Power AnalysisThis is a three-part assignment in which you w
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Power Analysis This is a three-part assignment in which you will demonstrate your ability to: Analyze components of a t test required for power analysis. Compute and interpret a post hoc power analysis. Compute and interpret an a priori power analysis. In addition to IBM SPSS, you will also use the G*Power software to complete this assignment. Answer each question, providing IBM SPSS or G*Power analysis output when necessary to support your answer. Save your work in a Word file. The deadline for submitting your work is 11:59 p.m. Central time on Sunday of week 2. The data file for this assignment, BP Study Dataset, is given in the resources. You will be conducting a post hoc power analysis and an a priori power analysis on an independent samples t test of gender as the grouping variable (male = 1; female = 2) and HR1 (heart rate) as the outcome variable. There are three sections of this assignment. After reporting the t test results, you will then conduct a post hoc power analysis followed by an a priori power analysis. Section 1: Reporting the t Test Results Using BP Study Dataset, conduct an independent samples t test in SPSS with gender as the grouping variable (male = 1; female = 2) and HR1 (heart rate) as the outcome variable. Paste the SPSS output and then report: The sample size for males ( n 1) and sample size for females ( n 2). The means for males ( M 1) and females ( M 2) on HR1. The calculated mean difference ( M 1 – M 2). The standard deviations for males ( s 1) and females ( s 2) on HR1. The Levene test (homogeneity of variance assumption) and interpretation. t, degrees of freedom, t value, and probability value. State whether or not to reject the null hypothesis. Interpret the results. Calculate Cohen's d effect size from the SPSS output and interpret it. Specifically, if the homogeneity of variance assumption is met, divide the mean difference ( M 1 – M 2) by either s 1 or s 2. Violation of the homogeneity of variance assumption requires calculation of S pooled. Homogeneity assumed: Cohen's d = ( M 1 – M 2) ÷ s 1 or Cohen's d = ( M 1 – M 2) ÷ s 2 To be comprehensive, report Cohen's d based on a calculation with s 1 and a calculation with s 2. Round the effect size to two decimal places. Interpret Cohen's d with Table 5.2 of your Warner text. Section 2: Post Hoc Power Analysis Open G*Power. Select the following options: Test family = t tests. Statistical test = Means: Difference between two independent groups (two groups). Type of power analysis = Post hoc: Compute achieved power. Tails(s) = Two. Effect size d = Cohen's d obtained from Section 1 above (using either s 1 or s 2). α err prob = standard alpha level. Sample size group 1 = n 1 from Section 1 above. Sample size group 2 = n 2 from Section 1 above. Click Calculate . Provide a screenshot of your G*Power output. Report the observed power of this post hoc power analysis ...
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Recommended
Using bpstudy.sav, conduct an independent samples t test in
Using bpstudy.sav, conduct an independent samples
t
test in SPSS with gender as the grouping variable (male = 1; female = 2) and HR1 (heart rate) as the outcome variable.
Paste the SPSS output and then report:
The sample size for males (
n
1) and sample size for females (
n
2).
The means for males (
M
1) and females (
M
2) on HR1.
The calculated mean difference (
M
1 –
M
2).
The standard deviations for males (
s
1) and females (
s
2) on HR1.
The Levene test (homogeneity of variance assumption) and interpretation.
t,
degrees of freedom,
t
value, and probability value. State whether or not to reject the null hypothesis. Interpret the results.
Calculate Cohen's
d
effect size from the SPSS output and interpret it. Specifically, if the homogeneity of variance assumption is met, divide the mean difference (
M
1 –
M
2) by either
s
1 or
s
2. Violation of the homogeneity of variance assumption requires calculation of
S
pooled. Homogeneity assumed:
Cohen's
d
= (
M
1 –
M
2) ÷
s
1 or Cohen's
d
= (
M
1 –
M
2) ÷
s
2
To be comprehensive, report Cohen's
d
based on a calculation with
s
1 and a calculation with
s
2. Round the effect size to two decimal places. Interpret Cohen's
d
with Table 5.2 of your Warner text.
Section 2: Post-hoc Power Analysis
Open G*Power. Select the following options:
Test family =
t
tests.
Statistical test = Means: Difference between two independent groups (two groups).
Type of power analysis = Post hoc: Compute achieved power.
Tails(s) = Two.
Effect size
d
= Cohen's
d
obtained from Section 1 above (using either
s
1 or
s
2).
α err prob = standard alpha level.
Sample size group 1 =
n
1 from Section 1 above.
Sample size group 2 =
n
2 from Section 1 above.
Click
Calculate
.
Provide a screen shot of your G*Power output. Report the observed power of this post-hoc power analysis. Interpret the level of power in terms of rejecting a null hypothesis. Do you have sufficient power to reject a false null hypothesis? Interpret power in terms of committing a Type II error.
Section 3: A Priori Power Analysis
In G*Power, now select:
Type of power analysis = A priori: Compute required sample size.
Input effect size
d
from Section 1.
Specify α err prob.
Specify Power (1 - β) = .80.
Set the Allocation ratio to 1 (i.e., equal sample sizes).
Press Calculate.
Provide a screen shot of your G*Power output. Interpret the meaning of a .80 power value. Specifically, report the estimated
n
1,
n
2, and total
N
to achieve obtain a power of .80. How many total subjects (
N
) would be needed to obtain a power of .80? Would you have expected a required
N
of this size? Why or why not?
Next, in G*Power, change the Cohen's
d
effect size value obtained in Section 1 and set it to .50 (conventional "medium" effect size). Click
Calculate
. How many total subjects (
N)
are needed to obtain a power of .80? Compare and contrast these two estimated
N
s.
In co ...
GPowerManual.pdf
This document is a manual for G*Power 3.1, software for performing statistical power analyses. It provides an introduction to the software, describing the types of analyses it can perform and how to use it. The manual is not yet complete, and the user is advised to check the G*Power website for updates. It includes sections describing the main program window, how to select a statistical test and perform analyses, and an embedded calculator for statistical computations.
HW1 MIT Fall 2005
This document provides instructions for Homework 1 for the course 6.867. It is due on September 28 and will be 10% off for each day late. The homework involves exploring bias-variance tradeoffs in estimating the mean of different distributions from sample data. It provides questions to answer about maximum likelihood estimators for the mean of uniform distributions on intervals of different lengths. It also covers Bayesian estimation of probabilities for a "thick coin" that can land on heads, tails, or edge. Finally, it includes questions on Gaussian distributions, analyzing a presidential debate poll, and decision theory concepts.
Assessment 3 – Hypothesis, Effect Size, Power, and t Tests.docx
Assessment 3 – Hypothesis, Effect Size, Power, and
t
Tests
Complete the following problems within this Word document. Do not submit other files. Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Hypothesis, Effect Size, and Power
Problem Set 3.1: Sampling Distribution of the Mean Exercise
Criterion:
Interpret population mean and variance.
Instructions:
Read the information below and answer the questions.
Suppose a researcher wants to learn more about the mean attention span of individuals in some hypothetical population. The researcher cites that the attention span (the time in minutes attending to some task) in this population is normally distributed with the following characteristics: 20
36
. Based on the parameters given in this example, answer the following questions:
1. What is the population mean (μ)? __________________________
2. What is the population variance
? __________________________
3. Sketch the distribution of this population. Make sure you draw the shape of the distribution and label the mean plus and minus three standard deviations.
Problem Set 3.2: Effect Size and Power
Criterion:
Explain effect size and power.
Instructions:
Read each of the following three scenarios and answer the questions.
Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher A determines that the effect size in the population of males is
d
= 0.36; Researcher B determines that the effect size in the population of females is
d
= 0.20. All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples (
n
= 22); Researcher B collects a sample of 40 married couples (
n
= 40). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 (
); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 (
). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Problem Set 3.3: Hypothesis, Direction, and Population Mean
Criterion:
Explain the relationship between hypothesis, tests, and population mean.
Instructions:
Read the following and answer the questions.
ch02.pdf
The document provides information about models and parameter estimation for t-tests and analysis of variance. It discusses the means model and effects model, and how to estimate the parameters of each using least squares. It explains that the sample averages provide estimates of the factor level means in the means model. It also describes how to construct a normal probability plot and check assumptions like normality using residuals.
Multiple comparison - Descriptive Statistic
1) The document describes how to perform a one-way ANOVA to compare multiple means. It outlines the descriptive statistics, assumptions of ANOVA including equal variance, and post-hoc comparisons using methods like LSD and Bonferroni.
2) It provides an example using data on heart rates of participants exposed to stress in different groups. Descriptive statistics and plots are used to explore differences before ANOVA.
3) ANOVA finds a significant difference between the group means. Post-hoc tests further examine differences between specific group pairs while controlling for multiple comparisons.
Descriptive Statistics Formula Sheet Sample Populatio.docx
Descriptive Statistics Formula Sheet
Sample Population
Characteristic statistic Parameter
raw scores x, y, . . . . . X, Y, . . . . .
mean (central tendency) M =
∑ x
n
μ =
∑ X
N
range (interval/ratio data) highest minus lowest value highest minus lowest value
deviation (distance from mean) Deviation = (x − M ) Deviation = (X − μ )
average deviation (average
distance from mean)
∑(x − M )
n
= 0
∑(X − μ )
N
sum of the squares (SS)
(computational formula) SS = ∑ x
2 −
(∑ x)2
n
SS = ∑ X2 −
(∑ X)2
N
variance ( average deviation2 or
standard deviation
2
)
(computational formula)
s2 =
∑ x2 −
(∑ x)2
n
n − 1
=
SS
df
σ2 =
∑ X2 −
(∑ X)2
N
N
standard deviation (average
deviation or distance from mean)
(computational formula) s =
√∑ x
2 −
(∑ x)2
n
n − 1
σ =
√∑ X
2 −
(∑ X)2
N
N
Z scores (standard scores)
mean = 0
standard deviation = ± 1.0
Z =
x − M
s
=
deviation
stand. dev.
X = M + Zs
Z =
X − μ
σ
X = μ + Zσ
Area Under the Normal Curve -1s to +1s = 68.3%
-2s to +2s = 95.4%
-3s to +3s = 99.7%
Using Z Score Table for Normal Distribution
(Note: see graph and table in A-23)
for percentiles (proportion or %) below X
for positive Z scores – use body column
for negative Z scores – use tail column
for proportions or percentage above X
for positive Z scores – use tail column
for negative Z scores – use body column
to discover percentage / proportion between two X values
1. Convert each X to Z score
2. Find appropriate area (body or tail) for each Z score
3. Subtract or add areas as appropriate
4. Change area to % (area × 100 = %)
Regression lines
(central tendency line for all
points; used for predictions
only) formula uses raw
scores
b = slope
a = y-intercept
y = bx + a
(plug in x
to predict y)
b =
∑ xy −
(∑ x)(∑ y)
n
∑ x2 −
(∑ x)2
n
a = My - bMx
where My is mean of y
and Mx is mean of x
SEest (measures accuracy of predictions; same properties as standard deviation)
Pearson Correlation Coefficient
(used to measure relationship;
uses Z scores)
r =
∑ xy−
(∑ x)(∑ y)
n
√(∑ x2−
(∑ x)2
n
)(∑ y2−
(∑ y)2
n
)
r =
degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑡𝑜𝑔𝑒𝑡ℎ𝑒𝑟
degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑒𝑙𝑦
r
2
= estimate or % of accuracy of predictions
PSYC 2317 Mark W. Tengler, M.S.
Assignment #9
Hypothesis Testing
9.1 Briefly explain in your own words the advantage of using an alpha level (α) = .01
versus an α = .05. In general, what is the disadvantage of using a smaller alpha
level?
9.2 Discuss in your own words the errors that can be made in hypothesis testing.
a. What is a type I error? Why might it occur?
b. What is a type II error? How does it happen?
9.3 The term error is used in two different ways in the context of a hypothesis test.
First, there is the concept of sta
Ashford 4 - Week 3 - Discussion 1Your initial discussio.docx
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: ...
Recommended
Using bpstudy.sav, conduct an independent samples t test in
Using bpstudy.sav, conduct an independent samples
t
test in SPSS with gender as the grouping variable (male = 1; female = 2) and HR1 (heart rate) as the outcome variable.
Paste the SPSS output and then report:
The sample size for males (
n
1) and sample size for females (
n
2).
The means for males (
M
1) and females (
M
2) on HR1.
The calculated mean difference (
M
1 –
M
2).
The standard deviations for males (
s
1) and females (
s
2) on HR1.
The Levene test (homogeneity of variance assumption) and interpretation.
t,
degrees of freedom,
t
value, and probability value. State whether or not to reject the null hypothesis. Interpret the results.
Calculate Cohen's
d
effect size from the SPSS output and interpret it. Specifically, if the homogeneity of variance assumption is met, divide the mean difference (
M
1 –
M
2) by either
s
1 or
s
2. Violation of the homogeneity of variance assumption requires calculation of
S
pooled. Homogeneity assumed:
Cohen's
d
= (
M
1 –
M
2) ÷
s
1 or Cohen's
d
= (
M
1 –
M
2) ÷
s
2
To be comprehensive, report Cohen's
d
based on a calculation with
s
1 and a calculation with
s
2. Round the effect size to two decimal places. Interpret Cohen's
d
with Table 5.2 of your Warner text.
Section 2: Post-hoc Power Analysis
Open G*Power. Select the following options:
Test family =
t
tests.
Statistical test = Means: Difference between two independent groups (two groups).
Type of power analysis = Post hoc: Compute achieved power.
Tails(s) = Two.
Effect size
d
= Cohen's
d
obtained from Section 1 above (using either
s
1 or
s
2).
α err prob = standard alpha level.
Sample size group 1 =
n
1 from Section 1 above.
Sample size group 2 =
n
2 from Section 1 above.
Click
Calculate
.
Provide a screen shot of your G*Power output. Report the observed power of this post-hoc power analysis. Interpret the level of power in terms of rejecting a null hypothesis. Do you have sufficient power to reject a false null hypothesis? Interpret power in terms of committing a Type II error.
Section 3: A Priori Power Analysis
In G*Power, now select:
Type of power analysis = A priori: Compute required sample size.
Input effect size
d
from Section 1.
Specify α err prob.
Specify Power (1 - β) = .80.
Set the Allocation ratio to 1 (i.e., equal sample sizes).
Press Calculate.
Provide a screen shot of your G*Power output. Interpret the meaning of a .80 power value. Specifically, report the estimated
n
1,
n
2, and total
N
to achieve obtain a power of .80. How many total subjects (
N
) would be needed to obtain a power of .80? Would you have expected a required
N
of this size? Why or why not?
Next, in G*Power, change the Cohen's
d
effect size value obtained in Section 1 and set it to .50 (conventional "medium" effect size). Click
Calculate
. How many total subjects (
N)
are needed to obtain a power of .80? Compare and contrast these two estimated
N
s.
In co ...
GPowerManual.pdf
This document is a manual for G*Power 3.1, software for performing statistical power analyses. It provides an introduction to the software, describing the types of analyses it can perform and how to use it. The manual is not yet complete, and the user is advised to check the G*Power website for updates. It includes sections describing the main program window, how to select a statistical test and perform analyses, and an embedded calculator for statistical computations.
HW1 MIT Fall 2005
This document provides instructions for Homework 1 for the course 6.867. It is due on September 28 and will be 10% off for each day late. The homework involves exploring bias-variance tradeoffs in estimating the mean of different distributions from sample data. It provides questions to answer about maximum likelihood estimators for the mean of uniform distributions on intervals of different lengths. It also covers Bayesian estimation of probabilities for a "thick coin" that can land on heads, tails, or edge. Finally, it includes questions on Gaussian distributions, analyzing a presidential debate poll, and decision theory concepts.
Assessment 3 – Hypothesis, Effect Size, Power, and t Tests.docx
Assessment 3 – Hypothesis, Effect Size, Power, and
t
Tests
Complete the following problems within this Word document. Do not submit other files. Show your work for problem sets that require calculations. Ensure that your answer to each problem is clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Hypothesis, Effect Size, and Power
Problem Set 3.1: Sampling Distribution of the Mean Exercise
Criterion:
Interpret population mean and variance.
Instructions:
Read the information below and answer the questions.
Suppose a researcher wants to learn more about the mean attention span of individuals in some hypothetical population. The researcher cites that the attention span (the time in minutes attending to some task) in this population is normally distributed with the following characteristics: 20
36
. Based on the parameters given in this example, answer the following questions:
1. What is the population mean (μ)? __________________________
2. What is the population variance
? __________________________
3. Sketch the distribution of this population. Make sure you draw the shape of the distribution and label the mean plus and minus three standard deviations.
Problem Set 3.2: Effect Size and Power
Criterion:
Explain effect size and power.
Instructions:
Read each of the following three scenarios and answer the questions.
Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher A determines that the effect size in the population of males is
d
= 0.36; Researcher B determines that the effect size in the population of females is
d
= 0.20. All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning the levels of marital satisfaction among military families. Researcher A collects a sample of 22 married couples (
n
= 22); Researcher B collects a sample of 40 married couples (
n
= 40). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Two researchers make a test concerning standardized exam performance among senior high school students in one of two local communities. Researcher A tests performance from the population in the northern community, where the standard deviation of test scores is 110 (
); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 (
). All other things being equal, which researcher has more power to detect an effect? Explain. ______________________________________________________________________
Problem Set 3.3: Hypothesis, Direction, and Population Mean
Criterion:
Explain the relationship between hypothesis, tests, and population mean.
Instructions:
Read the following and answer the questions.
ch02.pdf
The document provides information about models and parameter estimation for t-tests and analysis of variance. It discusses the means model and effects model, and how to estimate the parameters of each using least squares. It explains that the sample averages provide estimates of the factor level means in the means model. It also describes how to construct a normal probability plot and check assumptions like normality using residuals.
Multiple comparison - Descriptive Statistic
1) The document describes how to perform a one-way ANOVA to compare multiple means. It outlines the descriptive statistics, assumptions of ANOVA including equal variance, and post-hoc comparisons using methods like LSD and Bonferroni.
2) It provides an example using data on heart rates of participants exposed to stress in different groups. Descriptive statistics and plots are used to explore differences before ANOVA.
3) ANOVA finds a significant difference between the group means. Post-hoc tests further examine differences between specific group pairs while controlling for multiple comparisons.
Descriptive Statistics Formula Sheet Sample Populatio.docx
Descriptive Statistics Formula Sheet
Sample Population
Characteristic statistic Parameter
raw scores x, y, . . . . . X, Y, . . . . .
mean (central tendency) M =
∑ x
n
μ =
∑ X
N
range (interval/ratio data) highest minus lowest value highest minus lowest value
deviation (distance from mean) Deviation = (x − M ) Deviation = (X − μ )
average deviation (average
distance from mean)
∑(x − M )
n
= 0
∑(X − μ )
N
sum of the squares (SS)
(computational formula) SS = ∑ x
2 −
(∑ x)2
n
SS = ∑ X2 −
(∑ X)2
N
variance ( average deviation2 or
standard deviation
2
)
(computational formula)
s2 =
∑ x2 −
(∑ x)2
n
n − 1
=
SS
df
σ2 =
∑ X2 −
(∑ X)2
N
N
standard deviation (average
deviation or distance from mean)
(computational formula) s =
√∑ x
2 −
(∑ x)2
n
n − 1
σ =
√∑ X
2 −
(∑ X)2
N
N
Z scores (standard scores)
mean = 0
standard deviation = ± 1.0
Z =
x − M
s
=
deviation
stand. dev.
X = M + Zs
Z =
X − μ
σ
X = μ + Zσ
Area Under the Normal Curve -1s to +1s = 68.3%
-2s to +2s = 95.4%
-3s to +3s = 99.7%
Using Z Score Table for Normal Distribution
(Note: see graph and table in A-23)
for percentiles (proportion or %) below X
for positive Z scores – use body column
for negative Z scores – use tail column
for proportions or percentage above X
for positive Z scores – use tail column
for negative Z scores – use body column
to discover percentage / proportion between two X values
1. Convert each X to Z score
2. Find appropriate area (body or tail) for each Z score
3. Subtract or add areas as appropriate
4. Change area to % (area × 100 = %)
Regression lines
(central tendency line for all
points; used for predictions
only) formula uses raw
scores
b = slope
a = y-intercept
y = bx + a
(plug in x
to predict y)
b =
∑ xy −
(∑ x)(∑ y)
n
∑ x2 −
(∑ x)2
n
a = My - bMx
where My is mean of y
and Mx is mean of x
SEest (measures accuracy of predictions; same properties as standard deviation)
Pearson Correlation Coefficient
(used to measure relationship;
uses Z scores)
r =
∑ xy−
(∑ x)(∑ y)
n
√(∑ x2−
(∑ x)2
n
)(∑ y2−
(∑ y)2
n
)
r =
degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑡𝑜𝑔𝑒𝑡ℎ𝑒𝑟
degree x & 𝑦 𝑣𝑎𝑟𝑦 𝑠𝑒𝑝𝑎𝑟𝑎𝑡𝑒𝑙𝑦
r
2
= estimate or % of accuracy of predictions
PSYC 2317 Mark W. Tengler, M.S.
Assignment #9
Hypothesis Testing
9.1 Briefly explain in your own words the advantage of using an alpha level (α) = .01
versus an α = .05. In general, what is the disadvantage of using a smaller alpha
level?
9.2 Discuss in your own words the errors that can be made in hypothesis testing.
a. What is a type I error? Why might it occur?
b. What is a type II error? How does it happen?
9.3 The term error is used in two different ways in the context of a hypothesis test.
First, there is the concept of sta
Ashford 4 - Week 3 - Discussion 1Your initial discussio.docx
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: ...
Mva 06 principal_component_analysis_2010_11
Principal component analysis (PCA) is a technique used to reduce the dimensionality of large data sets by transforming correlated variables into a smaller number of uncorrelated variables called principal components. PCA identifies patterns in data and expresses the data in such a way as to highlight their similarities and differences. The main goals of PCA are data reduction and interpretation. It works by identifying the directions (principal components) along which the variation in the data is maximized.
1 P a g e ME 350 Project 2 Posted February 26.docx
1 | P a g e
ME 350 Project 2
Posted February 26, 2019, Due March 5 2019
Higher level tools for roots of f(x) = 0 problems
Q. 1. The velocity of a falling parachutist is given by the following formula:
1
Where g=9.81 m/s2, the drag coefficient c=13.5 kg/s.
Compute the mass (m) of the parachutist so that v = 40.7 m/s when t = 12.8 s
Hint. This is an f(x) = 0 type problem, with corresponding variables v(m) = 0
(a) Rearrange the terms and write a simple m-file, then use this file to use a
regular plot command to locate the approximate root. Submit the m-file and
the corresponding plot. Here you will need to experiment with a range of
values of ‘m’ .
(b) Modify the m-file from (a) into a function file that can be used with the
fzero function to compute a refined root. Submit your function and the
solution it displays in the MATLAB command window.
Q.2. Consider the square cross section beam anchored on one end and supporting a
500 lb weight. Other details are shown in figure below. Ref. Musto ch. 6. This
exercise will help you review methods for solving f(x) = 0 problems.
According to strength of materials principles, the maximum bending stress
experienced by the cantilever beam shown above is:
2 | P a g e
σ = 335,000/x3 + 92,600/x (1)
This reflects the suspended weight, the specific weight (weight per unit length),
and the length of the beam. From materials science, the maximum allowable stress
(i.e. limiting stress before the onset of yielding) for the beam material is 17,750
psi. We now need to determine the minimum dimension ‘x’ in inches that will satisfy
this stress constraint. Solve this problem using four different techniques as
itemized below.
Hint: The solution approaches involve solving a problem of the form: f(x) = 0
a) Rewrite equation 1 in polynomial form in descending coefficients of the
powers of x then use the built-in MATLAB function roots to compute the
representative solution.
b) Rewrite equation 1 into a MATLAB function file (beam2b.m) which can be
used by MATLAB’s fzero function. Use the fzero function to compute the
solution for this problem, using an initial guess of 43.
c) Rationalize the denominators of beam2b.m to generate a more standard
polynomial form and name it beam2c.m . Use fplot to generate a plot of
the function in the range -5≤x≤15; insert grid lines to spot the
approximate location of the real root. Use the fzero function to compute
the solution for this problem using and initial guess of -125. Submit the
function file, the plot and the solution computed using fzero.
d) Refer to the plot from (c). Use the bisectrr function to compute a root for
this function in the interval -5≤x≤5.
i. Comment on the outcome of the attempt in (d).
ii. Select an alternative range that would yield the root for this
function. What is the solution?
3 | P a g e
Q.3. In designing a spherical tank whose schematic i.
Suggest one psychological research question that could be answered.docx
Suggest one psychological research question that could be answered by each of the following types of statistical tests:
z test
t test for independent samples, and
t test for dependent samples
FINAL EXAM
STAT 5201
Fall 2016
Due on the class Moodle site or in Room 313 Ford Hall
on Tuesday, December 20 at 11:00 AM
In the second case please deliver to the office staff
of the School of Statistics
READ BEFORE STARTING
You must work alone and may discuss these questions only with the TA or Glen Meeden. You
may use the class notes, the text and any other sources of printed material.
Put each answer on a single sheet of paper. You may use both sides and additional sheets if
needed. Number the question and put your name on each sheet.
If I discover a misprint or error in a question I will post a correction on the class web page. In
case you think you have found an error you should check the class home page before contacting us.
1
1. Find a recent survey reported in a newspaper, magazine or on the web. Briefly describe
the survey. What are the target population and sampled population? What conclusions are drawn
from the survey in the article. Do you think these conclusions are justified? What are the possible
sources of bias in the survey? Please be brief.
2. In a small country a governmental department is interested in getting a sample of school
children from grades three through six. Because of a shortage of buildings many of the schools had
two shifts. That is one group of students came in the morning and a different group came in the
afternoon. The department has a list of all the schools in the country and knows which schools
have two shifts of students and which do not. Devise a sampling plan for selecting the students to
appear in the sample.
3. For some population of size N and some fixed sampling design let π1 be the inclusion
probability for unit i. Assume a sample of size n was used to select a sample.
i) If unit i appears in the sample what is the weight we associate with it?
ii) Suppose the population can be partitioned into four disjoint groups or categories. Let Nj be
the size of the j’th category. For this part of the problem we assume that the Nj’s are not known.
Assume that for units in category j there is a constant probability, say γi that they will respond if
selected in the sample. These γj’s are unknown. Suppose in our sample we see nj units in category
j and 0 < rj ≤ nj respond. Note n1 + n2 + n3 + n4 = n. In this case how much weight should be
assigned to a responder in category j.
iii) Answer the same question in part ii) but now assume that the Nj’s are known.
iv) Instead of categories suppose that there is a real valued auxiliary variable, say age, attached
to each unit and it is known that the probability of response depends on age. That is units of
a similar age have a similar probability of responding when selected in the sample. Very briefly
explain how you would assign adjusted weights o ...
Memorization of Various Calculator shortcuts
The document provides guidance on using statistical functions on the TI-83/84 calculator. It discusses how to input data into lists, calculate descriptive statistics, create graphs, and perform probability, confidence interval, and hypothesis tests. For descriptive statistics, the user selects STAT > CALC > 1-Var Stats and inputs the appropriate data list. Graphs are made by selecting 2nd STAT PLOT and choosing the desired plot type and lists. Probability, interval, and hypothesis tests are accessed through the TESTS and TESTS menus and require selecting the appropriate function and inputting parameters like sample sizes, means, and standard deviations.
Correlation
The document discusses correlation, regression, and hypothesis testing involving two variables. It defines correlation and the correlation coefficient r, which measures the strength of a linear relationship between two variables. Regression analyzes the relationship between variables to determine if it is positive/negative and linear/nonlinear. Hypothesis tests using r evaluate whether a linear correlation exists between two variables in a population. Confidence intervals and predictions can be made from significant relationships.
Hypothesis testing - II.pptx
trdhgjhgfgcvbvhhgjghbntewghbnmbnbnbjhguyghjbnuyyuyfgbnbjhbhgbbhuiyti7rjfhgvhgrrtfgfugiuyuyjuiyyjhyt76yttyyupiuiojoioii0909ooeoreferfergergferfewfwefwef2d33rf34
Chapter11
The document discusses hypothesis testing methods for comparing two population or treatment means. It covers notation, sampling distributions, large sample hypothesis testing, confidence intervals, and paired t-tests. An example compares the mean fill volumes of two beer can filling machines and constructs a 98% confidence interval for the difference in tensile strengths of two thread types.
Two Sample Tests
This document summarizes statistical tests for comparing two samples, including paired and independent samples t-tests, confidence intervals, and effect sizes. For paired samples from within-subject designs, a paired t-test is used to test for differences between means. For independent samples from between-subject designs, an independent samples t-test is used. Both tests calculate a t-statistic based on the mean difference and standard error. Confidence intervals and effect sizes can also be calculated for paired and independent sample designs. Examples are provided to demonstrate how to perform the statistical tests and calculations.
Multiple Regression.ppt
This document discusses multiple regression analysis. It begins by introducing multiple regression as an extension of simple linear regression that allows for modeling relationships between a response variable and multiple explanatory variables. It then covers topics such as examining variable distributions, building regression models, estimating model parameters, and assessing overall model fit and significance of individual predictors. An example demonstrates using multiple regression to build a model for predicting cable television subscribers based on advertising rates, station power, number of local families, and number of competing stations.
Quality Engineering material
This document provides an overview of one-way analysis of variance (ANOVA). It begins by explaining the basic concepts and settings for ANOVA, including comparing population means across three or more groups. It then covers the hypotheses, ideas, assumptions, and calculations involved in one-way ANOVA. These include splitting total variability into parts between and within groups, computing an F-statistic to test if population means are equal, and potentially performing multiple comparisons between pairs of groups if the F-test is significant. Worked examples are provided to illustrate key ANOVA concepts and calculations.
Correlation and regression
This document provides an introduction to correlation and regression analysis. It defines correlation as a measure of the association between two variables and regression as using one variable to predict another. The key aspects covered are:
- Calculating correlation using Pearson's correlation coefficient r to measure the strength and direction of association between variables.
- Performing simple linear regression to find the "line of best fit" to predict a dependent variable from an independent variable.
- Using a TI-83 calculator to graphically display scatter plots of data and calculate the regression equation and correlation coefficient.
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
SWOT Analysis
HCS/499 Version 3
2
University of Phoenix Material
SWOT Analysis
Based on review of the performance analysis of Stevens District Hospital, consider what you perceive to be the strengths, weaknesses, opportunities and threats for this hospital.
· Strengths and weaknesses are traits internal to the hospital, i.e. strong physician loyalty to hospital, aging building, and availability of financial resources.
· Opportunities and threats are external to the hospital, such as a mall facility available for lease or a competitor hospital opening two physician practices in your market.
SWOT Analysis
Review the SWOT Analysis PowerPoint® prior to completing this assignment.
Based on the review of the Stevens District Hospital strategic planning scenario, conduct a SWOT analysis to generate a list of perceived strengths, weaknesses, opportunities, and threats for the hospital.
· Strengths and weaknesses are traits internal to the hospital (i.e., strong physician loyalty to hospital, aging building, and availability of financial resources).
· Opportunities and threats are external to the hospital, such as a mall facility available for lease or a competitor hospital opening two physician practices in your market.
Write a 700- to 1,050-word analysis that incorporates the key components of a SWOT analysis for the scenario described in Week One to generate a list of perceived strengths, weaknesses, opportunities, and threats. The analysis will include the following:
· Analyze the purpose of conducting the analysis in the context of the scenario.
· Analyze the limitations and advantages of conducting a SWOT analysis on your own (vs. with a group of stakeholders).
· Use the table provided to record your analysis of the information from the strategic planning scenario and generate two factors for each of the SWOT categories (strengths, weaknesses, opportunities, and threats).
Cite at least 1 peer-reviewed, scholarly, or similar references to support your assignment.
Click the Assignment Files tab to submit your assignment.
Table 1: SWOT Analysis
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived strength (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived strength (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived weakness (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived weakness (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived opportunity (external)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived opportunity (external)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived threat (external)
Analysis of existing informa ...
PSYC 354Homework 8Single-Sample T-TestWhen submitting th.docx
A homework assignment for PSYC 354 involves completing several statistical analyses and writing questions. The document provides instructions and data for completing single-sample t-tests, calculating percentiles and effect sizes, and hypothesis testing using z-tests. Students are asked to analyze provided data sets using SPSS and answer conceptual questions related to confidence intervals, statistical power, and descriptive statistics.
Elementary statistics for Food Indusrty
The document discusses elementary statistics and statistical methodology. It covers descriptive statistics topics like mean, median, mode, variance and standard deviation. It also covers inferential statistics topics like hypothesis testing, t-tests, z-tests, F-tests, ANOVA, correlation, and regression. Examples of applying statistical analyses in Excel are provided, including calculating confidence intervals and performing hypothesis tests to compare sample means.
1 Computer Assignment 3 --- Hypothesis tests about m.docx
1
Computer Assignment 3 --- Hypothesis tests about means
Statistics, Fall 2014, Singleton
Microsoft Excel has two data analysis tools that are very useful for hypothesis testing about
population means as done in the textbook, chapters 9 and 10. These are
1) t-Test: Two-Sample Assuming Equal Variances
2) t-Test: Two-Sample Assuming Unequal Variances
These tools utilize the two sets of equations in Chapter 10 of the text, namely (1) on page 368
assuming equal variances, and (2) on page 369 assuming unequal variances.
Number 1 tool (equal variances) is strictly for Chapter 10 problems with two samples, each
from its own population, and you are attempting to compare the two population means,
and by hypothesis tests involving .
Number 2 tool (unequal variances) can be used for Chapter 9 or Chapter 10 problems. In
previous online classes taught by Dr Revere, she had students use a combination of various Excel
functions to do Chapter 9 t-tests about . It seems to me that using the unequal-variance tool is
easier. On page 353 of the text there is an almost-correct description of how to use the Chapter-
10-style t-test for Chapter 9. In using a Chapter 10 test for Chapter 9, instead of comparing 2
sets of data, the second set of data is replaced with a fixed hypothesized value (which has zero
variation).
Steps are (for Ch 9 problems)
---Enter a column of your n values of experimental data to be tested.
---Enter another column of at least two of the hypothesized value being tested against (if the null
hypothesis has =1.84 or ≤1.84 or ≥1.84 enter at a column of at least two 1.84’s (contrary to
what the book says, you do not have to use n 1.84’s).
---With menus open the “t-Test: Two-Sample Assuming Unequal Variances” analysis tool.
---Select the “Variable 1 Range” to contain the experimental data.
---Select the “Variable 2 Range” to contain at least two identical values of the number in the
null hypothesis (see the example below which has 1.84). (The book says enter n of them.)
2
---Enter 0 for the “Hypothesized Mean Difference”
---Set the “Labels” checkbox using the rules you obeyed for data in Computer Assignment 1.
In many of the problems the data are set up NOT to use labels.
---Make sure you set “Alpha” to your specified value. Also typing it on the worksheet is helpful
as a reminder.
---The output is going to be compact and I suggest that you set “Output Range” to a cell near the
data.
---Click OK
When you do a Chapter 9 problem this way you are comparing your sample data, which has a
variance that is calculated by Excel, with your hypothesized value, which has a variance of zero
since you entered 2 or more identical values for it. Your “Hypothesized Mean Difference”
must always be zero. Of course this requires the “t-Test: Two-Sample Assuming Unequal
Variances” tool.
Why does this work?
If s22 and are both zero in the equat ...
elementary statistic
This document provides an overview of elementary statistics topics including descriptive statistics, inferential statistics, probability, different types of data and scales of measurement, common statistical tests like t-tests, z-tests, F-tests, chi-square tests, ANOVA, correlation, and regression. It also includes examples of how to calculate and interpret descriptive statistics like the mean, median, mode, variance, and standard deviation. Examples are provided on how to set up and conduct hypothesis tests using Excel.
Hypothesis Testing: Relationships (Compare 2+ Factors)
An extension on hypothesis testing, this lesson reviews the multiple regression and GLM as part of measuring statistical relationships.
Environmental Engineering Assignment Help
I am Simon M. I am an Environmental Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. in Environmental Engineering, Glasgow University, UK. I have been helping students with their assignments for the past 8 years. I solve assignments related to Environmental Engineering.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com. You can also call on +1 678 648 4277 for any assistance with Environmental Engineering Assignments.
Introduction to the t test
The document discusses the one-sample t-test and how it addresses limitations of the z-test. The t-test can be used to compare a sample mean to a population mean or hypothetical mean when the population standard deviation is unknown. It uses the sample standard deviation and degrees of freedom to calculate the t-statistic, which follows a t-distribution. The t-test procedure involves stating hypotheses, determining critical values, calculating statistics, and making conclusions, similar to the z-test. Effect sizes can also be measured.
Monte carlo analysis
This document discusses Monte Carlo simulation techniques for power analysis of circuits. It explains that Monte Carlo simulation requires a large number of input vectors to accurately estimate power dissipation. The key points are:
- Monte Carlo simulation collects switching activity from many input vectors to apply to a power model.
- More input vectors lead to higher accuracy but diminishing returns. There is a point where additional vectors do not meaningfully improve accuracy.
- Statistical techniques can determine the optimal number of vectors needed to estimate power within a given error tolerance with a specific confidence level, such as 90%. This avoids wasting computation on unnecessary vectors.
The Fair Market Value of Land andor Buildings Given as a Gift to Co.docx
The Fair Market Value of Land and/or Buildings Given as a Gift to Corporations by Communities as an Incentive to Locate in their Area is called _ _ _ by Accountants.
A.
Relocation Incentives
B.
Donated
Capital
C.
A Freebie
D.
A Free Good
.
The essay will be a sociological explanation of a specific aspec.docx
The essay will be
a sociological explanation of a specific aspect of urban life. Students, for example, can focus on urban dependence on mass transit, or unbearable congestion, excessive trash, physical buildings and social interaction, flooding or drought, sustainability or green technologies, immigrant labor, or parks/green spaces. Both the picture collage and the essay should be provocative; this work should solicit a reaction so they need to be creative.
Format, each picture essay should be delivered in two parts:
1 poster size collage of a minimum of 5 photos
1 4pp essay (hint: 3 questions, each should probably be 1pp - add cites if you use ideas from other authors or statistics from official/newspaper sources) (cites can be on an additional page - Use APA style)
Each essay will cover three essential questions:
1. Why is this aspect of the urban experience important and how does it affect the urban experience?
2. Currently, what is the state of the profound aspect of urban life? Provide an overview of the condition with statistics from official sources or ones gleaned from newspaper articles, etc.
3. In light of the profound aspect of the urban experience that you chose, what should be done? Use lessons from the course to offer well thought out advice on new directions.
***i chose
excessive trash*** its 4 pages.
.
More Related Content
Similar to Power AnalysisThis is a three-part assignment in which you w
Mva 06 principal_component_analysis_2010_11
Principal component analysis (PCA) is a technique used to reduce the dimensionality of large data sets by transforming correlated variables into a smaller number of uncorrelated variables called principal components. PCA identifies patterns in data and expresses the data in such a way as to highlight their similarities and differences. The main goals of PCA are data reduction and interpretation. It works by identifying the directions (principal components) along which the variation in the data is maximized.
1 P a g e ME 350 Project 2 Posted February 26.docx
1 | P a g e
ME 350 Project 2
Posted February 26, 2019, Due March 5 2019
Higher level tools for roots of f(x) = 0 problems
Q. 1. The velocity of a falling parachutist is given by the following formula:
1
Where g=9.81 m/s2, the drag coefficient c=13.5 kg/s.
Compute the mass (m) of the parachutist so that v = 40.7 m/s when t = 12.8 s
Hint. This is an f(x) = 0 type problem, with corresponding variables v(m) = 0
(a) Rearrange the terms and write a simple m-file, then use this file to use a
regular plot command to locate the approximate root. Submit the m-file and
the corresponding plot. Here you will need to experiment with a range of
values of ‘m’ .
(b) Modify the m-file from (a) into a function file that can be used with the
fzero function to compute a refined root. Submit your function and the
solution it displays in the MATLAB command window.
Q.2. Consider the square cross section beam anchored on one end and supporting a
500 lb weight. Other details are shown in figure below. Ref. Musto ch. 6. This
exercise will help you review methods for solving f(x) = 0 problems.
According to strength of materials principles, the maximum bending stress
experienced by the cantilever beam shown above is:
2 | P a g e
σ = 335,000/x3 + 92,600/x (1)
This reflects the suspended weight, the specific weight (weight per unit length),
and the length of the beam. From materials science, the maximum allowable stress
(i.e. limiting stress before the onset of yielding) for the beam material is 17,750
psi. We now need to determine the minimum dimension ‘x’ in inches that will satisfy
this stress constraint. Solve this problem using four different techniques as
itemized below.
Hint: The solution approaches involve solving a problem of the form: f(x) = 0
a) Rewrite equation 1 in polynomial form in descending coefficients of the
powers of x then use the built-in MATLAB function roots to compute the
representative solution.
b) Rewrite equation 1 into a MATLAB function file (beam2b.m) which can be
used by MATLAB’s fzero function. Use the fzero function to compute the
solution for this problem, using an initial guess of 43.
c) Rationalize the denominators of beam2b.m to generate a more standard
polynomial form and name it beam2c.m . Use fplot to generate a plot of
the function in the range -5≤x≤15; insert grid lines to spot the
approximate location of the real root. Use the fzero function to compute
the solution for this problem using and initial guess of -125. Submit the
function file, the plot and the solution computed using fzero.
d) Refer to the plot from (c). Use the bisectrr function to compute a root for
this function in the interval -5≤x≤5.
i. Comment on the outcome of the attempt in (d).
ii. Select an alternative range that would yield the root for this
function. What is the solution?
3 | P a g e
Q.3. In designing a spherical tank whose schematic i.
Suggest one psychological research question that could be answered.docx
Suggest one psychological research question that could be answered by each of the following types of statistical tests:
z test
t test for independent samples, and
t test for dependent samples
FINAL EXAM
STAT 5201
Fall 2016
Due on the class Moodle site or in Room 313 Ford Hall
on Tuesday, December 20 at 11:00 AM
In the second case please deliver to the office staff
of the School of Statistics
READ BEFORE STARTING
You must work alone and may discuss these questions only with the TA or Glen Meeden. You
may use the class notes, the text and any other sources of printed material.
Put each answer on a single sheet of paper. You may use both sides and additional sheets if
needed. Number the question and put your name on each sheet.
If I discover a misprint or error in a question I will post a correction on the class web page. In
case you think you have found an error you should check the class home page before contacting us.
1
1. Find a recent survey reported in a newspaper, magazine or on the web. Briefly describe
the survey. What are the target population and sampled population? What conclusions are drawn
from the survey in the article. Do you think these conclusions are justified? What are the possible
sources of bias in the survey? Please be brief.
2. In a small country a governmental department is interested in getting a sample of school
children from grades three through six. Because of a shortage of buildings many of the schools had
two shifts. That is one group of students came in the morning and a different group came in the
afternoon. The department has a list of all the schools in the country and knows which schools
have two shifts of students and which do not. Devise a sampling plan for selecting the students to
appear in the sample.
3. For some population of size N and some fixed sampling design let π1 be the inclusion
probability for unit i. Assume a sample of size n was used to select a sample.
i) If unit i appears in the sample what is the weight we associate with it?
ii) Suppose the population can be partitioned into four disjoint groups or categories. Let Nj be
the size of the j’th category. For this part of the problem we assume that the Nj’s are not known.
Assume that for units in category j there is a constant probability, say γi that they will respond if
selected in the sample. These γj’s are unknown. Suppose in our sample we see nj units in category
j and 0 < rj ≤ nj respond. Note n1 + n2 + n3 + n4 = n. In this case how much weight should be
assigned to a responder in category j.
iii) Answer the same question in part ii) but now assume that the Nj’s are known.
iv) Instead of categories suppose that there is a real valued auxiliary variable, say age, attached
to each unit and it is known that the probability of response depends on age. That is units of
a similar age have a similar probability of responding when selected in the sample. Very briefly
explain how you would assign adjusted weights o ...
Memorization of Various Calculator shortcuts
The document provides guidance on using statistical functions on the TI-83/84 calculator. It discusses how to input data into lists, calculate descriptive statistics, create graphs, and perform probability, confidence interval, and hypothesis tests. For descriptive statistics, the user selects STAT > CALC > 1-Var Stats and inputs the appropriate data list. Graphs are made by selecting 2nd STAT PLOT and choosing the desired plot type and lists. Probability, interval, and hypothesis tests are accessed through the TESTS and TESTS menus and require selecting the appropriate function and inputting parameters like sample sizes, means, and standard deviations.
Correlation
The document discusses correlation, regression, and hypothesis testing involving two variables. It defines correlation and the correlation coefficient r, which measures the strength of a linear relationship between two variables. Regression analyzes the relationship between variables to determine if it is positive/negative and linear/nonlinear. Hypothesis tests using r evaluate whether a linear correlation exists between two variables in a population. Confidence intervals and predictions can be made from significant relationships.
Hypothesis testing - II.pptx
trdhgjhgfgcvbvhhgjghbntewghbnmbnbnbjhguyghjbnuyyuyfgbnbjhbhgbbhuiyti7rjfhgvhgrrtfgfugiuyuyjuiyyjhyt76yttyyupiuiojoioii0909ooeoreferfergergferfewfwefwef2d33rf34
Chapter11
The document discusses hypothesis testing methods for comparing two population or treatment means. It covers notation, sampling distributions, large sample hypothesis testing, confidence intervals, and paired t-tests. An example compares the mean fill volumes of two beer can filling machines and constructs a 98% confidence interval for the difference in tensile strengths of two thread types.
Two Sample Tests
This document summarizes statistical tests for comparing two samples, including paired and independent samples t-tests, confidence intervals, and effect sizes. For paired samples from within-subject designs, a paired t-test is used to test for differences between means. For independent samples from between-subject designs, an independent samples t-test is used. Both tests calculate a t-statistic based on the mean difference and standard error. Confidence intervals and effect sizes can also be calculated for paired and independent sample designs. Examples are provided to demonstrate how to perform the statistical tests and calculations.
Multiple Regression.ppt
This document discusses multiple regression analysis. It begins by introducing multiple regression as an extension of simple linear regression that allows for modeling relationships between a response variable and multiple explanatory variables. It then covers topics such as examining variable distributions, building regression models, estimating model parameters, and assessing overall model fit and significance of individual predictors. An example demonstrates using multiple regression to build a model for predicting cable television subscribers based on advertising rates, station power, number of local families, and number of competing stations.
Quality Engineering material
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SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
SWOT Analysis
HCS/499 Version 3
2
University of Phoenix Material
SWOT Analysis
Based on review of the performance analysis of Stevens District Hospital, consider what you perceive to be the strengths, weaknesses, opportunities and threats for this hospital.
· Strengths and weaknesses are traits internal to the hospital, i.e. strong physician loyalty to hospital, aging building, and availability of financial resources.
· Opportunities and threats are external to the hospital, such as a mall facility available for lease or a competitor hospital opening two physician practices in your market.
SWOT Analysis
Review the SWOT Analysis PowerPoint® prior to completing this assignment.
Based on the review of the Stevens District Hospital strategic planning scenario, conduct a SWOT analysis to generate a list of perceived strengths, weaknesses, opportunities, and threats for the hospital.
· Strengths and weaknesses are traits internal to the hospital (i.e., strong physician loyalty to hospital, aging building, and availability of financial resources).
· Opportunities and threats are external to the hospital, such as a mall facility available for lease or a competitor hospital opening two physician practices in your market.
Write a 700- to 1,050-word analysis that incorporates the key components of a SWOT analysis for the scenario described in Week One to generate a list of perceived strengths, weaknesses, opportunities, and threats. The analysis will include the following:
· Analyze the purpose of conducting the analysis in the context of the scenario.
· Analyze the limitations and advantages of conducting a SWOT analysis on your own (vs. with a group of stakeholders).
· Use the table provided to record your analysis of the information from the strategic planning scenario and generate two factors for each of the SWOT categories (strengths, weaknesses, opportunities, and threats).
Cite at least 1 peer-reviewed, scholarly, or similar references to support your assignment.
Click the Assignment Files tab to submit your assignment.
Table 1: SWOT Analysis
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived strength (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived strength (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived weakness (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived weakness (internal)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived opportunity (external)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived opportunity (external)
Analysis of existing information from Stevens District Hospital strategic planning scenario
Perceived threat (external)
Analysis of existing informa ...
PSYC 354Homework 8Single-Sample T-TestWhen submitting th.docx
A homework assignment for PSYC 354 involves completing several statistical analyses and writing questions. The document provides instructions and data for completing single-sample t-tests, calculating percentiles and effect sizes, and hypothesis testing using z-tests. Students are asked to analyze provided data sets using SPSS and answer conceptual questions related to confidence intervals, statistical power, and descriptive statistics.
Elementary statistics for Food Indusrty
The document discusses elementary statistics and statistical methodology. It covers descriptive statistics topics like mean, median, mode, variance and standard deviation. It also covers inferential statistics topics like hypothesis testing, t-tests, z-tests, F-tests, ANOVA, correlation, and regression. Examples of applying statistical analyses in Excel are provided, including calculating confidence intervals and performing hypothesis tests to compare sample means.
1 Computer Assignment 3 --- Hypothesis tests about m.docx
1
Computer Assignment 3 --- Hypothesis tests about means
Statistics, Fall 2014, Singleton
Microsoft Excel has two data analysis tools that are very useful for hypothesis testing about
population means as done in the textbook, chapters 9 and 10. These are
1) t-Test: Two-Sample Assuming Equal Variances
2) t-Test: Two-Sample Assuming Unequal Variances
These tools utilize the two sets of equations in Chapter 10 of the text, namely (1) on page 368
assuming equal variances, and (2) on page 369 assuming unequal variances.
Number 1 tool (equal variances) is strictly for Chapter 10 problems with two samples, each
from its own population, and you are attempting to compare the two population means,
and by hypothesis tests involving .
Number 2 tool (unequal variances) can be used for Chapter 9 or Chapter 10 problems. In
previous online classes taught by Dr Revere, she had students use a combination of various Excel
functions to do Chapter 9 t-tests about . It seems to me that using the unequal-variance tool is
easier. On page 353 of the text there is an almost-correct description of how to use the Chapter-
10-style t-test for Chapter 9. In using a Chapter 10 test for Chapter 9, instead of comparing 2
sets of data, the second set of data is replaced with a fixed hypothesized value (which has zero
variation).
Steps are (for Ch 9 problems)
---Enter a column of your n values of experimental data to be tested.
---Enter another column of at least two of the hypothesized value being tested against (if the null
hypothesis has =1.84 or ≤1.84 or ≥1.84 enter at a column of at least two 1.84’s (contrary to
what the book says, you do not have to use n 1.84’s).
---With menus open the “t-Test: Two-Sample Assuming Unequal Variances” analysis tool.
---Select the “Variable 1 Range” to contain the experimental data.
---Select the “Variable 2 Range” to contain at least two identical values of the number in the
null hypothesis (see the example below which has 1.84). (The book says enter n of them.)
2
---Enter 0 for the “Hypothesized Mean Difference”
---Set the “Labels” checkbox using the rules you obeyed for data in Computer Assignment 1.
In many of the problems the data are set up NOT to use labels.
---Make sure you set “Alpha” to your specified value. Also typing it on the worksheet is helpful
as a reminder.
---The output is going to be compact and I suggest that you set “Output Range” to a cell near the
data.
---Click OK
When you do a Chapter 9 problem this way you are comparing your sample data, which has a
variance that is calculated by Excel, with your hypothesized value, which has a variance of zero
since you entered 2 or more identical values for it. Your “Hypothesized Mean Difference”
must always be zero. Of course this requires the “t-Test: Two-Sample Assuming Unequal
Variances” tool.
Why does this work?
If s22 and are both zero in the equat ...
elementary statistic
This document provides an overview of elementary statistics topics including descriptive statistics, inferential statistics, probability, different types of data and scales of measurement, common statistical tests like t-tests, z-tests, F-tests, chi-square tests, ANOVA, correlation, and regression. It also includes examples of how to calculate and interpret descriptive statistics like the mean, median, mode, variance, and standard deviation. Examples are provided on how to set up and conduct hypothesis tests using Excel.
Hypothesis Testing: Relationships (Compare 2+ Factors)
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Environmental Engineering Assignment Help
I am Simon M. I am an Environmental Engineering Assignment Expert at matlabassignmentexperts.com. I hold a Ph.D. in Environmental Engineering, Glasgow University, UK. I have been helping students with their assignments for the past 8 years. I solve assignments related to Environmental Engineering.
Visit matlabassignmentexperts.com or email info@matlabassignmentexperts.com. You can also call on +1 678 648 4277 for any assistance with Environmental Engineering Assignments.
Introduction to the t test
The document discusses the one-sample t-test and how it addresses limitations of the z-test. The t-test can be used to compare a sample mean to a population mean or hypothetical mean when the population standard deviation is unknown. It uses the sample standard deviation and degrees of freedom to calculate the t-statistic, which follows a t-distribution. The t-test procedure involves stating hypotheses, determining critical values, calculating statistics, and making conclusions, similar to the z-test. Effect sizes can also be measured.
Monte carlo analysis
This document discusses Monte Carlo simulation techniques for power analysis of circuits. It explains that Monte Carlo simulation requires a large number of input vectors to accurately estimate power dissipation. The key points are:
- Monte Carlo simulation collects switching activity from many input vectors to apply to a power model.
- More input vectors lead to higher accuracy but diminishing returns. There is a point where additional vectors do not meaningfully improve accuracy.
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Similar to Power AnalysisThis is a three-part assignment in which you w (20)
1 P a g e ME 350 Project 2 Posted February 26.docx
1 P a g e ME 350 Project 2 Posted February 26.docx
Suggest one psychological research question that could be answered.docx
Suggest one psychological research question that could be answered.docx
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
SWOT AnalysisHCS499 Version 32University of Phoenix Mater.docx
PSYC 354Homework 8Single-Sample T-TestWhen submitting th.docx
PSYC 354Homework 8Single-Sample T-TestWhen submitting th.docx
1 Computer Assignment 3 --- Hypothesis tests about m.docx
1 Computer Assignment 3 --- Hypothesis tests about m.docx
Hypothesis Testing: Relationships (Compare 2+ Factors)
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Denis is a dynamic and results-driven Chief Information Officer (CIO) with a distinguished career spanning information systems analysis and technical project management. With a proven track record of spearheading the design and delivery of cutting-edge Information Management solutions, he has consistently elevated business operations, streamlined reporting functions, and maximized process efficiency.
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His expertise extends across a diverse spectrum of reporting, database, and web development applications, underpinned by an exceptional grasp of data storage and virtualization technologies. His proficiency in application testing, database administration, and data cleansing ensures seamless execution of complex projects.
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Date: May 29, 2024
Tags: Information Security, ISO/IEC 27001, ISO/IEC 42001, Artificial Intelligence, GDPR
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This will be used as part of your Personal Professional Portfolio once graded.
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- 5. Tails(s) = Two. Effect size d = Cohen's d obtained from Section 1 above (using either s 1 or s 2). α err prob = standard alpha level. Sample size group 1 = n 1 from Section 1 above. Sample size group 2 = n 2 from Section 1 above. Click Calculate . Provide a screenshot of your G*Power output. Report the observed power of this post hoc power analysis. Interpret the level of power in terms of rejecting a null hypothesis. Do you have sufficient power to reject a false null hypothesis? Interpret power in terms of committing a Type II error. Section 3: A Priori Power Analysis
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- 7. d effect size value obtained in Section 1 and set it to .50 (conventional "medium" effect size). Click Calculate . How many total subjects ( N) are needed to obtain a power of .80? Compare and contrast these two estimated N s. In conclusion, reflect on the importance of conducting an a priori power analysis in psychological research plans.