maintains our desired alpha
significance level.
Excel Example. To test the mean salaries by grade and gender at the same time, we
would set up our hypothesis test as follows.
Step 1: Ho1: All salary means are equal across grades.
Ha1: At least one mean differs.
Ho2: All gender (male and female) means are equal.
Ha2: At least one mean differs.
Note that in this test, we need to have a hypothesis statement pair for each variable being
tested.
Step 2: ANOVA: Two sample without replication.
Step 3: Reject the null hypothesis if the p-value is < alpha = .05.
Step 4: Perform the test. W.
4
DDBA 8307 Week 7 Assignment Template
John Doe
DDBA 8307-6
Dr. Jane Doe
1
Two-Way Contingency Table Analysis
Type text here. You will describe and defend using the two-way contingency table analysis. Use at least two outside resources—that is, resources not provided in the course resources, readings, etc. These citations will be presented in the References section. This exercise will give you practice for addressing Rubric Item 2.13b, which states, “Describes and defends, in detail, the statistical analyses that the student will conduct….” This section should be no more than two paragraphs.
Research Question
Type appropriate research question here?
Hypotheses
H0: Type appropriate null hypothesis here.
H1: Type appropriate alternative hypothesis here.
Results
Type introduction here.
Descriptive Statistics
Present the descriptive statistics here—use appropriate table and figures.
Inferential Results
Type the inferential results here.
2
References
Type references here in proper APA format.
Appendix – Two-Way Contingency Table Analysis
SPSS Output
BUS 308 Week 2 Lecture 2
Statistical Testing for Differences – Part 1
After reading this lecture, the student should know:
1. How statistical distributions are used in hypothesis testing.
2. How to interpret the F test (both options) produced by Excel
3. How to interpret the T-test produced by Excel
Overview
Lecture 1 introduced the logic of statistical testing using the hypothesis testing procedure.
It also mentioned that we will be looking at two different tests this week. The t-test is used to
determine if means differ, from either a standard or claim or from another group. The F-test is
used to examine variance differences between groups.
This lecture starts by looking at statistical distributions – they underline the entire
statistical testing approach. They are kind of like the detective’s base belief that crimes are
committed for only a couple of reasons – money, vengeance, or love. The statistical distribution
that underlies each test assumes that statistical measures (such as the F value when comparing
variances and the t value when looking at means) follow a particular pattern, and this can be used
to make decisions.
While the underlying distributions differ for the different tests we will be looking at
throughout the course, they all have some basic similarities that allow us to examine the t
distribution and extrapolate from it to interpreting results based on other distributions.
Distributions. The basic logic for all statistical tests: If the null hypothesis claim is
correct, then the distribution of the statistical outcome will be distributed around a central value,
and larger and smaller values will be increasingly rare. At some point (and we define this as our
alpha value), we can say that the likelihood of getting a difference this large is extremely
unlikely and we will say that our results do.
BUS 308 Week 3 Lecture 1 Examining Differences - Continued.docxcurwenmichaela
BUS 308 Week 3 Lecture 1
Examining Differences - Continued
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. Issues around multiple testing
2. The basics of the Analysis of Variance test
3. Determining significant differences between group means
4. The basics of the Chi Square Distribution.
Overview
Last week, we found out ways to examine differences between a measure taken on two
groups (two-sample test situation) as well as comparing that measure to a standard (a one-sample
test situation). We looked at the F test which let us test for variance equality. We also looked at
the t-test which focused on testing for mean equality. We noted that the t-test had three distinct
versions, one for groups that had equal variances, one for groups that had unequal variances, and
one for data that was paired (two measures on the same subject, such as salary and midpoint for
each employee). We also looked at how the 2-sample unequal t-test could be used to use Excel
to perform a one-sample mean test against a standard or constant value. This week we expand
our tool kit to let us compare multiple groups for similar mean values.
A second tool will let us look at how data values are distributed – if graphed, would they
look the same? Different shapes or patterns often means the data sets differ in significant ways
that can help explain results.
Multiple Groups
As interesting as comparing two groups is, often it is a bit limiting as to what it tells us.
One obvious issue that we are missing in the comparisons made last week was equal work. This
idea is still somewhat hard to get a clear handle on. Typically, as we look at this issue, questions
arise about things such as performance appraisal ratings, education distribution, seniority impact,
etc.
Some of these can be tested with the tools introduced last week. We can see, for
example, if the performance rating average is the same for each gender. What we couldn’t do, at
this point however, is see if performance ratings differ by grade, do the more senior workers
perform relatively better? Is there a difference between ratings for each gender by grade level?
The same questions can be asked about seniority impact. This week will give us tools to expand
how we look at the clues hidden within the data set about equal pay for equal work.
ANOVA
So, let’s start taking a look at these questions. The first tool for this week is the Analysis
of Variance – ANOVA for short. ANOVA is often confusing for students; it says it analyzes
variance (which it does) but the purpose of an ANOVA test is to determine if the means of
different groups are the same! Now, so far, we have considered means and variance to be two
distinct characteristics of data sets; characteristics that are not related, yet here we are saying that
looking at one will give us insight into the other.
The reason is due to the way the variance is an.
Ashford 4: - Week 3 - Discussion 1
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
ANOVA
In many ways, comparing multiple sample means is simply an extension of what we covered last week. Just as we had 3 versions of the t-test (1 sample, 2 sample (with and without equal variance), and paired; we have several versions of ANOVA – single factor, factorial (called 2-factor with replication in Excel), and within-subjects (2-factor without replication in Excel). What examples (professional, personal, social) can you provide on when we might use each type? What would be the appropriate hypotheses statements for each example?
Guided Response: Review several of your classmates’ posts. Respond to at least two classmates by commenting on why you agree or disagree with the statistical test that your peers have described as appropriate in this scenario.
Ashford 4: - Week 3 - Discussion 2
Your initial discussion thread is due on Day 3 (Thursday) and you have until Day 7 (Monday) to respond to your classmates. Your grade will reflect both the quality of your initial post and the depth of your responses. Reference the Discussion Forum Grading Rubric for guidance on how your discussion will be evaluated.
Effect Size
Several statistical tests have a way to measure effect size. What is this, and when might you want to use it in looking at results from these tests on job related data?
Ashford 4: - Week 3 - Assignment
Problem Set Week Three
Complete the problems included in the resources below and submit your work in an Excel document. Be sure to show all of your work and clearly label all calculations.
All statistical calculations will use the Employee Salary Data Set and the Week 3 assignment sheet.
Carefully review the Grading Rubric for the criteria that will be used to evaluate your assignment.
See comments at the right of the data set.
ID
Salary
Compa
Midpoint
Age
Performance Rating
Service
Gender
Raise
Degree
Gender1
Grade
8
23
1.000
23
32
90
9
1
5.8
0
F
A
The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)?
10
22
0.956
23
30
80
7
1
4.7
0
F
A
Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.
11
23
1.000
23
41
100
19
1
4.8
0
F
A
14
24
1.043
23
32
90
12
1
6
0
F
A
The column labels in the table mean:
15
24
1.043
23
32
80
8
1
4.9
0
F
A
ID – Employee sample number
Salary – Salary in thousands
23
23
1.000
23
36
65
6
1
3.3
1
F
A
Age – Age in years
Performance Rating – Appraisal rating (Employee evaluation score)
26
24
1.043
23
22
95
2
1
6.2
1
F
A
Service – Years of service (rounded)
Gender: ...
BUS 308 Week 3 Lecture 3 Setting up ANOVA and Chi Square .docxjasoninnes20
BUS 308 Week 3 Lecture 3
Setting up ANOVA and Chi Square
Expected Outcomes
After reading this lecture, the student should know how to:
1. Set-up the data for an ANOVA analysis.
2. Set-up and perform an ANOVA test.
3. Set-up a table of mean differences.
4. Set-up and perform a Chi Square test.
Overview
Setting up the ANOVA test is quite similar to how the t and F tests were set up. The Chi
Square set-up is a bit more complex, as it is not found in the Data Analysis list of tools.
ANOVA
The set-up of ANOVA within Excel is very similar to how we set up the F and T tests
last week; place the data set in appropriate groups and then use the ANOVA input box. One
difference this week is that the Fx (or Formulas) list does not include an option for ANOVA, so
we need to use the Data | Analysis tools.
Data Set-up
Single Factor. As with the t-test, ANOVA has a couple of versions to select between.
Each is used to answer slightly different questions, and these will be examined below. The most
significant difference lies in the data table used for each version.
We will be working primarily with the ANOAV Single Factor, which deals with
examining possible differences between the means of a single variable within different groups.
A question of whether or not the mean compa-ratios are equal across the grades is an example of
the kind of question answered with this approach.
Question 1. Week 3’s first question is about salary mean equality across the grades. Our
lecture example will deal with compa-ratio mean equality across the grades. The set-up for the
Single Factor ANOVA we just went through assumed this. The initial steps in the hypothesis
testing process are similar to what we have done before:
Step 1: Ho: All Compa-Ratio means are equal across the grades
Ha: At least one compa-ratio mean differs
Notice that these are the standard ANOVA – Single factor null and alternate hypothesis
statements that identify the specific variable (compa-ratio) and statistic (mean) that we
are testing, and merely say “no difference” and “at least one differs.”
Step 2: Alpha = 0.05
Step 3: F statistic and Single Factor ANOVA; used to test multiple means
Step 4: Decision Rule: Reject Ho if the p-value < 0.05
Step 5: Conduct the test – place the test function in cell K08.
As with the F and T tests, we need to group the data into distinct groups. For example, if
we are going to test the compa-ratio mean across grades, then the data must be set-up in a
table with grades across the top, as in the screen shot below. Note that as was done with
the T and F test input data, the raw or initial data was listed and then sorted. Values were
then copied into related groups; we used male and female groups for the F and t tests and
grade groups for this test.
Test Set-up. Go to the Data | Analysis and select ANOVA Single Factor gives us the
following input screen. This is completed for our compa-ratio ...
BUS 308 Week 3 Lecture 3 Setting up ANOVA and Chi Square .docxcurwenmichaela
BUS 308 Week 3 Lecture 3
Setting up ANOVA and Chi Square
Expected Outcomes
After reading this lecture, the student should know how to:
1. Set-up the data for an ANOVA analysis.
2. Set-up and perform an ANOVA test.
3. Set-up a table of mean differences.
4. Set-up and perform a Chi Square test.
Overview
Setting up the ANOVA test is quite similar to how the t and F tests were set up. The Chi
Square set-up is a bit more complex, as it is not found in the Data Analysis list of tools.
ANOVA
The set-up of ANOVA within Excel is very similar to how we set up the F and T tests
last week; place the data set in appropriate groups and then use the ANOVA input box. One
difference this week is that the Fx (or Formulas) list does not include an option for ANOVA, so
we need to use the Data | Analysis tools.
Data Set-up
Single Factor. As with the t-test, ANOVA has a couple of versions to select between.
Each is used to answer slightly different questions, and these will be examined below. The most
significant difference lies in the data table used for each version.
We will be working primarily with the ANOAV Single Factor, which deals with
examining possible differences between the means of a single variable within different groups.
A question of whether or not the mean compa-ratios are equal across the grades is an example of
the kind of question answered with this approach.
Question 1. Week 3’s first question is about salary mean equality across the grades. Our
lecture example will deal with compa-ratio mean equality across the grades. The set-up for the
Single Factor ANOVA we just went through assumed this. The initial steps in the hypothesis
testing process are similar to what we have done before:
Step 1: Ho: All Compa-Ratio means are equal across the grades
Ha: At least one compa-ratio mean differs
Notice that these are the standard ANOVA – Single factor null and alternate hypothesis
statements that identify the specific variable (compa-ratio) and statistic (mean) that we
are testing, and merely say “no difference” and “at least one differs.”
Step 2: Alpha = 0.05
Step 3: F statistic and Single Factor ANOVA; used to test multiple means
Step 4: Decision Rule: Reject Ho if the p-value < 0.05
Step 5: Conduct the test – place the test function in cell K08.
As with the F and T tests, we need to group the data into distinct groups. For example, if
we are going to test the compa-ratio mean across grades, then the data must be set-up in a
table with grades across the top, as in the screen shot below. Note that as was done with
the T and F test input data, the raw or initial data was listed and then sorted. Values were
then copied into related groups; we used male and female groups for the F and t tests and
grade groups for this test.
Test Set-up. Go to the Data | Analysis and select ANOVA Single Factor gives us the
following input screen. This is completed for our compa-ratio.
Week 3 Lecture 9 Effect Size When we reject the null h.docxcockekeshia
Week 3 Lecture 9
Effect Size
When we reject the null hypothesis with an ANOVA test, we have two questions that
arise. The first, which pair of means differs significantly, we have dealt with already. The
second question, similar to what we asked with the t-test null hypothesis rejection is; what
caused the rejection, the sample size or the variable interactions? This question is again
answered using an effect size measure.
Recall that the effect size measure shows how likely the variable interaction caused the
null hypothesis rejection. Large values lead us to say the variables caused the outcome, while
small values lead us to say the outcome has little to no practical significance as the sample size
was the most likely cause of the rejection of the null.
With the single factor ANOVA, the effect size measure is eta squared, and equals the
SS(between)/SS(total) (Tanner & Youssef-Morgan, 2013). For our salary example in Lecture 8,
eta squared equals 17686.02 (SS(between) / 18066 (SS(total) = 0.979 (rounded). Eta squared
effect size measures have different interpretation values than Cohen’s d (from the t-
test). According to Nandy (2012), a small eta squared effect size has a value of 0.01, a medium
of 0.06, and a large value of 0.14 or more. This means we have a large effect size, and the
variables of salary and grade interaction are the most likely cause of our rejecting the null
hypothesis rather than the sample size.
Side note: Eta squared can also be interpreted as the percent of “differences between
group scores that can be explained by the independent variable” (Tanner & Youssef-Morgan,
2013, p. 123). This is consistent with our saying the variable interactions caused the outcome.
Different Forms of ANOVA
Just as the t-test has several forms, so does the ANOVA test. Excel has three versions
available. While we will focus only on the single factor test, a brief description of the other two
versions will be presented.
ANOVA: Two factor without replication
The ANOVA – two factor without replication tests mean differences from two different
variables at the same time. If we are interested in knowing if the mean salary differs by grade
and also by gender, we can perform one two-factor test rather than two separate tests. As
mentioned in lecture two for this week, this is more efficient and maintains our desired alpha
significance level.
Excel Example. To test the mean salaries by grade and gender at the same time, we
would set up our hypothesis test as follows.
Step 1: Ho1: All salary means are equal across grades.
Ha1: At least one mean differs.
Ho2: All gender (male and female) means are equal.
Ha2: At least one mean differs.
Note that in this test, we need to have a hypothesis statement pair for each variable being
tested.
Step 2: ANOVA: Two sample without replication.
Step 3: Reject the null hypothesis if the p-value is < alpha = .05.
Step 4: Perform the test. W.
4
DDBA 8307 Week 7 Assignment Template
John Doe
DDBA 8307-6
Dr. Jane Doe
1
Two-Way Contingency Table Analysis
Type text here. You will describe and defend using the two-way contingency table analysis. Use at least two outside resources—that is, resources not provided in the course resources, readings, etc. These citations will be presented in the References section. This exercise will give you practice for addressing Rubric Item 2.13b, which states, “Describes and defends, in detail, the statistical analyses that the student will conduct….” This section should be no more than two paragraphs.
Research Question
Type appropriate research question here?
Hypotheses
H0: Type appropriate null hypothesis here.
H1: Type appropriate alternative hypothesis here.
Results
Type introduction here.
Descriptive Statistics
Present the descriptive statistics here—use appropriate table and figures.
Inferential Results
Type the inferential results here.
2
References
Type references here in proper APA format.
Appendix – Two-Way Contingency Table Analysis
SPSS Output
BUS 308 Week 2 Lecture 2
Statistical Testing for Differences – Part 1
After reading this lecture, the student should know:
1. How statistical distributions are used in hypothesis testing.
2. How to interpret the F test (both options) produced by Excel
3. How to interpret the T-test produced by Excel
Overview
Lecture 1 introduced the logic of statistical testing using the hypothesis testing procedure.
It also mentioned that we will be looking at two different tests this week. The t-test is used to
determine if means differ, from either a standard or claim or from another group. The F-test is
used to examine variance differences between groups.
This lecture starts by looking at statistical distributions – they underline the entire
statistical testing approach. They are kind of like the detective’s base belief that crimes are
committed for only a couple of reasons – money, vengeance, or love. The statistical distribution
that underlies each test assumes that statistical measures (such as the F value when comparing
variances and the t value when looking at means) follow a particular pattern, and this can be used
to make decisions.
While the underlying distributions differ for the different tests we will be looking at
throughout the course, they all have some basic similarities that allow us to examine the t
distribution and extrapolate from it to interpreting results based on other distributions.
Distributions. The basic logic for all statistical tests: If the null hypothesis claim is
correct, then the distribution of the statistical outcome will be distributed around a central value,
and larger and smaller values will be increasingly rare. At some point (and we define this as our
alpha value), we can say that the likelihood of getting a difference this large is extremely
unlikely and we will say that our results do.
BUS 308 Week 3 Lecture 1 Examining Differences - Continued.docxcurwenmichaela
BUS 308 Week 3 Lecture 1
Examining Differences - Continued
Expected Outcomes
After reading this lecture, the student should be familiar with:
1. Issues around multiple testing
2. The basics of the Analysis of Variance test
3. Determining significant differences between group means
4. The basics of the Chi Square Distribution.
Overview
Last week, we found out ways to examine differences between a measure taken on two
groups (two-sample test situation) as well as comparing that measure to a standard (a one-sample
test situation). We looked at the F test which let us test for variance equality. We also looked at
the t-test which focused on testing for mean equality. We noted that the t-test had three distinct
versions, one for groups that had equal variances, one for groups that had unequal variances, and
one for data that was paired (two measures on the same subject, such as salary and midpoint for
each employee). We also looked at how the 2-sample unequal t-test could be used to use Excel
to perform a one-sample mean test against a standard or constant value. This week we expand
our tool kit to let us compare multiple groups for similar mean values.
A second tool will let us look at how data values are distributed – if graphed, would they
look the same? Different shapes or patterns often means the data sets differ in significant ways
that can help explain results.
Multiple Groups
As interesting as comparing two groups is, often it is a bit limiting as to what it tells us.
One obvious issue that we are missing in the comparisons made last week was equal work. This
idea is still somewhat hard to get a clear handle on. Typically, as we look at this issue, questions
arise about things such as performance appraisal ratings, education distribution, seniority impact,
etc.
Some of these can be tested with the tools introduced last week. We can see, for
example, if the performance rating average is the same for each gender. What we couldn’t do, at
this point however, is see if performance ratings differ by grade, do the more senior workers
perform relatively better? Is there a difference between ratings for each gender by grade level?
The same questions can be asked about seniority impact. This week will give us tools to expand
how we look at the clues hidden within the data set about equal pay for equal work.
ANOVA
So, let’s start taking a look at these questions. The first tool for this week is the Analysis
of Variance – ANOVA for short. ANOVA is often confusing for students; it says it analyzes
variance (which it does) but the purpose of an ANOVA test is to determine if the means of
different groups are the same! Now, so far, we have considered means and variance to be two
distinct characteristics of data sets; characteristics that are not related, yet here we are saying that
looking at one will give us insight into the other.
The reason is due to the way the variance is an.
BUS 308 Week 2 Lecture 2 Statistical Testing for Differenc.docxjasoninnes20
BUS 308 Week 2 Lecture 2
Statistical Testing for Differences – Part 1
After reading this lecture, the student should know:
1. How statistical distributions are used in hypothesis testing.
2. How to interpret the F test (both options) produced by Excel
3. How to interpret the T-test produced by Excel
Overview
Lecture 1 introduced the logic of statistical testing using the hypothesis testing procedure.
It also mentioned that we will be looking at two different tests this week. The t-test is used to
determine if means differ, from either a standard or claim or from another group. The F-test is
used to examine variance differences between groups.
This lecture starts by looking at statistical distributions – they underline the entire
statistical testing approach. They are kind of like the detective’s base belief that crimes are
committed for only a couple of reasons – money, vengeance, or love. The statistical distribution
that underlies each test assumes that statistical measures (such as the F value when comparing
variances and the t value when looking at means) follow a particular pattern, and this can be used
to make decisions.
While the underlying distributions differ for the different tests we will be looking at
throughout the course, they all have some basic similarities that allow us to examine the t
distribution and extrapolate from it to interpreting results based on other distributions.
Distributions. The basic logic for all statistical tests: If the null hypothesis claim is
correct, then the distribution of the statistical outcome will be distributed around a central value,
and larger and smaller values will be increasingly rare. At some point (and we define this as our
alpha value), we can say that the likelihood of getting a difference this large is extremely
unlikely and we will say that our results do not seem to come from a population that matches the
claims of the null hypothesis.
Note that this logic has several key elements:
1. The test is based on an assumption that the null hypothesis is correct. This gives us a
starting point, even if later proven wrong.
2. All sample results are turned into a statistic that matches the test selected (for
example, the F statistic when using the F-test, or the t-statistic when using the T-test.)
3. The calculated statistic is compared to a related statistical distribution to see how
likely an outcome we have.
4. The larger the test statistic, the more unlikely it is that the result matches or comes
from the population described by the null hypothesis claim.
We will demonstrate these ideas by looking at the questions being asked in this week’s
homework. We will show results of the related Excel tests, and discuss how to interpret the
output.
We need to remember that seeing different value (mean, variance, etc.) from different
samples does not tell us that the population parameters we are estimating are, in fact, different.
The ...
Chapter 18 – Pricing Setting in the Business WorldThere are few .docxrobert345678
Chapter 18 – Pricing Setting in the Business World
There are few Methods for setting pricing – costs methods vs demand methods
Formulas considering costs and mark up will help you to do the Problem set assignment:
1. Markup for setting prices (Mark up $ = SP-CP); MARK UP % = (MU $/SP) X100)
Formula for setting price with the markup method
SP = Cost/(1- Markup %)
Example - retailer buys A hat for $15 and wants a 40% markup, his selling price would be….
SP = 15/(1-.40)=.60
= $25.00
2. Understand Role of different costs – fixed, variable, total costs and average costs
3. What is the breakeven point? Formula for calculating the Break Even point.
BE = Total Fixed Cost/Fixed cost contribution
Fixed Cost Contribution=Price – variable cost
4. Average Cost = when there are many flavors/types of the same product, producer determines average cost and then add the mark up to set a common selling price.
.ANOVA
Analysis of Variance is a method of testing the equality of three or more population
means by analyzing sample variance.
One-Way ANOVA
The one-way ANOVA is used to compare three or more population means when there is
one factor of interest.
Requirements
The populations have distributions that are approximately normal.
The populations have the same variance.
The samples are simple random samples of quantitative data.
The samples are independent of each other.
The different samples are from populations that are categorized in only one.
way
One-Way ANOVA is a hypothesis test. There are seven steps for a hypothesis test.
Example
A professor at a local University believes there is a relationship between head size and
the major of the students in her biostatistics classes. She takes a random sample of 20
students from each of three classes and records their major and head circumference.
The data are shown in the following table.
Step 1: State the null hypothesis.
Mean 1 equals mean 2 equals mean 3 equals mean 4.
Step 2: State the Alternative hypothesis.
At least one mean is different.
Step 3: State the Level of Significance.
The level of significance is 0.05.
Step 4: State the test statistic.
variance between samples
variance within samples
F
The test statistic follows the F distribution which has two degrees of freedom, one for
the numerator and one for the denominator.
The calculations for the test statistic are complicated, so a software program is
generally used for the calculations. We will be using Microsoft Excel for this example.
Step 5: Calculate
The calculations are done in Microsoft Excel using the data analysis toolpak. Enter the
data into the spread sheet as shown here. Click on data and the data analysis tookpak
button is on the right.
When you click on the button a dialogue box appears.
Choose ANOVA One Factor. Then another dialogue box appears.
Input range is where the data is in the table. Be sure to put a check in the box for labels
in.
Article Write-upsTo help you connect what you’re learning in cl.docxdavezstarr61655
Article Write-ups
To help you connect what you’re learning in class with current events, you are required to find an economics-related news article, read it, and write a short paper connecting your findings to topics we’ve discussed in class. You should select your article from a reputable source like The Economist, New York Times, or Wall Street Journal (read: not a blog post or obscure website). Students must read the selected piece, summarize the content, relate it to subjects covered in class, and turn in a short (1-2 pages) typed paper with these elements. Please note that this means you need to pick an article substantial enough to write more than one page about it.
Some suggested topics:
Tradeoffs or opportunity costs
Supply & Demand (including input costs, other nonprice determinants)
Substitute & complementary goods
Elasticity
Market efficiency
Behavioral economics (framing, heuristics)
Consumer choice (utility maximization, diminishing marginal utility)
Write-up Requirements:
-Minimum 1 page of text not including header or references (double spaced, 12 point font, standard margins).
-A discussion of how your selected article directly relates to or relies upon a particular economic principle we have covered in class. This should include defining and explaining the concept, in addition to discussing how it is used in your article. (I.e. “This article uses the concept of opportunity costs, which means…” or “This article discusses using sales prices to frame consumer decisions. From behavioral economics we learned that framing is….”)
-A summary of the contents that demonstrates you read the article.
-A review and general evaluation based upon what you’ve learned in class.
-A properly formatted reference for your article (citation style of your choice – APA, MLA, etc.). For online sources please provide a link.
-You must submit your assignment on Moodle as a Word document (.doc or .docx)
Week 3 Lecture 9
Effect Size
When we reject the null hypothesis with an ANOVA test, we have two questions that arise. The first, which pair of means differs significantly, we have dealt with already. The second question, similar to what we asked with the t-test null hypothesis rejection is; what caused the rejection, the sample size or the variable interactions? This question is again answered using an effect size measure.
Recall that the effect size measure shows how likely the variable interaction caused the null hypothesis rejection. Large values lead us to say the variables caused the outcome, while small values lead us to say the outcome has little to no practical significance as the sample size was the most likely cause of the rejection of the null.
With the single factor ANOVA, the effect size measure is eta squared, and equals the SS(between)/SS(total) (Tanner & Youssef-Morgan, 2013). For our salary example in Lecture 8, eta squared equals 17686.02 (SS(between) / 18066 (SS(total) = 0.979 (rounded). Eta squared effect s.
ScoreWeek 3ANOVA and Paired T-test.docxpotmanandrea
Score:
Week 3
ANOVA and Paired T-test
At this point we know the following about male and female salaries.
a.
Male and female overall average salaries are not equal in the population.
b.
Male and female overall average compas are equal in the population, but males are a bit more spread out.
c.
The male and female salary range are almost the same, as is their age and service.
d.
Average performance ratings per gender are equal.
Let's look at some other factors that might influence pay - education(degree) and performance ratings.
<1 point>
1
Last week, we found that average performance ratings do not differ between males and females in the population.
Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?
(Assume variances are equal across the grades for this ANOVA.)
You can use these columns to place grade Perf Ratings if desired.
A
B
C
D
E
F
Null Hypothesis:
Alt. Hypothesis:
Place
B17 in Outcome range box.
Interpretation:
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If
the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What does that decision mean in terms of our equal pay question:
<1 point>
2
While it appears that average salaries per each grade differ, we need to test this assumption.
Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
Use the input table to the right to list salaries under each grade level.
Null Hypothesis:
If desired, place salaries per grade in these columns
Alt. Hypothesis:
A
B
C
D
E
F
.
DataSalCompaMidAgeEESSERGRaiseDegGen1Gr1581.017573485805.70METhe ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? 2270.870315280703.90MBNote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.3341.096313075513.61FB4661.15757421001605.51METhe column labels in the table mean:5470.9794836901605.71MDID – Employee sample number Sal – Salary in thousands 6761.1346736701204.51MFAge – Age in yearsEES – Appraisal rating (Employee evaluation score)7411.0254032100815.71FCSER – Years of serviceG – Gender (0 = male, 1 = female) 8231.000233290915.81FAMid – salary grade midpoint Raise – percent of last raise9771.149674910010041MFGrade – job/pay gradeDeg (0= BS\BA 1 = MS)10220.956233080714.71FAGen1 (Male or Female)Compa - salary divided by midpoint, a measure of salary that removes the impact of grade11231.00023411001914.81FA12601.0525752952204.50METhis data should be treated as a sample of employees taken from a company that has about 1,000 13421.0504030100214.70FCemployees using a random sampling approach.14241.04323329012161FA15241.043233280814.91FA16471.175404490405.70MCMac Users: The homework in this course assumes students have Windows Excel, and17691.2105727553131FEcan load the Analysis ToolPak into their version of Excel.18361.1613131801115.60FBThe analysis tool pak has been removed from Excel for Windows, but a free third-party 19241.043233285104.61MAtool that can be used (found on an answers Microsoft site) is:20341.0963144701614.80FBhttp://www.analystsoft.com/en/products/statplusmacle21761.1346743951306.31MFLike the Microsoft site, I make cannot guarantee the program, but do know that 22571.187484865613.81FDStatplus is a respected statistical package.You may use other approaches or tools23231.000233665613.30FAas desired to complete the assignments.24501.041483075913.80FD25241.0432341704040MA26241.043232295216.20FA27401.000403580703.91MC28751.119674495914.40FF29721.074675295505.40MF30491.0204845901804.30MD31241.043232960413.91FA32280.903312595405.60MB33641.122573590905.51ME34280.903312680204.91MB35241.043232390415.30FA36231.000232775314.30FA37220.956232295216.20FA38560.9825745951104.50ME39351.129312790615.50FB40251.086232490206.30MA41431.075402580504.30MC42241.0432332100815.71FA43771.1496742952015.50FF44601.0525745901605.21ME45551.145483695815.21FD46651.1405739752003.91ME47621.087573795505.51ME48651.1405734901115.31FE49601.0525741952106.60ME50661.1575738801204.60MEhttp://www.analystsoft.com/en/products/statplusmacle
Week 1Week 1.Describing the data.<Use right click on the row numbers at the left to insert rows below each question for your results and comments.>1Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set.a. For which variables in the data set does this function not work correctly for? W.
Week 2 – Lecture 3 Making judgements about differences bet.docxcockekeshia
Week 2 – Lecture 3
Making judgements about differences between group statistics is one of the most
powerful things that statistics can do for us. It is also one of the most counter-intuitive things
that we need to master in the class.
Lecture 1 introduced the hypothesis testing procedure used in statistical testing. Lecture
2 examined how to set up, perform, and interpret the F test for variance equality. This lecture
will focus on t-tests for testing mean equality. Again, these examples will use the compa-ratio
variable, while the homework should use the Salary variable.
The T-Test
While we test for variance equality with an F test, we use the T-Test to test for mean
equality testing. The t-test also uses the degree of freedom (df) value in providing us with our
probability result; but again, Excel does the work for us.
There are three versions of the T-Test done for us by Excel. The first two are similar
except one version is done if the variances are equal and the other if the variances are not equal.
(Now we see the second reason for performing the F-test first.)
The third version of the T-test is for paired data, and is called T-test Paired Two Sample
for Means. Paired data are two measures taken on the same subject. Examples include a math
and English test score for students, preference for different drinks, and, in our data set the salary
and midpoint values. Note that paired data must be measured in the same units, and be from the
same subjects. Students in the past have incorrectly used the paired t-test on male and female
salaries. These are not paired, as the measures are taken on different people and cannot be paired
together for analysis.
In many ways, setting up Excel’s T-tests, and virtually all the functions we will study,
follow the same steps as we just went through:
1. Set up the data into distinct groups.
2. Select the test function from either the Fx or Analysis list
3. Input the data ranges and output ranges into the appropriate entry boxes, checking
Labels if appropriate.
4. Clicking on OK to produce the output.
As with the F-test, the T-test has a couple of options depending upon what you want your
output to look like. The Fx (or Formulas) option returns simply the p-value for the selected
version of the test. The Data | Analysis selection provides descriptive statistics that are useful for
additional analysis (some of which we will discuss later in the course).
The t-test requires that we select between three versions, one assuming equal variances
between the populations, one assuming unequal variances in the populations, and one requiring
paired data (two measures on each element in the sample, such as salary and midpoint for each
person in our data set.) All have the same data set-up approach, so only one will be shown.
Question 2
The second question for this week asks about salary mean equality between males and
females. The data and test se.
1
Running head: RESEARCH PROJECT PROPOSAL
1
3
RESEARCH PROJECT PROPOSAL
Research Project Proposal
Name Here
South University Online
Research Project Proposal
Provide a brief, general introduction to the topic and importance to your role (do not use first person anywhere in the paper). Conclude with a thesis statement.
Background and Significance of the Problem
Discuss here.
Statement of the Problem and Purpose of the Study
Discuss here.
Literature Review
Discuss here.
Research Questions, Hypothesis, and Variables
Discuss here.
Theoretical Framework
Overview and Guiding Propositions
Discuss here.
Application of Theory to Study Focus
Discuss here.
Methodology
Sample/Setting
Discuss here.
Sampling Strategy
Discuss here.
Research Design
Discuss here.
Extraneous Variables
Discuss here.
Instruments
Discuss here.
Description of the Intervention
Discuss here.
Data Collection Procedures
Discuss here.
Data Analysis Plans
Discuss here.
Ethical Issues
Discuss here.
Limitations of Proposed Study
Discuss here.
Implications for Practice
Discuss here.
References
Appendices
Lecture 6
(Additional information on t-tests and hypothesis testing)
Lecture 5 focused on perhaps the most common of the t-tests, the two sample assuming
equal variance. There are other versions as well; Excel lists two others, the two sample assuming
unequal variance and the paired t-test. We will end with some comments about rejecting the null
hypothesis.
Choosing between the t-test options
As the names imply each of the three forms of the t-test deal with different types of data
sets. The simplest distinction is between the equal and unequal variance tests. Both require that
the data be at least interval in nature, come from a normally distributed population, and be
independent of each other – that is, collected from different subjects.
The F-test for variance.
To determine if the population variances of two groups are statistically equal – in order to
correctly choose the equal variance version of the t-test – we use the F statistic, which is
calculated by dividing one variance by the other variance. If the outcome is less than 1.0, the
rejection region is in the left tail; if the value is greater than 1.0, the rejection region is in the
right tail. In either case, Excel provides the information we need.
To perform a hypothesis test for variance equality we use Excel’s F-Test Two-Sample for
Variances found in the Data Analysis section under the Data tab. The test set-up is very similar
to that of the t-test, entering data ranges, checking Labels box if they are included in the data
ranges, and identifying the start of the output range. The only unique element in this test is the
identification of our alpha level.
Since we are testing for equality of variances, we have a two sample test and the rejection
region is again in both tails. This means that our rejection region in each tail is 0.25. The F-test
id ...
can i get a quote. i got one from barzzy but she never replied.docxchestnutkaitlyn
can i get a quote. i got one from barzzy but she never replied
At this point we know the following about male and female salaries.
a.
Male and female overall average salaries are not equal in the population.
b.
Male and female overall average compas are equal in the population, but males are a bit more spread out.
c.
The male and female salary range are almost the same, as is their age and service.
d.
Average performance ratings per gender are equal.
Let's look at some other factors that might influence pay - education(degree) and performance ratings.
1
Last week, we found that average performance ratings do not differ between males and females in the population.
Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?
(Assume variances are equal across the grades for this ANOVA.)
You can use these columns to place grade Perf Ratings if desired.
A
B
C
D
E
F
Null Hypothesis:
Alt. Hypothesis:
Place
B17 in Outcome range box.
Interpretation:
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If
the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What does that decision mean in terms of our equal pay question:
2
While it appears that average salaries per each grade differ, we need to test this assumption.
Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
Use the input table to the right to list salaries under each grade level.
Null Hypothesis:
If desired, place salaries per grade in these columns
Alt. Hypothesis:
A
B
C
D
E
F
Place
B55 in Outcome range box.
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If
the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
Interpretation:
3
The table and analysis below demonstrate a 2-way ANOVA with replication.
Please interpret the results.
BA
MA
Ho: Average compas by gender are equal
Male
1.017
1.157
Ha: Ave.
Chi-square tests are great to show if distributions differ or i.docxMARRY7
Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you?
DataSee comments at the right of the data set.IDSalaryCompaMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1Grade8231.000233290915.80FAThe ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? 10220.956233080714.70FANote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.11231.00023411001914.80FA14241.04323329012160FAThe column labels in the table mean:15241.043233280814.90FAID – Employee sample number Salary – Salary in thousands 23231.000233665613.31FAAge – Age in yearsPerformance Rating – Appraisal rating (Employee evaluation score)26241.043232295216.21FAService – Years of service (rounded)Gender: 0 = male, 1 = female 31241.043232960413.90FAMidpoint – salary grade midpoint Raise – percent of last raise35241.043232390415.31FAGrade – job/pay gradeDegree (0= BS\BA 1 = MS)36231.000232775314.31FAGender1 (Male or Female)Compa - salary divided by midpoint37220.956232295216.21FA42241.0432332100815.70FA3341.096313075513.60FB18361.1613131801115.61FB20341.0963144701614.81FB39351.129312790615.51FB7411.0254032100815.70FC13421.0504030100214.71FC22571.187484865613.80FD24501.041483075913.81FD45551.145483695815.20FD17691.2105727553130FE48651.1405734901115.31FE28751.119674495914.41FF43771.1496742952015.51FF19241.043233285104.61MA25241.0432341704040MA40251.086232490206.30MA2270.870315280703.90MB32280.903312595405.60MB34280.903312680204.91MB16471.175404490405.70MC27401.000403580703.91MC41431.075402580504.30MC5470.9794836901605.71MD30491.0204845901804.30MD1581.017573485805.70ME4661.15757421001605.51ME12601.0525752952204.50ME33641.122573590905.51ME38560.9825745951104.50ME44601.0525745901605.21ME46651.1405739752003.91ME47621.087573795505.51ME49601.0525741952106.60ME50661.1575738801204.60ME6761.1346736701204.51MF9771.149674910010041MF21761.1346743951306.31MF29721.074675295505.40MF
Week 1Week 1.Measurement and Description - chapters 1 and 21Measurement issues. Data, even numerically coded variables, can be one of 4 levels - nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, asthis impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data.Please list under each label, the variables in our data set that belong in each group.NominalOrdinalIntervalRatiob.For each variable that you did not call ratio, why did you make that decision?2The first step in analyzing data sets is to find some summary descriptive statistics for key variables.For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: ...
Week 5 Lecture 14 The Chi Square Test Quite often, pat.docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are
generally the result of counting how many things fit into a particular category. Whenever we
make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes
in these visual patterns will be our first clues that things have changed, and the first clue that we
need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving
counts (how many fit into this category, how many into that, etc.) is the chi-square. It is
extremely easy to calculate and has many more uses than we will cover. Examining patterns
involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of
these uses have a common trait: they involve counts per group. In fact, the chi-square is the only
statistic we will look at that we use when we have counts per multiple groups (Tanner &
Youssef-Morgan, 2013).
Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches
some pattern we are interested in. Example: Are the employees in our example company
distributed equal across the grades? Or, a more reasonable expectation for a company might be
are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by
generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all
of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we
determine the p-value of getting a result as large or larger to determine if we reject or not reject
our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx
Statistics window rather than the Data Analysis where we found the t and ANOVA test
functions. The most important for us are:
• CHISQ.TEST (actual range, expected range) – returns the p-value for the test
• CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value
or probability value used.
• CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual
range, expected range) will provide us with the p-value of the calculated chi square value (but
does not give us the actual calculated chi square value for the test). We can compare this value
against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting
the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated
value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df).
Excel Files AssingmentsCopy of Student_Assignment_File.11.01..docxSANSKAR20
Excel Files Assingments/Copy of Student_Assignment_File.11.01.2016.xlsx
DataIDSalaryCompa-ratioMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1GradeCopy Employee Data set to this page.The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.The column labels in the table mean:ID – Employee sample number Salary – Salary in thousands Age – Age in yearsPerformance Rating – Appraisal rating (Employee evaluation score)SERvice – Years of serviceGender: 0 = male, 1 = female Midpoint – salary grade midpoint Raise – percent of last raiseGrade – job/pay gradeDegree (0= BS\BA 1 = MS)Gender1 (Male or Female)Compa-ratio - salary divided by midpoint
Week 2This assignment covers the material presented in weeks 1 and 2.Six QuestionsBefore starting this assignment, make sure the the assignment data from the Employee Salary Data Set file is copied over to this Assignment file.You can do this either by a copy and paste of all the columns or by opening the data file, right clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file(Weekly Assignment Sheet or whatever you are calling your master assignment file).It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whatever you do will not disrupt the original data values and relationships.To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks for several data values. If you obtain them using descriptive statistics,then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in the descriptive statistics table. If you choose to generate each value using fxfunctions, then each function should be located in the cell and the location of the data values should be shown.So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerical value will not earn full credit.The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need to see how the results were obtained.In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity.1The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since the assignment problems willfocus mostly on the compa-ratios, we need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall.Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio and Gender1 columns, and then sort on Gender1.The values for age, performance rating, and service are prov ...
Week 5 Lecture 14 The Chi Square TestQuite often, patterns of .docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are generally the result of counting how many things fit into a particular category. Whenever we make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes in these visual patterns will be our first clues that things have changed, and the first clue that we need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving counts (how many fit into this category, how many into that, etc.) is the chi-square. It is extremely easy to calculate and has many more uses than we will cover. Examining patterns involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of these uses have a common trait: they involve counts per group. In fact, the chi-square is the only statistic we will look at that we use when we have counts per multiple groups (Tanner & Youssef-Morgan, 2013). Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches some pattern we are interested in. Example: Are the employees in our example company distributed equal across the grades? Or, a more reasonable expectation for a company might be are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we determine the p-value of getting a result as large or larger to determine if we reject or not reject our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx Statistics window rather than the Data Analysis where we found the t and ANOVA test functions. The most important for us are:
· CHISQ.TEST (actual range, expected range) – returns the p-value for the test
· CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value or probability value used.
· CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual range, expected range) will provide us with the p-value of the calculated chi square value (but does not give us the actual calculated chi square value for the test). We can compare this value against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df) function, the value for probability is .
DataIDSalaryCompaMidpoint AgePerformance RatingServiceGenderRaiseDegreeGender1GrStudents: Copy the Student Data file data values into this sheet to assist in doing your weekly assignments.The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.The column labels in the table mean:ID – Employee sample number Salary – Salary in thousands Age – Age in yearsPerformance Rating - Appraisal rating (employee evaluation score)Service – Years of service (rounded)Gender – 0 = male, 1 = female Midpoint – salary grade midpoint Raise – percent of last raiseGrade – job/pay gradeDegree (0= BS\BA 1 = MS)Gender1 (Male or Female)Compa - salary divided by midpoint
Week 1Week 1.Measurement and Description - chapters 1 and 2The goal this week is to gain an understanding of our data set - what kind of data we are looking at, some descriptive measurse, and a look at how the data is distributed (shape).1Measurement issues. Data, even numerically coded variables, can be one of 4 levels - nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, asthis impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data.Please list under each label, the variables in our data set that belong in each group.NominalOrdinalIntervalRatiob.For each variable that you did not call ratio, why did you make that decision?2The first step in analyzing data sets is to find some summary descriptive statistics for key variables.For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: overall sample, Females, and Males.You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. (the range must be found using the difference between the =max and =min functions with Fx) functions.Note: Place data to the right, if you use Descriptive statistics, place that to the right as well.Some of the values are completed for you - please finish the table.SalaryCompaAgePerf. Rat.ServiceOverallMean35.785.99.0Standard Deviation8.251311.41475.7177Note - data is a sample from the larger company populationRange304521FemaleMean32.584.27.9Standard Deviation6.913.64.9Range26.045.018.0MaleMean38.987.610.0Standard Deviation8.48.76.4Range28.030.021.03What is the probability for a:Probabilitya. Randomly selected person being a male in grade E?b. Randomly selected male being in grade E? Note part b is the same as given a male, what is probabilty of being in grade E?c. Why are the results different?4A key issue in comparing data sets is to see if they are distributed/shaped the same. We can do this by looking at some measures of wheresome selected values are within each data set - that .
ScoreWeek 5 Correlation and Regressio.docxpotmanandrea
Score:
Week 5
Correlation and Regression
<1 point>
1.
Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)
a.
Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?
b. Place table here (C8):
c.
Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are
significantly related to Salary?
To compa?
d.
Looking at the above correlations - both significant or not - are there any surprises -by that I
mean any relationships you expected to be meaningful and are not and vice-versa?
e.
Does this help us answer our equal pay for equal work question?
<1 point>
2
Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint,
age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways of
expressing an employee’s salary, we do not want to have both used in the same regression.)
Plase interpret the findings.
Ho: The regression equation is not significant.
Ha: The regression equation is significant.
Ho: The regression coefficient for each variable is not significant
Note: technically we have one for each input variable.
Ha: The regression coefficient for each variable is significant
Listing it this way to save space.
Sal
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9915591
R Square
0.9831894
Adjusted R Square
0.9808437
Standard Error
2.6575926
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
6
17762.3
2960.38
419.1516
1.812E-36
Residual
43
303.7003
7.0628
Total
49
18066
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-1.749621
3.618368
-0.4835
0.631166
-9.046755
5.5475126
-9.04675504
5.54751262
Midpoint
1.2167011
0.031902
38.1383
8.66E-35
1.1523638
1.2810383
1.152363828
1.28103827
Age
-0.004628
0.065197
-0.071
0.943739
-0.136111
0.1268547
-0.13611072
0.1268547
Performace Rating
-0.056596
0.034495
-1.6407
0.108153
-0.126162
0.0129695
-0.12616237
0.01296949
Service
-0.0425
0.084337
-0.5039
0.616879
-0.212582
0.1275814
-0.2125.
Week 4 Lecture 10 We have been examining the question of equal p.docxcockekeshia
Week 4 Lecture 10
We have been examining the question of equal pay for equal work for several weeks now; but have been somewhat frustrated with the equal work part. We suspect that salary varies with grade level, so that equal work is not done if we compare salaries across grades. We found that we could control the effect of grades with either of two techniques. The first is by choosing a variable that does not include grade level variation such as compa-ratios (the salary divided by midpoint). The second by statistically removing the impact of grade level using the ANOVA Two-factor without replication. Both of these gave us different outcomes on the question of male and female pay equality than examining salary only.
However, we still have not gotten a “clean” measure of equal work as there are still other factors that may impact work done such as performance levels (measured by the performance appraisal rating), seniority, education, etc. And, there could be gender bias (and, for real world companies, ethnic bias as well. We will not cover this, but it can be dealt with the same way as we will examine gender). We need to find a way to eliminate the impact of these variables on our pay measure as well.
This week we will look at two techniques that are very good at examining and explaining the influence of variables on outcomes. These are correlation and regression techniques. Linear Correlation
Correlation is a measure of how variables/things relate – that is, if one variable changes does another variable change in a predictable pattern as well? One very well-known example is the correlation (or relationship) between length/height of children and weight. As children become longer/taller their weight also increases (Tanner & Youssef-Morgan, 2013). Using this relationship, we can make predictions (using the technique of regression discussed in Lecture 11 for this week) about how heavy a child should be for any given height.
For variables that are at least interval in nature, two types of correlation exist for a bivariable (two variables only) relationship– linear and curvilinear. As they sound, linear correlations show the extent to which the data variables move in a straight line. Curvilinear correlations – which we will not cover – show the extent that variables move in curved lines.
Scatter Diagrams
An effective way to see if the data do relate in predictable ways involves generating a scatter diagram (AKA scatter chart) – a visual display of how the data points – (variable 1 value, corresponding variable 2 value) relate together (Lind, Marchel, & Wathen, 2008).
Example1. One relationship we might expect to show a positive (both values increasing) relationship would be salary and performance rating, either for the entire salary range or at least within grades. The following scatter diagram (made with the Excel Insert Graph functions) show the relationship with Performance Rating on the bottom and Salary on the on the .
1-2paragraphsapa formatWelcome to Module 6. Divers.docxjasoninnes20
1-2
paragraphs
apa format
Welcome to Module 6. Diversity can help ensure that a team has the skills and knowledge necessary for the successful completion of tasks. Diverse teams, as long as they are well managed, tend to be more creative and achieve goals more efficiently. Leaders must understand and appreciate the diversity that exists in their team. Answer the following question as you think about the diversity that exists within your own organization.
How does this diversity help your team achieve its goals?
Have you noticed any barriers to team unity that may be attributed to the diversity of team members' backgrounds?
How has your background and experience prepared you to be an effective leader in an organization that holds diversity and inclusion as core to its mission and values?
.
1-Post a two-paragraph summary of the lecture; 2- Review the li.docxjasoninnes20
1-Post a two-paragraph summary of the lecture;
2- Review the links and select one. Briefly explain how they support our curse.
http://www.fldoe.org/
http://www.eric.ed.gov/ERICWebPortal/Home.portal
http://firn.edu/doe/sas/ftce/ftcecomp.htm
Use APA 7.
each work separately.
.
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BUS 308 Week 2 Lecture 2 Statistical Testing for Differenc.docxjasoninnes20
BUS 308 Week 2 Lecture 2
Statistical Testing for Differences – Part 1
After reading this lecture, the student should know:
1. How statistical distributions are used in hypothesis testing.
2. How to interpret the F test (both options) produced by Excel
3. How to interpret the T-test produced by Excel
Overview
Lecture 1 introduced the logic of statistical testing using the hypothesis testing procedure.
It also mentioned that we will be looking at two different tests this week. The t-test is used to
determine if means differ, from either a standard or claim or from another group. The F-test is
used to examine variance differences between groups.
This lecture starts by looking at statistical distributions – they underline the entire
statistical testing approach. They are kind of like the detective’s base belief that crimes are
committed for only a couple of reasons – money, vengeance, or love. The statistical distribution
that underlies each test assumes that statistical measures (such as the F value when comparing
variances and the t value when looking at means) follow a particular pattern, and this can be used
to make decisions.
While the underlying distributions differ for the different tests we will be looking at
throughout the course, they all have some basic similarities that allow us to examine the t
distribution and extrapolate from it to interpreting results based on other distributions.
Distributions. The basic logic for all statistical tests: If the null hypothesis claim is
correct, then the distribution of the statistical outcome will be distributed around a central value,
and larger and smaller values will be increasingly rare. At some point (and we define this as our
alpha value), we can say that the likelihood of getting a difference this large is extremely
unlikely and we will say that our results do not seem to come from a population that matches the
claims of the null hypothesis.
Note that this logic has several key elements:
1. The test is based on an assumption that the null hypothesis is correct. This gives us a
starting point, even if later proven wrong.
2. All sample results are turned into a statistic that matches the test selected (for
example, the F statistic when using the F-test, or the t-statistic when using the T-test.)
3. The calculated statistic is compared to a related statistical distribution to see how
likely an outcome we have.
4. The larger the test statistic, the more unlikely it is that the result matches or comes
from the population described by the null hypothesis claim.
We will demonstrate these ideas by looking at the questions being asked in this week’s
homework. We will show results of the related Excel tests, and discuss how to interpret the
output.
We need to remember that seeing different value (mean, variance, etc.) from different
samples does not tell us that the population parameters we are estimating are, in fact, different.
The ...
Chapter 18 – Pricing Setting in the Business WorldThere are few .docxrobert345678
Chapter 18 – Pricing Setting in the Business World
There are few Methods for setting pricing – costs methods vs demand methods
Formulas considering costs and mark up will help you to do the Problem set assignment:
1. Markup for setting prices (Mark up $ = SP-CP); MARK UP % = (MU $/SP) X100)
Formula for setting price with the markup method
SP = Cost/(1- Markup %)
Example - retailer buys A hat for $15 and wants a 40% markup, his selling price would be….
SP = 15/(1-.40)=.60
= $25.00
2. Understand Role of different costs – fixed, variable, total costs and average costs
3. What is the breakeven point? Formula for calculating the Break Even point.
BE = Total Fixed Cost/Fixed cost contribution
Fixed Cost Contribution=Price – variable cost
4. Average Cost = when there are many flavors/types of the same product, producer determines average cost and then add the mark up to set a common selling price.
.ANOVA
Analysis of Variance is a method of testing the equality of three or more population
means by analyzing sample variance.
One-Way ANOVA
The one-way ANOVA is used to compare three or more population means when there is
one factor of interest.
Requirements
The populations have distributions that are approximately normal.
The populations have the same variance.
The samples are simple random samples of quantitative data.
The samples are independent of each other.
The different samples are from populations that are categorized in only one.
way
One-Way ANOVA is a hypothesis test. There are seven steps for a hypothesis test.
Example
A professor at a local University believes there is a relationship between head size and
the major of the students in her biostatistics classes. She takes a random sample of 20
students from each of three classes and records their major and head circumference.
The data are shown in the following table.
Step 1: State the null hypothesis.
Mean 1 equals mean 2 equals mean 3 equals mean 4.
Step 2: State the Alternative hypothesis.
At least one mean is different.
Step 3: State the Level of Significance.
The level of significance is 0.05.
Step 4: State the test statistic.
variance between samples
variance within samples
F
The test statistic follows the F distribution which has two degrees of freedom, one for
the numerator and one for the denominator.
The calculations for the test statistic are complicated, so a software program is
generally used for the calculations. We will be using Microsoft Excel for this example.
Step 5: Calculate
The calculations are done in Microsoft Excel using the data analysis toolpak. Enter the
data into the spread sheet as shown here. Click on data and the data analysis tookpak
button is on the right.
When you click on the button a dialogue box appears.
Choose ANOVA One Factor. Then another dialogue box appears.
Input range is where the data is in the table. Be sure to put a check in the box for labels
in.
Article Write-upsTo help you connect what you’re learning in cl.docxdavezstarr61655
Article Write-ups
To help you connect what you’re learning in class with current events, you are required to find an economics-related news article, read it, and write a short paper connecting your findings to topics we’ve discussed in class. You should select your article from a reputable source like The Economist, New York Times, or Wall Street Journal (read: not a blog post or obscure website). Students must read the selected piece, summarize the content, relate it to subjects covered in class, and turn in a short (1-2 pages) typed paper with these elements. Please note that this means you need to pick an article substantial enough to write more than one page about it.
Some suggested topics:
Tradeoffs or opportunity costs
Supply & Demand (including input costs, other nonprice determinants)
Substitute & complementary goods
Elasticity
Market efficiency
Behavioral economics (framing, heuristics)
Consumer choice (utility maximization, diminishing marginal utility)
Write-up Requirements:
-Minimum 1 page of text not including header or references (double spaced, 12 point font, standard margins).
-A discussion of how your selected article directly relates to or relies upon a particular economic principle we have covered in class. This should include defining and explaining the concept, in addition to discussing how it is used in your article. (I.e. “This article uses the concept of opportunity costs, which means…” or “This article discusses using sales prices to frame consumer decisions. From behavioral economics we learned that framing is….”)
-A summary of the contents that demonstrates you read the article.
-A review and general evaluation based upon what you’ve learned in class.
-A properly formatted reference for your article (citation style of your choice – APA, MLA, etc.). For online sources please provide a link.
-You must submit your assignment on Moodle as a Word document (.doc or .docx)
Week 3 Lecture 9
Effect Size
When we reject the null hypothesis with an ANOVA test, we have two questions that arise. The first, which pair of means differs significantly, we have dealt with already. The second question, similar to what we asked with the t-test null hypothesis rejection is; what caused the rejection, the sample size or the variable interactions? This question is again answered using an effect size measure.
Recall that the effect size measure shows how likely the variable interaction caused the null hypothesis rejection. Large values lead us to say the variables caused the outcome, while small values lead us to say the outcome has little to no practical significance as the sample size was the most likely cause of the rejection of the null.
With the single factor ANOVA, the effect size measure is eta squared, and equals the SS(between)/SS(total) (Tanner & Youssef-Morgan, 2013). For our salary example in Lecture 8, eta squared equals 17686.02 (SS(between) / 18066 (SS(total) = 0.979 (rounded). Eta squared effect s.
ScoreWeek 3ANOVA and Paired T-test.docxpotmanandrea
Score:
Week 3
ANOVA and Paired T-test
At this point we know the following about male and female salaries.
a.
Male and female overall average salaries are not equal in the population.
b.
Male and female overall average compas are equal in the population, but males are a bit more spread out.
c.
The male and female salary range are almost the same, as is their age and service.
d.
Average performance ratings per gender are equal.
Let's look at some other factors that might influence pay - education(degree) and performance ratings.
<1 point>
1
Last week, we found that average performance ratings do not differ between males and females in the population.
Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?
(Assume variances are equal across the grades for this ANOVA.)
You can use these columns to place grade Perf Ratings if desired.
A
B
C
D
E
F
Null Hypothesis:
Alt. Hypothesis:
Place
B17 in Outcome range box.
Interpretation:
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If
the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What does that decision mean in terms of our equal pay question:
<1 point>
2
While it appears that average salaries per each grade differ, we need to test this assumption.
Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
Use the input table to the right to list salaries under each grade level.
Null Hypothesis:
If desired, place salaries per grade in these columns
Alt. Hypothesis:
A
B
C
D
E
F
.
DataSalCompaMidAgeEESSERGRaiseDegGen1Gr1581.017573485805.70METhe ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? 2270.870315280703.90MBNote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.3341.096313075513.61FB4661.15757421001605.51METhe column labels in the table mean:5470.9794836901605.71MDID – Employee sample number Sal – Salary in thousands 6761.1346736701204.51MFAge – Age in yearsEES – Appraisal rating (Employee evaluation score)7411.0254032100815.71FCSER – Years of serviceG – Gender (0 = male, 1 = female) 8231.000233290915.81FAMid – salary grade midpoint Raise – percent of last raise9771.149674910010041MFGrade – job/pay gradeDeg (0= BS\BA 1 = MS)10220.956233080714.71FAGen1 (Male or Female)Compa - salary divided by midpoint, a measure of salary that removes the impact of grade11231.00023411001914.81FA12601.0525752952204.50METhis data should be treated as a sample of employees taken from a company that has about 1,000 13421.0504030100214.70FCemployees using a random sampling approach.14241.04323329012161FA15241.043233280814.91FA16471.175404490405.70MCMac Users: The homework in this course assumes students have Windows Excel, and17691.2105727553131FEcan load the Analysis ToolPak into their version of Excel.18361.1613131801115.60FBThe analysis tool pak has been removed from Excel for Windows, but a free third-party 19241.043233285104.61MAtool that can be used (found on an answers Microsoft site) is:20341.0963144701614.80FBhttp://www.analystsoft.com/en/products/statplusmacle21761.1346743951306.31MFLike the Microsoft site, I make cannot guarantee the program, but do know that 22571.187484865613.81FDStatplus is a respected statistical package.You may use other approaches or tools23231.000233665613.30FAas desired to complete the assignments.24501.041483075913.80FD25241.0432341704040MA26241.043232295216.20FA27401.000403580703.91MC28751.119674495914.40FF29721.074675295505.40MF30491.0204845901804.30MD31241.043232960413.91FA32280.903312595405.60MB33641.122573590905.51ME34280.903312680204.91MB35241.043232390415.30FA36231.000232775314.30FA37220.956232295216.20FA38560.9825745951104.50ME39351.129312790615.50FB40251.086232490206.30MA41431.075402580504.30MC42241.0432332100815.71FA43771.1496742952015.50FF44601.0525745901605.21ME45551.145483695815.21FD46651.1405739752003.91ME47621.087573795505.51ME48651.1405734901115.31FE49601.0525741952106.60ME50661.1575738801204.60MEhttp://www.analystsoft.com/en/products/statplusmacle
Week 1Week 1.Describing the data.<Use right click on the row numbers at the left to insert rows below each question for your results and comments.>1Using the Excel Analysis ToolPak function descriptive statistics, generate and show the descriptive statistics for each appropriate variable in the sample data set.a. For which variables in the data set does this function not work correctly for? W.
Week 2 – Lecture 3 Making judgements about differences bet.docxcockekeshia
Week 2 – Lecture 3
Making judgements about differences between group statistics is one of the most
powerful things that statistics can do for us. It is also one of the most counter-intuitive things
that we need to master in the class.
Lecture 1 introduced the hypothesis testing procedure used in statistical testing. Lecture
2 examined how to set up, perform, and interpret the F test for variance equality. This lecture
will focus on t-tests for testing mean equality. Again, these examples will use the compa-ratio
variable, while the homework should use the Salary variable.
The T-Test
While we test for variance equality with an F test, we use the T-Test to test for mean
equality testing. The t-test also uses the degree of freedom (df) value in providing us with our
probability result; but again, Excel does the work for us.
There are three versions of the T-Test done for us by Excel. The first two are similar
except one version is done if the variances are equal and the other if the variances are not equal.
(Now we see the second reason for performing the F-test first.)
The third version of the T-test is for paired data, and is called T-test Paired Two Sample
for Means. Paired data are two measures taken on the same subject. Examples include a math
and English test score for students, preference for different drinks, and, in our data set the salary
and midpoint values. Note that paired data must be measured in the same units, and be from the
same subjects. Students in the past have incorrectly used the paired t-test on male and female
salaries. These are not paired, as the measures are taken on different people and cannot be paired
together for analysis.
In many ways, setting up Excel’s T-tests, and virtually all the functions we will study,
follow the same steps as we just went through:
1. Set up the data into distinct groups.
2. Select the test function from either the Fx or Analysis list
3. Input the data ranges and output ranges into the appropriate entry boxes, checking
Labels if appropriate.
4. Clicking on OK to produce the output.
As with the F-test, the T-test has a couple of options depending upon what you want your
output to look like. The Fx (or Formulas) option returns simply the p-value for the selected
version of the test. The Data | Analysis selection provides descriptive statistics that are useful for
additional analysis (some of which we will discuss later in the course).
The t-test requires that we select between three versions, one assuming equal variances
between the populations, one assuming unequal variances in the populations, and one requiring
paired data (two measures on each element in the sample, such as salary and midpoint for each
person in our data set.) All have the same data set-up approach, so only one will be shown.
Question 2
The second question for this week asks about salary mean equality between males and
females. The data and test se.
1
Running head: RESEARCH PROJECT PROPOSAL
1
3
RESEARCH PROJECT PROPOSAL
Research Project Proposal
Name Here
South University Online
Research Project Proposal
Provide a brief, general introduction to the topic and importance to your role (do not use first person anywhere in the paper). Conclude with a thesis statement.
Background and Significance of the Problem
Discuss here.
Statement of the Problem and Purpose of the Study
Discuss here.
Literature Review
Discuss here.
Research Questions, Hypothesis, and Variables
Discuss here.
Theoretical Framework
Overview and Guiding Propositions
Discuss here.
Application of Theory to Study Focus
Discuss here.
Methodology
Sample/Setting
Discuss here.
Sampling Strategy
Discuss here.
Research Design
Discuss here.
Extraneous Variables
Discuss here.
Instruments
Discuss here.
Description of the Intervention
Discuss here.
Data Collection Procedures
Discuss here.
Data Analysis Plans
Discuss here.
Ethical Issues
Discuss here.
Limitations of Proposed Study
Discuss here.
Implications for Practice
Discuss here.
References
Appendices
Lecture 6
(Additional information on t-tests and hypothesis testing)
Lecture 5 focused on perhaps the most common of the t-tests, the two sample assuming
equal variance. There are other versions as well; Excel lists two others, the two sample assuming
unequal variance and the paired t-test. We will end with some comments about rejecting the null
hypothesis.
Choosing between the t-test options
As the names imply each of the three forms of the t-test deal with different types of data
sets. The simplest distinction is between the equal and unequal variance tests. Both require that
the data be at least interval in nature, come from a normally distributed population, and be
independent of each other – that is, collected from different subjects.
The F-test for variance.
To determine if the population variances of two groups are statistically equal – in order to
correctly choose the equal variance version of the t-test – we use the F statistic, which is
calculated by dividing one variance by the other variance. If the outcome is less than 1.0, the
rejection region is in the left tail; if the value is greater than 1.0, the rejection region is in the
right tail. In either case, Excel provides the information we need.
To perform a hypothesis test for variance equality we use Excel’s F-Test Two-Sample for
Variances found in the Data Analysis section under the Data tab. The test set-up is very similar
to that of the t-test, entering data ranges, checking Labels box if they are included in the data
ranges, and identifying the start of the output range. The only unique element in this test is the
identification of our alpha level.
Since we are testing for equality of variances, we have a two sample test and the rejection
region is again in both tails. This means that our rejection region in each tail is 0.25. The F-test
id ...
can i get a quote. i got one from barzzy but she never replied.docxchestnutkaitlyn
can i get a quote. i got one from barzzy but she never replied
At this point we know the following about male and female salaries.
a.
Male and female overall average salaries are not equal in the population.
b.
Male and female overall average compas are equal in the population, but males are a bit more spread out.
c.
The male and female salary range are almost the same, as is their age and service.
d.
Average performance ratings per gender are equal.
Let's look at some other factors that might influence pay - education(degree) and performance ratings.
1
Last week, we found that average performance ratings do not differ between males and females in the population.
Now we need to see if they differ among the grades. Is the average performace rating the same for all grades?
(Assume variances are equal across the grades for this ANOVA.)
You can use these columns to place grade Perf Ratings if desired.
A
B
C
D
E
F
Null Hypothesis:
Alt. Hypothesis:
Place
B17 in Outcome range box.
Interpretation:
What is the p-value:
Is P-value < 0.05?
Do we REJ or Not reject the null?
If
the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
What does that decision mean in terms of our equal pay question:
2
While it appears that average salaries per each grade differ, we need to test this assumption.
Is the average salary the same for each of the grade levels? (Assume equal variance, and use the analysis toolpak function ANOVA.)
Use the input table to the right to list salaries under each grade level.
Null Hypothesis:
If desired, place salaries per grade in these columns
Alt. Hypothesis:
A
B
C
D
E
F
Place
B55 in Outcome range box.
What is the p-value:
Is P-value < 0.05?
Do you reject or not reject the null hypothesis:
If
the null hypothesis was rejected, what is the effect size value (eta squared):
Meaning of effect size measure:
Interpretation:
3
The table and analysis below demonstrate a 2-way ANOVA with replication.
Please interpret the results.
BA
MA
Ho: Average compas by gender are equal
Male
1.017
1.157
Ha: Ave.
Chi-square tests are great to show if distributions differ or i.docxMARRY7
Chi-square tests are great to show if distributions differ or if two variables interact in producing outcomes. What are some examples of variables that you might want to check using the chi-square tests? What would these results tell you?
DataSee comments at the right of the data set.IDSalaryCompaMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1Grade8231.000233290915.80FAThe ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? 10220.956233080714.70FANote: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.11231.00023411001914.80FA14241.04323329012160FAThe column labels in the table mean:15241.043233280814.90FAID – Employee sample number Salary – Salary in thousands 23231.000233665613.31FAAge – Age in yearsPerformance Rating – Appraisal rating (Employee evaluation score)26241.043232295216.21FAService – Years of service (rounded)Gender: 0 = male, 1 = female 31241.043232960413.90FAMidpoint – salary grade midpoint Raise – percent of last raise35241.043232390415.31FAGrade – job/pay gradeDegree (0= BS\BA 1 = MS)36231.000232775314.31FAGender1 (Male or Female)Compa - salary divided by midpoint37220.956232295216.21FA42241.0432332100815.70FA3341.096313075513.60FB18361.1613131801115.61FB20341.0963144701614.81FB39351.129312790615.51FB7411.0254032100815.70FC13421.0504030100214.71FC22571.187484865613.80FD24501.041483075913.81FD45551.145483695815.20FD17691.2105727553130FE48651.1405734901115.31FE28751.119674495914.41FF43771.1496742952015.51FF19241.043233285104.61MA25241.0432341704040MA40251.086232490206.30MA2270.870315280703.90MB32280.903312595405.60MB34280.903312680204.91MB16471.175404490405.70MC27401.000403580703.91MC41431.075402580504.30MC5470.9794836901605.71MD30491.0204845901804.30MD1581.017573485805.70ME4661.15757421001605.51ME12601.0525752952204.50ME33641.122573590905.51ME38560.9825745951104.50ME44601.0525745901605.21ME46651.1405739752003.91ME47621.087573795505.51ME49601.0525741952106.60ME50661.1575738801204.60ME6761.1346736701204.51MF9771.149674910010041MF21761.1346743951306.31MF29721.074675295505.40MF
Week 1Week 1.Measurement and Description - chapters 1 and 21Measurement issues. Data, even numerically coded variables, can be one of 4 levels - nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, asthis impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data.Please list under each label, the variables in our data set that belong in each group.NominalOrdinalIntervalRatiob.For each variable that you did not call ratio, why did you make that decision?2The first step in analyzing data sets is to find some summary descriptive statistics for key variables.For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: ...
Week 5 Lecture 14 The Chi Square Test Quite often, pat.docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are
generally the result of counting how many things fit into a particular category. Whenever we
make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes
in these visual patterns will be our first clues that things have changed, and the first clue that we
need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving
counts (how many fit into this category, how many into that, etc.) is the chi-square. It is
extremely easy to calculate and has many more uses than we will cover. Examining patterns
involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of
these uses have a common trait: they involve counts per group. In fact, the chi-square is the only
statistic we will look at that we use when we have counts per multiple groups (Tanner &
Youssef-Morgan, 2013).
Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches
some pattern we are interested in. Example: Are the employees in our example company
distributed equal across the grades? Or, a more reasonable expectation for a company might be
are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by
generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all
of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we
determine the p-value of getting a result as large or larger to determine if we reject or not reject
our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx
Statistics window rather than the Data Analysis where we found the t and ANOVA test
functions. The most important for us are:
• CHISQ.TEST (actual range, expected range) – returns the p-value for the test
• CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value
or probability value used.
• CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual
range, expected range) will provide us with the p-value of the calculated chi square value (but
does not give us the actual calculated chi square value for the test). We can compare this value
against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting
the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated
value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df).
Excel Files AssingmentsCopy of Student_Assignment_File.11.01..docxSANSKAR20
Excel Files Assingments/Copy of Student_Assignment_File.11.01.2016.xlsx
DataIDSalaryCompa-ratioMidpointAgePerformance RatingServiceGenderRaiseDegreeGender1GradeCopy Employee Data set to this page.The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.The column labels in the table mean:ID – Employee sample number Salary – Salary in thousands Age – Age in yearsPerformance Rating – Appraisal rating (Employee evaluation score)SERvice – Years of serviceGender: 0 = male, 1 = female Midpoint – salary grade midpoint Raise – percent of last raiseGrade – job/pay gradeDegree (0= BS\BA 1 = MS)Gender1 (Male or Female)Compa-ratio - salary divided by midpoint
Week 2This assignment covers the material presented in weeks 1 and 2.Six QuestionsBefore starting this assignment, make sure the the assignment data from the Employee Salary Data Set file is copied over to this Assignment file.You can do this either by a copy and paste of all the columns or by opening the data file, right clicking on the Data tab, selecting Move or Copy, and copying the entire sheet to this file(Weekly Assignment Sheet or whatever you are calling your master assignment file).It is highly recommended that you copy the data columns (with labels) and paste them to the right so that whatever you do will not disrupt the original data values and relationships.To Ensure full credit for each question, you need to show how you got your results. For example, Question 1 asks for several data values. If you obtain them using descriptive statistics,then the cells should have an "=XX" formula in them, where XX is the column and row number showing the value in the descriptive statistics table. If you choose to generate each value using fxfunctions, then each function should be located in the cell and the location of the data values should be shown.So, Cell D31 - as an example - shoud contain something like "=T6" or "=average(T2:T26)". Having only a numerical value will not earn full credit.The reason for this is to allow instructors to provide feedback on Excel tools if the answers are not correct - we need to see how the results were obtained.In starting the analysis on a research question, we focus on overall descriptive statistics and seeing if differences exist. Probing into reasons and mitigating factors is a follow-up activity.1The first step in analyzing data sets is to find some summary descriptive statistics for key variables. Since the assignment problems willfocus mostly on the compa-ratios, we need to find the mean, standard deviations, and range for our groups: Males, Females, and Overall.Sorting the compa-ratios into male and females will require you copy and paste the Compa-ratio and Gender1 columns, and then sort on Gender1.The values for age, performance rating, and service are prov ...
Week 5 Lecture 14 The Chi Square TestQuite often, patterns of .docxcockekeshia
Week 5 Lecture 14
The Chi Square Test
Quite often, patterns of responses or measures give us a lot of information. Patterns are generally the result of counting how many things fit into a particular category. Whenever we make a histogram, bar, or pie chart we are looking at the pattern of the data. Frequently, changes in these visual patterns will be our first clues that things have changed, and the first clue that we need to initiate a research study (Lind, Marchel, & Wathen, 2008).
One of the most useful test in examining patterns and relationships in data involving counts (how many fit into this category, how many into that, etc.) is the chi-square. It is extremely easy to calculate and has many more uses than we will cover. Examining patterns involves two uses of the Chi-square - the goodness of fit and the contingency table. Both of these uses have a common trait: they involve counts per group. In fact, the chi-square is the only statistic we will look at that we use when we have counts per multiple groups (Tanner & Youssef-Morgan, 2013). Chi Square Goodness of Fit Test
The goodness of fit test checks to see if the data distribution (counts per group) matches some pattern we are interested in. Example: Are the employees in our example company distributed equal across the grades? Or, a more reasonable expectation for a company might be are the employees distributed in a pyramid fashion – most on the bottom and few at the top?
The Chi Square test compares the actual versus a proposed distribution of counts by generating a measure for each cell or count: (actual – expected)2/actual. Summing these for all of the cells or groups provides us with the Chi Square Statistic. As with our other tests, we determine the p-value of getting a result as large or larger to determine if we reject or not reject our null hypothesis. An example will show the approach using Excel.
Regardless of the Chi Square test, the chi square related functions are found in the fx Statistics window rather than the Data Analysis where we found the t and ANOVA test functions. The most important for us are:
· CHISQ.TEST (actual range, expected range) – returns the p-value for the test
· CHISQ.INV.RT(p-value, df) – returns the actual Chi Square value for the p-value or probability value used.
· CHISQ.DIST.RT(X, df) – returns the p-value for a given value.
When we have a table of actual and expected results, using the =CHISQ.TEST(actual range, expected range) will provide us with the p-value of the calculated chi square value (but does not give us the actual calculated chi square value for the test). We can compare this value against our alpha criteria (generally 0.05) to make our decision about rejecting or not rejecting the null hypothesis.
If, after finding the p-value for our chi square test, we want to determine the calculated value of the chi square statistic, we can use the =CHISQ.INV.RT(probability, df) function, the value for probability is .
DataIDSalaryCompaMidpoint AgePerformance RatingServiceGenderRaiseDegreeGender1GrStudents: Copy the Student Data file data values into this sheet to assist in doing your weekly assignments.The ongoing question that the weekly assignments will focus on is: Are males and females paid the same for equal work (under the Equal Pay Act)? Note: to simplfy the analysis, we will assume that jobs within each grade comprise equal work.The column labels in the table mean:ID – Employee sample number Salary – Salary in thousands Age – Age in yearsPerformance Rating - Appraisal rating (employee evaluation score)Service – Years of service (rounded)Gender – 0 = male, 1 = female Midpoint – salary grade midpoint Raise – percent of last raiseGrade – job/pay gradeDegree (0= BS\BA 1 = MS)Gender1 (Male or Female)Compa - salary divided by midpoint
Week 1Week 1.Measurement and Description - chapters 1 and 2The goal this week is to gain an understanding of our data set - what kind of data we are looking at, some descriptive measurse, and a look at how the data is distributed (shape).1Measurement issues. Data, even numerically coded variables, can be one of 4 levels - nominal, ordinal, interval, or ratio. It is important to identify which level a variable is, asthis impact the kind of analysis we can do with the data. For example, descriptive statistics such as means can only be done on interval or ratio level data.Please list under each label, the variables in our data set that belong in each group.NominalOrdinalIntervalRatiob.For each variable that you did not call ratio, why did you make that decision?2The first step in analyzing data sets is to find some summary descriptive statistics for key variables.For salary, compa, age, performance rating, and service; find the mean, standard deviation, and range for 3 groups: overall sample, Females, and Males.You can use either the Data Analysis Descriptive Statistics tool or the Fx =average and =stdev functions. (the range must be found using the difference between the =max and =min functions with Fx) functions.Note: Place data to the right, if you use Descriptive statistics, place that to the right as well.Some of the values are completed for you - please finish the table.SalaryCompaAgePerf. Rat.ServiceOverallMean35.785.99.0Standard Deviation8.251311.41475.7177Note - data is a sample from the larger company populationRange304521FemaleMean32.584.27.9Standard Deviation6.913.64.9Range26.045.018.0MaleMean38.987.610.0Standard Deviation8.48.76.4Range28.030.021.03What is the probability for a:Probabilitya. Randomly selected person being a male in grade E?b. Randomly selected male being in grade E? Note part b is the same as given a male, what is probabilty of being in grade E?c. Why are the results different?4A key issue in comparing data sets is to see if they are distributed/shaped the same. We can do this by looking at some measures of wheresome selected values are within each data set - that .
ScoreWeek 5 Correlation and Regressio.docxpotmanandrea
Score:
Week 5
Correlation and Regression
<1 point>
1.
Create a correlation table for the variables in our data set. (Use analysis ToolPak or StatPlus:mac LE function Correlation.)
a.
Reviewing the data levels from week 1, what variables can be used in a Pearson's Correlation table (which is what Excel produces)?
b. Place table here (C8):
c.
Using r = approximately .28 as the signicant r value (at p = 0.05) for a correlation between 50 values, what variables are
significantly related to Salary?
To compa?
d.
Looking at the above correlations - both significant or not - are there any surprises -by that I
mean any relationships you expected to be meaningful and are not and vice-versa?
e.
Does this help us answer our equal pay for equal work question?
<1 point>
2
Below is a regression analysis for salary being predicted/explained by the other variables in our sample (Midpoint,
age, performance rating, service, gender, and degree variables. (Note: since salary and compa are different ways of
expressing an employee’s salary, we do not want to have both used in the same regression.)
Plase interpret the findings.
Ho: The regression equation is not significant.
Ha: The regression equation is significant.
Ho: The regression coefficient for each variable is not significant
Note: technically we have one for each input variable.
Ha: The regression coefficient for each variable is significant
Listing it this way to save space.
Sal
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.9915591
R Square
0.9831894
Adjusted R Square
0.9808437
Standard Error
2.6575926
Observations
50
ANOVA
df
SS
MS
F
Significance F
Regression
6
17762.3
2960.38
419.1516
1.812E-36
Residual
43
303.7003
7.0628
Total
49
18066
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-1.749621
3.618368
-0.4835
0.631166
-9.046755
5.5475126
-9.04675504
5.54751262
Midpoint
1.2167011
0.031902
38.1383
8.66E-35
1.1523638
1.2810383
1.152363828
1.28103827
Age
-0.004628
0.065197
-0.071
0.943739
-0.136111
0.1268547
-0.13611072
0.1268547
Performace Rating
-0.056596
0.034495
-1.6407
0.108153
-0.126162
0.0129695
-0.12616237
0.01296949
Service
-0.0425
0.084337
-0.5039
0.616879
-0.212582
0.1275814
-0.2125.
Week 4 Lecture 10 We have been examining the question of equal p.docxcockekeshia
Week 4 Lecture 10
We have been examining the question of equal pay for equal work for several weeks now; but have been somewhat frustrated with the equal work part. We suspect that salary varies with grade level, so that equal work is not done if we compare salaries across grades. We found that we could control the effect of grades with either of two techniques. The first is by choosing a variable that does not include grade level variation such as compa-ratios (the salary divided by midpoint). The second by statistically removing the impact of grade level using the ANOVA Two-factor without replication. Both of these gave us different outcomes on the question of male and female pay equality than examining salary only.
However, we still have not gotten a “clean” measure of equal work as there are still other factors that may impact work done such as performance levels (measured by the performance appraisal rating), seniority, education, etc. And, there could be gender bias (and, for real world companies, ethnic bias as well. We will not cover this, but it can be dealt with the same way as we will examine gender). We need to find a way to eliminate the impact of these variables on our pay measure as well.
This week we will look at two techniques that are very good at examining and explaining the influence of variables on outcomes. These are correlation and regression techniques. Linear Correlation
Correlation is a measure of how variables/things relate – that is, if one variable changes does another variable change in a predictable pattern as well? One very well-known example is the correlation (or relationship) between length/height of children and weight. As children become longer/taller their weight also increases (Tanner & Youssef-Morgan, 2013). Using this relationship, we can make predictions (using the technique of regression discussed in Lecture 11 for this week) about how heavy a child should be for any given height.
For variables that are at least interval in nature, two types of correlation exist for a bivariable (two variables only) relationship– linear and curvilinear. As they sound, linear correlations show the extent to which the data variables move in a straight line. Curvilinear correlations – which we will not cover – show the extent that variables move in curved lines.
Scatter Diagrams
An effective way to see if the data do relate in predictable ways involves generating a scatter diagram (AKA scatter chart) – a visual display of how the data points – (variable 1 value, corresponding variable 2 value) relate together (Lind, Marchel, & Wathen, 2008).
Example1. One relationship we might expect to show a positive (both values increasing) relationship would be salary and performance rating, either for the entire salary range or at least within grades. The following scatter diagram (made with the Excel Insert Graph functions) show the relationship with Performance Rating on the bottom and Salary on the on the .
Similar to Business Email Rubric Subject Line Subject line clea.docx (20)
1-2paragraphsapa formatWelcome to Module 6. Divers.docxjasoninnes20
1-2
paragraphs
apa format
Welcome to Module 6. Diversity can help ensure that a team has the skills and knowledge necessary for the successful completion of tasks. Diverse teams, as long as they are well managed, tend to be more creative and achieve goals more efficiently. Leaders must understand and appreciate the diversity that exists in their team. Answer the following question as you think about the diversity that exists within your own organization.
How does this diversity help your team achieve its goals?
Have you noticed any barriers to team unity that may be attributed to the diversity of team members' backgrounds?
How has your background and experience prepared you to be an effective leader in an organization that holds diversity and inclusion as core to its mission and values?
.
1-Post a two-paragraph summary of the lecture; 2- Review the li.docxjasoninnes20
1-Post a two-paragraph summary of the lecture;
2- Review the links and select one. Briefly explain how they support our curse.
http://www.fldoe.org/
http://www.eric.ed.gov/ERICWebPortal/Home.portal
http://firn.edu/doe/sas/ftce/ftcecomp.htm
Use APA 7.
each work separately.
.
1-What are the pros and cons of parole. Discuss!2-Discuss ways t.docxjasoninnes20
1-What are the pros and cons of parole. Discuss!
2-Discuss ways to improve parole so that offenders have a better chance of being successful in the community
3-What are the barriers that parolees face when they return to the community that contribute to them failing. Give a relative example!
Submit in 3 paragraphs
.
1-page (max) proposal including a Title, Executive Summary, Outline,.docxjasoninnes20
1-page (max) proposal including a Title, Executive Summary, Outline, Team members, Task Assignment and Duration (who is doing what part). Include your anticipated dataset(s) and techniques/software. Please provide a list of the main references you want to use for your project in any appropriate format, e.g. Vancouver or APA style.
proposal is due by october 7th 2020 at 12pm est
project by 25th october
instructions for project are in the folder
.
1-Identify the benefits of sharing your action research with oth.docxjasoninnes20
1-Identify the benefits of sharing your action research with others.
-How does sharing your action research assist you in achieving your goal to improve the lives of your students?
2-Describe the criteria used to judge action research.
-What determines if your action research study gets published?
3-Identify one Web site resource (ERIC)and describe how it assisted you in designing, implementing, evaluating, writing and/or sharing your action research. Choose any one of the Web site sources listed in chapter 10(last page of attachment)
4-Why does Mills suggest in the last chapter of his book that this is really the beginning of your work?( start page 291)
Source:
Mills, G. E. (2000). Action research: A guide for the teacher researcher. Prentice-Hall, Inc., One Lake Street, Upper Saddle River, New Jersey 07458.
.
1-page APA 7 the edition No referenceDescription of Personal a.docxjasoninnes20
1-page APA 7 the edition / No reference
Description of Personal and Professional Goals My personal goal within the health care field is to become a successful and exceptional
nurse.
1-page APA 7 the edition / No reference
Reflection of the program Discussions about the program has helped my growth as a capable nurse. And talk about how good the program.
.
1-Pretend that you are a new teacher. You see that one of your st.docxjasoninnes20
1-Pretend that you are a new teacher. You see that one of your students likes to tease and joke on the other students. This student targets some students more than others and is meaner to them. The students who are targeted most often are those who appear to be less socially adept than some of the others. They may be younger, seem to have a more obvious disability or be overweight, wear glasses or not dress in trendy clothes. The student's behavior goes well beyond "friendly banter" and often leaves the other students feeling hurt and ashamed. How do you stop the student from bullying his or her peers and work to build the self-esteem of the students who have been picked on? What could be some of the causes of the student's bullying behavior and how might you work to address the root of the behavior?
2-Tiered Behavior Management and Response to Intervention (RtI
Please share a situation where you have worked with a challenging or difficult student. Was a tiered program or RtI a part of the program used to work with the student? How does a tiered program encourage student success? What are some of the challenges you have experienced while working with a tiered program? How have your students responded to the program or programs?
3-Special education teachers may work at different education levels at various points in their careers. Inclusion will be different in the lower grades than it would be in a high school classroom. How do you think that inclusion may look different for students at the elementary level as opposed to the high school level? What are some of the methods used to include students at all educational levels? What are some of the benefits and challenges you can see of the different inclusion models used with the different age students?
4-As a teacher of students with mild disabilities your class may be a diverse mix of students with various abilities and disabilities. How might inclusion and classroom management change when working with students with Autism and Autism Spectrum Disorders or other specific disabilities such as Down Syndrome? What would you need to take into account when developing behavior intervention plans (BIPs) and Individual Education Plans (IEPs)? How do you think these would change as the student grew and progressed through school?
5- This week you have a special task for the discussion. You will need to read about a disability category or specific disability that is of interest to you. Many of you may have a student, friend or family member with a specific disability we have not talked about so far in class. Use what you learn in the materials you read, the professional organization's website you visit or the videos you watch to talk about the specific inclusion and behavior management needs of students with that disability.
Example: My niece has ADHD and Asperger's Syndrome. She has been receiving services part time since she was in kindergarten. She also sees a counselor a.
1- What is the difference between a multi-valued attribute and a.docxjasoninnes20
1- What is the difference between a multi-valued attribute and a composite attribute? Give examples.
2- Create an ERD for the following requirements (You can use Dia diagramming tool to create your ERD):
Some Tiny College staff employees are information technology (IT) personnel. Some IT personnel provide technology support for academic programs, some provide technology infrastructure support, and some provide support for both. IT personnel are not professors; they are required to take periodic training to retain their technical expertise. Tiny College tracks all IT personnel training by date, type, and results (completed vs. not completed).
.
1- What is a Relational Algebra What are the operators. Explain.docxjasoninnes20
1- What is a Relational Algebra? What are the operators. Explain each.
2- What is the
INNER JOIN
operation between the following two relations (data sets or tables of data).
Hint: Use OWNER_ID column as common column between the two tables and list all columns of the two tables that have common OWNER_ID.
.
1- Watch the movie Don Quixote, which is an adaptation of Cerv.docxjasoninnes20
1-
Watch the movie
Don Quixote
, which is an adaptation of Cervantes' novel
Don Quixote
. Then, write at least two paragraphs (minimum five well-developed sentences per paragraph) to explain a lesson one could learn from the characters. You need to incorporate at least three of the ideas provided below:
The value of friendship
Humility and nobility
Importance of time
Importance of reading
Importance of optimism
The role of imagination and vision
Justifying commitment
Sense of self and disciple
Building leadership
.
1- reply to both below, no more than 75 words per each. PSY 771.docxjasoninnes20
1- reply to both below, no more than 75 words per each.
PSY 7710
4 days ago
Karissa Milano
unit 9 discussion scenario 3
COLLAPSE
ABA Procedure: A DRO (differential reinforcement of other behavior) to address SIB exhibited by a toddler in a home setting.
Special Methods: Any appropriate behaviors other than SIB will be reinforced through a specific amount of time (every five minutes). Reinforcement is only given when the individual does not engage in SIB behaviors.
Risks
Notes
1 Implementing the plan at home can be difficult.
1 The family might be concerned with their safety and the safety of the child. There should be a protocol before implementing this intervention.
2 Family members and client could be at risk for danger.
2 The parents might be concerned for the safety of themselves and their child.
3 Possible increase in SIB
3 SIB behaviors might increase before it decreases due to an extinction burst. The behavior analyst should have a protocol before implementing this intervention.
4 SIB behaviors could remain the same.
4 If there is no change in the clients SIB behaviors then a preference test should be conducted to determine motivating reinfoncers.
Benefits
Notes
1 Generalization
1 The client will learn to use this skill at home as well as be able generalize this skill into other settings.
2 Improved learning environment
2 SIB behaviors will decrease and appropriate behavior will be taught. SIB will no longer impact the client and family in the future.
3 Increase in appropriate behaviors
3 Appropriate behaviors will be taught and replace the SIB behavior.
4 Least intrusive intervention
4 Using reinforcement to decrease the problem behavior and increase appropriate behaviors. This is a least restrictive method of treatment.
5 Parent training and involvement
5 Parents will feel confident about implementing this evidence based treatment at home. This will can lead to an increase a buy in from the family and they will feel comfortable implementing other interventions in the future.
Summary: DRO is an intervention that is used when the client does not engage in the problem behavior (SIB) (Bailey & Burch, 2016). Reinforcement should only be given to the individual after a certain amount of time that the client is not engaging in the problem behavior; in this case it should be after five minutes of the client not engaging in SIB. The person who is implementing this treatment should not reinforce the problem behavior. The benefits of implementing DRO outweigh the risks of implementing DRO. DRO is a good intervention to use when decreasing SIB behavior. Although there are some risks, the individual who is implementing DRO should have the knowledge, training and experience and be confident when implementing DRO ( Bailey & Burch, 2016).
Reference
Bailey, J. S., & Burch, M. R. (2016).
Ethics for behavior analysts
(3rd ed.). New York, NY: Routledge.
PSY 7711
3 days ago
Emily Gentile
Unit 9 Discussion
C.
1- Pathogenesis 2- Organs affected in the body 3- Chain of i.docxjasoninnes20
1- Pathogenesis
2- Organs affected in the body
3- Chain of infection and its Links associated: Infectious agent, Reservoirs, Portal of Exit, Route of Transmission, portal of Entry, and Susceptible Host. All must to be defined in the chosen agent.
4- Incidence, Prevalence, and Prevention of this infectious disease
5- Treatment if possible
6- Please answer, being a Nurse. “How are you going to break down the chain of infection of the selected microorganisms, to avoid Cross Contamination ?
.
1- I can totally see where there would be tension between.docxjasoninnes20
1- I can totally see where there would be tension between these two, especially in today’s world. I am no expert on religion or science for that matter, but I do feel like some of the tension is unnecessary. I feel that the two can work to benefit our patients by balancing them with the needs of the patient. Let’s take my kids for instance, if they were sick with some known treatable disease there would be no other option in my mind to treat them with science and medicine that has been proven to work. I wouldn’t only pray for them to get better and not do anything about it, but I would pray for them and do whatever was necessary to help my family deal with the stress and worry of a child being sick. Here we have used them both to our benefit and they each serve a different purpose and effectiveness. Thanks again for your post!
2-My perception of the tension between science and religion is founded at first glance and then not when looked at more closely. Science and religion can coincide in health care if respected for their own strengths and limitations. I feel that a healthy balance of both can benefit our patients providing different needs when they’re needed. I have seen with my own eyes CRP markers drop in an infant receiving antibiotic treatment and I have also seen an infant that wasn’t supposed to live by scientific probability actually make it and thrive with prayer being the only obvious intervention. So, trying to single out one over the other as more effective than the other seems less beneficial than trying to work them both in when the patient requires such help.
I feel that science is good for some of the more usual cases and things we feel we can help with its information, and I also feel that we can use religion to help a patient with their mental aspects of healing. We can quantify an improvement in a patient through lab levels and such, but it's hard to do the same with religion and how a patient uses that tool as comfort or however they use it in their lives. “Some observational studies suggest that people who have regular spiritual practices tend to live longer. Another study points to a possible mechanism: interleukin (IL)-6. Increased levels of IL-6 are associated with an increased incidence of disease. A research study involving 1700 older adults showed that those who attended church were half as likely to have elevated levels of IL-6. The authors hypothesized that religious commitment may improve stress control by offering better coping mechanisms, richer social support, and the strength of personal values and worldview” (NCBI, 2001). In this example we see the benefits were surveyed to be founded, but the exact workings aren’t exactly known. The great thing about science is that usually we have some tangible results that are repeatable and there’s safety to be found in that. The great thing about religion is that we can have faith in whatever we believe in and that’s all that’s needed. It's our.
1- One of the most difficult challenges leaders face is to integrate.docxjasoninnes20
1- One of the most difficult challenges leaders face is to integrate their task and relationship behaviors. Do you see this as a challenge in your own leadership? How do you integrate task and relationship behaviors?
2- If you were to change in an effort to improve your leadership, what aspect of your style would you change? Would you try to be more task oriented or more relationship oriented?
.
1- Design one assignment of the Word Find (education word) and the o.docxjasoninnes20
1- Design one assignment of the Word Find (education word) and the one of Using Digital Technology in two separate attachments, each named. Note that a sample of each is located in attachment.
2- Read the lecture and post a one-paragraph summary of the lecture. (Graphic organizers).
.
1- This chapter suggests that emotional intelligence is an interpers.docxjasoninnes20
1- This chapter suggests that emotional intelligence is an interpersonal leadership whether you agree or disagree with this assumption. As you think about your own leadership, do emotions help or hinder your role as a leader? Discuss.
2- One unique aspect of leadership skills is that they can be practiced. List and briefly describe three things you could do to improve administrative skills.
.
1-2 pages APA format1. overall purpose of site 2. resources .docxjasoninnes20
1-2 pages APA format
1. overall purpose of site
2. resources available to social workers on the site and
3. how these resources can be specifically used in either the social worker assessment of or the social work intervention with children. Make certain to fully reference the site in a separate page. must include 3 headings that address Each requiremen.
.
1-Define Energy.2- What is Potential energy3- What is K.docxjasoninnes20
1-Define Energy.
2- What is Potential energy?
3- What is Kinetic energy?
4-Define Metabolism and name the two main types of metabolism.
5-Define an Enzyme and name the most important classes of Enzymes.
6- Name the three Metabolic Pathways.
7-What is Aerobic cellular respiration?
8-What is Anaerobic respiration?
9- Define Fermentation.
10.Name the final Products of Anaerobic Respiration.
1. - What is the main function of enzymes in our body?
2. - Please name the 6 types of enzymes:
3. - What is Energy of Activation, for the enzymes?
4. - Factors that affect enzyme activity include:
5. - What is a cofactor:
.
1- Find one quote from chapter 7-9. Explain why this quote stood.docxjasoninnes20
1- Find one quote from chapter 7-9. Explain why this quote stood out to you. What is its importance?
2- Discussion 7-9
1-Share your quote and ideas.
2- “violence is the only lever big enough to move the world”
3-Compare and contrast Elwood and Turner.
4-Why is Turner right? Why is he wrong?
5- Theme. reading vs reals world, inside vs outside, optimism vs pessimism, violence, division of lower class among racial lines.
7- “violence is the only lever big enough to move the world”
.
1-Confucianism2-ShintoChoose one of the religious system.docxjasoninnes20
1-Confucianism
2-Shinto
Choose one of the religious systems above; find some point of interest to discuss (350 wds). You may use your textbook OR any other reputable encyclopedia or source. ALWAYS CITE your source.
To support your response you are required to provide at least one supporting reference with proper citation
.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Ethnobotany and Ethnopharmacology:
Ethnobotany in herbal drug evaluation,
Impact of Ethnobotany in traditional medicine,
New development in herbals,
Bio-prospecting tools for drug discovery,
Role of Ethnopharmacology in drug evaluation,
Reverse Pharmacology.
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
Instructions for Submissions thorugh G- Classroom.pptxJheel Barad
This presentation provides a briefing on how to upload submissions and documents in Google Classroom. It was prepared as part of an orientation for new Sainik School in-service teacher trainees. As a training officer, my goal is to ensure that you are comfortable and proficient with this essential tool for managing assignments and fostering student engagement.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Business Email Rubric Subject Line Subject line clea.docx
1. Business Email Rubric
Subject Line
Subject line
clearly states the
main point of the
email
5points
Subject line is a
bit long (5+
words) or a bit
short (1 word) but
states the point of
the email
3points
Subject line does
not correspond to
the main point of
2. the email
2points
Subject line is
missing
0points
Greeting
Email includes a
professional
greeting that is
appropriate for the
audience; uses
the person's first
name
5points
Email includes a
professional
greeting that is
adequate for the
3. audience but uses
the person's first
and last name or
just the last name
3points
Email includes a
greeting but it is
not personalized
2points
Email lacks a
greeting
0points
Introductory
Comment
Email includes an
introductory
positive, relevant
comment
4. 5points
it Email includes
an introductory,
positive comment
but may be very
general
3points
Email includes an
introduction only
2points
Email lacks an
introductory
comment
0points
Content
Purpose of the
email is clear, as
is the outcome;
5. content is succinct
and well organized
and does not
include
unnecessary
information
5points
Purpose of the
email is clear, as
is the outcome;
content could be
better organized
3points
Purpose of the
email is not clear
and/or content is
poorly organized;
it took more than
6. one reading to
understand what
the email is about
2points
Email seems to be
a collection of
unrelated
statements; it is
difficult to figure
out what the
purpose is
0points
Closing and
Signature
Email includes a
complementary
closing and
signature with all
7. required items
(name,
title/position,
company name,
phone number)
5points
Email includes a
complementary
closing and
signature but the
signature is
incomplete
3points
Email may be
missing either a
complementary
closing or
signature
8. 2points
Email lacks a
closing and
signature
0points
Writing
Conventions
Email looks
professional and
does not have any
formatting or
writing errors
5points
Email is well
presented with
minimal (<3)
formatting or
writing errors
9. 3points
Email includes
several (3+)
formatting or
writing errors
2points
Email is poorly
presented and has
an accumulation
of writing errors
that interfere with
readability
0points
BUS308 Week 3 Lecture 2
Examining Differences – ANOVA and Chi Square
10. Expected Outcomes
After reading this lecture, the student should be familiar with:
1. Conducting hypothesis tests with the ANVOA and Chi Square
tests
2. How to interpret the Analysis of Variance test output
3. How to interpret Determining significant differences between
group means
4. The basics of the Chi Square Distribution.
Overview
This week we introduced the ANOVA test for multiple mean
equality and the Chi Square
tests for distributions. This lecture will focus on interpreting
the outcomes of both tests. The
process of setting them up will be covered in Lecture 3 for this
week.
ANOVA
Hypothesis Test
The week 3 question 1 asks if the average salary per grade is
equal? While this might
seem like a no-brainer (we expect each grade to have higher
average salaries), we need to test all
assumed relationships. This is much like our detectives saying
“we need to exclude you from the
suspect pool; where were you last night?” This example will, of
course use the compa-ratio
instead of the salary values you will use in the homework.
The ANOVA test is found in the Data | Analysis tab.
11. Step 5 in the hypothesis testing process asks us to “Perform the
test.” Here is a screen
shot of the ANOVA output for a test of the null hypothesis: “All
grade compa-ratio means are
equal.” For this question we will be using the ANOVA-Single
Factor option as we are testing
mean equality for a single factor, Grades. We will briefly cover
the other ANOVA options in
Lecture 3 for this week.
Note that The ANOVA single factor output includes the test
name, a summary table, and
an ANOVA table. The summary table that gives us the count,
sum, average, and variance for the
compa-ratios by the analysis groups (in this case our grades).
Note that we are assuming equal
variances within the grades within the population for this
example, and your assignment. This
may not actually be true for this example (note the values in the
Variance column), but we will
ignore this for now. ANOVA is somewhat robust around
violations on the variance equality
assumption – means it may still produce acceptable results with
unequal variances. There is a
non-parametric alternate if the variances are too different, but
we do not cover it in this course.
Please note that the column and row values are present in this
screenshot. These will be needed
as references in question 2.
The next table is the meat of the test. While for all practical
12. purposes, we are only
interested in the highlighted p-value, knowing what the other
values are is helpful. When we
introduced ANVOA in lecture 1, we discussed the between and
within groups variation. As you
recall, the between groups focused on the data set as a single
group and not distinct groups. For
the Between Groups row, we have an Sum of Squares (SS)
value, which is a raw estimate of the
variation that exists. The degrees of freedom (df) for Between
Groups equals the number of
groups (k) we have minus 1 (k-1), which equals 5 for our 6
groups. The Mean Square variation
estimate equals the SS divided by the df.
The Within Group focuses on the average variation for all our
groups. SS gives us the
same raw estimate as for the BG row. The df for Within Groups
is the total count (N) minus the
number of groups (N-k), or 44 for our 50 employees in the 6
groups. MSwg equals SS/df.
The F statistic is calculated by dividing the MSbg by MSwg.
The next column gives us
our p-value followed by the critical value of F (when the p-
value would be exactly 0.05). The
total line is the sum of the SS values and the overall df which
equal the total count -1 (N – 1).
(As with the t and F tests, we could make our decision by
comparing the calculated F
value (in cell O20, with critical value of F in cell Q20. We
reject the null when the calculated F
is greater than the critical F. The critical value of F or any
13. statistic in an Excel output table is the
value that exactly provides a p-value equaling our selected
value for Alpha. However, we will
continue to use the P-value in our decisions.)
Now that we have our test results, we can complete step 6 of the
hypothesis testing
procedure.
Step 6: Conclusions and Interpretation
What is the p-value? Found in the table, it is 0.0186 (rounded).
(Side note: at times Excel will produce a p-value that looks
something like 3.8E-14. This
is called the scientific or exponential format. It is the same as
writing 3.8 * 10-14 and
equals 0.000000000000038. A simple way of knowing how
many 0s go between the
decimal point and the first non-zero number is to subtract 1
from the E value, so with E-
14, we have 13 zeros. At any rate, any Excel p-value using E-
xx format will always be
less than 0.05.)
Decision: Reject the null hypothesis.
Why? P-value is less than 0.05.
Conclusion: at least one mean differs across the grades.
Question 2: Group Comparisons
Now that we know at least one grade compa-ratio mean is not
equal to the rest, we need
to determine which mean(s) differ. We do this by creating
14. ranges of the possible difference in
the population mean values. Remember, that our sample results
are only a close approximation
of the actual population mean. We can estimate the range of
values that the population mean
actually equals (remember that discussion of the sampling
distribution of the mean from last
week). So, using the variation that exists in our groups, we
estimate the range of differences
between means (the possible outcomes of subtracting one mean
from another).
The following screen shot shows a completed comparison table
for the grade related
compa-ratio means.
Let’s look at what this table tells us before focusing on how to
develop the values
(covered in Lecture 3 for this week). Looking at the Groups
Compared Column, we see the
comparison groups listed, A-B for grades A and B, A-C for
grades A and C, etc. The next
column is the difference between the average compa-ratio
values for each pair of grades. The T
value column is the value for a 95% two tail test for the degrees
of freedom we have. (Lecture 3
discusses how to identify the correct value). Note that it is the
same value for all of our
comparison groups, the explanation comes in Lecture 3.
The next column, labeled the +/- term, is the margin of error
that exists for the mean
difference being examined. This is a function of sampling error
15. that exists within each sample
mean. These are all of the values we need to create a range of
values that represent, with a 95%
confidence, what the actual population mean differences are
likely to be. We subtract this value
from the mean (in column B) to get our low-end estimate (Low
column values), and we add it to
the mean to get our high-end estimate (High column values).
Now, we need to decide which of these ranges indicates a
significantly different pair of
means (within the population) and which ranges indicate the
likelihood of equal population
means (non-significant differences). This is fairly simple, if the
range contains a 0 (that is, one
endpoint is negative and the other is positive), then the
difference is not significant (since a mean
difference of 0 would never be significant). Notice in the table,
that the A-B, A-C, and A-D
range all contain 0, and the results are not significant different.
The A-E and A-F comparisons,
however have positive values for each end, and do not contain
0; these means are different in the
population.
We now know how to interpret an ANOVA table and an
accompanying table of
differences for significant mean differences between and among
groups.
Chi Square Tests
With the Chi Square tests, we are going to move from looking at
population parameters,
such as means and standard deviations, and move to looking at
patterns or distributions. The
16. shape or distribution of variables is often an important way of
identifying differences that could
be important. For example, we already suspect that males and
females are not distributed across
the grades in a similar manner. We will confirm or refute this
idea in the weekly assignment.
Generally, when looking at distributions and patterns we can
create groups within our
variable of interest. For example, the Grades variable is already
divided into 6 groups, making it
easy to count how many employees exist in each group. But
what about a continuous variable
such as Compa-ratio, where no such clear division into separate
groups exists. This is not a
problem as we can always divide any range of values into
groups such as quartiles (4 groups) or
any other number of distinct ranges. Most variables can be
subdivided this way.
The Chi Square test is actually a group of comparisons that
depend upon the size of the
table the data is displayed in. We will examine different tables
and tests in Lecture 3, for this
lecture we want to focus on how to interpret the outcome of a
Chi Square test – as outcomes are
the same regardless of the table size. The details of setting up
the data will be covered in Lecture
3.
Example – Question 3
The third question for this week asks about employee grade
17. distribution. We are
concerned here about the possible impact of an uneven
distribution of males and females in
grades and how this might impact average salaries. While we
are concerned about an uneven
distribution, our null hypothesis is always about equality, so the
null would respond to a question
such as are males and females distributed across the grades in a
similar pattern; that is, we are
either males or females more likely to be in some grades rather
than others.
A similar question can be asked about degrees, are graduate and
undergraduate degrees
distributed across grades in a similar pattern? If not, this might
be part of the cause for unequal
salary averages.
The step 5 output for a Chi Square test is very simple, it is the
p-value, the probability of
getting a chi square value as large or larger than what we see if
the null hypothesis is true.
That’s it – the data is set up, the Chi Square test function is
selected from the Fx statistical list,
and we have the p-value. There is not output table to examine.
So, for an examination of are degrees distributed across grades
in a similar manner, we
would have an actual distribution table (counts of what exists)
looking like this:
Place the actual distribution in the table below.
A B C D E F Total
UnderG 7 5 3 2 5 3 25
Grad 8 2 2 3 7 3 25
18. Total 15 7 5 5 12 6 50
This table would be compared to an expected table where we
show what we expect if the null
hypothesis was correct. (Setting up this table is discussed in
Lecture 3.) Then we just get our
answer.
So, steps 5 and 6 would look like:
Step 5: Conduct the test. 0.85 (the Chi Square p-value from the
Chisq.Test function
Step 6: Conclusion and Interpretation
What is the p-value? 0.85
Decision on rejecting the null: Do Not Reject the null
hypothesis.
Why? P-value is > 0.05.
Conclusion on impact of degrees? Degrees are distributed
equally across the grades
and do not seem to have any correlation with grades. This
suggests they are not an
important factor in explaining differing salary averages among
grades.
Of course, a bit more of getting the Chi Square result depends
on the data set up than
with the other tests, but the overall interpretation is quite
19. similar – does the p-value indicate we
should reject or not reject the null hypothesis claim as a
description of the population?
Summary
Both the ANOVA and Chi Square tests follow the same basic
logic developed last week
with the F and t-tests. The analysis is started with developing
the first four (4) hypothesis testing
steps which set-up the purpose and decision-making rules for
the analysis.
Running the tests (step 5) will be covered in the third lecture
for this week.
Step 6 (Interpretation) is also done in the same fashion as last
week. Look for the p-value
for each test and compare it to the alpha criteria. If the p-value
is less than alpha, we reject the
null hypothesis.
When the null is rejected in the ANOVA test, we then create
difference intervals to
determine which pair of means differs. If any of these intervals
contains the value 0 (meaning
one end is a negative value and the other is a positive value),
we can say that those means are not
significantly different within the population.
The Chi Square has two tests that were presented. One test
looks at a single group
compared to an expected distribution, which we provide. The
other version compares two or
more groups to an expected distribution which is generated by
the existing distributions. How
20. these “expected” tables are generated will be discussed in
Lecture 3 for this week.
Please ask your instructor if you have any questions about this
material.
When you have finished with this lecture, please respond to
Discussion thread 2 for this
week with your initial response and responses to others over a
couple of days.