One Sample Hypothesis Tips
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The document outlines the general procedure for hypothesis testing, including defining the null and alternative hypotheses, calculating the test statistic, and making a decision based on significance levels and critical values. It then provides an example case study analyzing factors that may influence food servers' tips, such as day of week, party size, gender, and time of shift. Two hypothesis tests are conducted. The first finds Saturday and Sunday are the best days for tips. The second finds that larger parties tip better than smaller parties, on average. Based on the results, the recommendation is to schedule food servers on a rotating basis across days and shifts to ensure fair treatment.
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![General Procedure for Hypothesis Testing ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]](data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7)
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One Sample Hypothesis Tips
The document outlines the general procedure for hypothesis testing, including defining the null and alternative hypotheses, calculating test statistics, and making decisions based on significance levels and critical values. It then describes a case study analyzing factors that may influence food servers' tips, such as day of week, party size, gender, and time of day. Two hypothesis tests are presented, finding that Saturdays and Sundays have the best tips, and larger parties tip more on average than smaller parties. The conclusion recommends scheduling servers on alternating weekdays and shifts to avoid unfair treatment.
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1) The document describes the general procedure for hypothesis testing which includes defining the null and alternative hypotheses, calculating the test statistic, and making a decision by comparing the test statistic to critical values.
2) It then provides an example case study analyzing data from a restaurant server's tips to make recommendations to avoid unfair treatment of servers. Key findings include that Saturdays and Sundays have the best tips while smaller parties do not tip better than average.
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The document outlines the general procedure for hypothesis testing, including defining the null and alternative hypotheses, calculating test statistics, and making decisions based on significance levels and critical values. It then describes a case study analyzing factors that may influence food servers' tips, such as day of week, party size, gender, and time of day. Two hypothesis tests are presented, finding that Saturdays and Sundays have the best tips, and larger parties tip more on average than smaller parties. The conclusion recommends scheduling servers on alternating weekdays and shifts to avoid unfair treatment.
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One Sample Hypothesis Tips
The document outlines the general procedure for hypothesis testing, including defining the null and alternative hypotheses, calculating test statistics, and making decisions based on significance levels and critical values. It then describes a case study analyzing factors that may influence food servers' tips, such as day of week, party size, gender, and time of day. Two hypothesis tests are presented, finding that Saturdays and Sundays have the best tips, and larger parties tip more on average than smaller parties. The conclusion recommends scheduling servers on alternating weekdays and shifts to avoid unfair treatment.
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1) The document describes the general procedure for hypothesis testing which includes defining the null and alternative hypotheses, calculating the test statistic, and making a decision by comparing the test statistic to critical values.
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[DataSet1] \\Client\C$\Users\lauren.hazeltine\Downloads\Drinks.sav
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Price per 6-pack
35
1.59
7.19
3.0274
1.12343
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27
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35
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See next slide for how to select
State your research hypothesis and your null hypothesis
State them in English
Then in math
Describe the NULL distribution
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Compute the relevant standard error
Determine your critical value(s)
Keep in mind whether it is a directional or non-directional test
Compute the test statistic
Compare the test stat to the critical value(s) and make your decision
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All of these tests require that the measures be quantitative variables, that is interval/ratio
(Not all quantitative variables are normal, BUT all normal variables are quantitative. So if someone tells you a variable is normal, you know it is also quantitative.)
When to use each test, cont’d
1 Sample z-test
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And you do know σ (population SD)
2 sample z-test
Comparing two sample means to each other
And you do know σM1-M2 (standard error of difference of means)
1 sample t-test
Comparing one sample mean to a population mean
You only know s (sample SD)
2 sample t-test
Comparing two sample means to each other
You only know s1 and s2 (sample SDs)
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Compute the differences between the two scores, then treat like a 1 sample t
What is α?
Put on your skeptic’s hat: you believe the null hypothesis is true
But you’re willing to be convinced you’re wrong
If the test statistic is sufficiently improbable, you will change your mind and decide the null hypothesis is false
What is “sufficiently” improbable?
When your test statistic is more extreme than your critical values
Critical values are selected so that only a small fraction of the entire distribution is more extreme than the critical values
This “small fraction” is called α
Conventionally, α is usually set to .05, that is 5%
Directionality of a test
Is a test simply about whether there a difference, regardless of direction?
If so, it is a non-directed, or undirected, or two-tailed test
Your α must be evenly split between the two tails
For the conventional α = .05, that means each tail should have .025 or 2.5% of the total distribution
Is the test predicting one mean will be bigger than another? Or is it predicting one mean will be less than another?
If so, it a directional, or directed, or one-tailed test
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Special note on one-tailed tests
Step 3 of our procedure is a little awkward when we have one-tailed tests
How do you descr.
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Can descriptive statistical processes be used in determining relationships, differences, or effects in your research question and testable null hypothesis? Why or why not? Also, address the value of descriptive statistics for the forensic psychology research problem that you have identified for your course project. read an article for additional information on descriptive statistics and pictorial data presentations.
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Introduction
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Ordinal Data
In terms of ordinal data, the variables contained within the measurement instrument are ranked in order of importance. For example, a product-marketing specialist might be interested in how a consumer group would respond to a new product. To garner the information, the questionnaire administered to a group of consumers would include questions scaled as follows: 1 = Not Likely, 2 = Somewhat Likely, 3 = Likely, 4 = More Than Likely, and 5 = Most Likely. This creates a scale rank order from Not Likely to Most Likely with respect to acceptance of the new consumer product.
Interval Data
Oftentimes, in addition to being ordered, the differences (or intervals) between two adjacent measurement values on a measurement scale are identical. For example, the di ...
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www.gpowertools.com
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Introduction
Understanding and interpreting data is a vital component to a learner’s research as it reflects the study results. Properly analyzing the data is also crucial as this portrays the outcomes and delivers research findings which is the purpose of completing the study initially. Once data is extracted and analyzed, further development of the topic is discussed and shared allowing for a deeper sense of knowledge of the included variable, perceptions, and anything discovered throughout the study. Astroth and Chung (2018) discussed the importance of reviewing quantitative research studies highlighting the importance of ensuring the results are presenting and interpreted correctly. This article is geared towards nurses as they utilize evidence-based practices throughout many health care settings therefore properly analyzing data and accurately reporting results is critical in the potential care provided. For the purpose of this paper, the learner completed the assigned tasks of Module 2 Problem set which is provided below.
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1. Create standardized scores for all scale variables (price through alcohol).
[DataSet1] \\Client\C$\Users\lauren.hazeltine\Downloads\Drinks.sav
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Price per 6-pack
35
1.59
7.19
3.0274
1.12343
Cost per 12 Fluid Ounces
35
.27
1.20
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35
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175
139.77
24.447
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35
6
27
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2.30
5.50
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35
a. Which beverages have positive standardized scores on every variable?
· The beverages including each variable with positive standardized scores includes UA, UH, UL, UR, and SA.
b. What does this mean?
· Based on the raw data, these beverages are at or above the mean average or group mean
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a.
Variable
Product
Z-Score
price
SA
3.70524
cost
SA
3.70636
calories
UNR
-2.93581
sodium
PF & PJ
2.00859
alcohol
UNR
-3.77651
b.
cost
SA
3.70636
3. What beverage is most typical of all beverages, that is, has z-score values closest to 0 for these variables?
a. The most common beverage is UIR having the closest z-score value to 0.
4. (a) If the variable is normally distributed, what percentage of cases should be above 1 standard deviation from the mean or below 1 standard deviation from the mean?
a. 68%
(b) Calculate this percentage for a couple of the variables. Is the percentage of beverages with an absolute z-score above 1 close to the theoretical value?
b. Upon running calculations for some of the variables, the percentages were above 1 with an absolute z-score and cl ...
Steps of hypothesis testingSelect the appropriate testSo far.docx
Steps of hypothesis testing
Select the appropriate test
So far we’ve learned a couple variation on z- and t-tests
See next slide for how to select
State your research hypothesis and your null hypothesis
State them in English
Then in math
Describe the NULL distribution
Starting here is where you be a skeptic and assume the null is true!
For one-sample tests, you will need to determine μ
(For two-tailed tests, you don’t need to worry about μ)
Compute the relevant standard error
Determine your critical value(s)
Keep in mind whether it is a directional or non-directional test
Compute the test statistic
Compare the test stat to the critical value(s) and make your decision
When to use each test
All of these tests require that the sampling distribution is normal
Either because population is normal or, thanks to central limit theorem, sample size is very large
All of these tests require that the measures be quantitative variables, that is interval/ratio
(Not all quantitative variables are normal, BUT all normal variables are quantitative. So if someone tells you a variable is normal, you know it is also quantitative.)
When to use each test, cont’d
1 Sample z-test
Comparing one sample mean to a population mean
And you do know σ (population SD)
2 sample z-test
Comparing two sample means to each other
And you do know σM1-M2 (standard error of difference of means)
1 sample t-test
Comparing one sample mean to a population mean
You only know s (sample SD)
2 sample t-test
Comparing two sample means to each other
You only know s1 and s2 (sample SDs)
Dependent sample t-test
You have two scores coming from each person, such as if you measured them before and after an experimental manipulation.
Compute the differences between the two scores, then treat like a 1 sample t
What is α?
Put on your skeptic’s hat: you believe the null hypothesis is true
But you’re willing to be convinced you’re wrong
If the test statistic is sufficiently improbable, you will change your mind and decide the null hypothesis is false
What is “sufficiently” improbable?
When your test statistic is more extreme than your critical values
Critical values are selected so that only a small fraction of the entire distribution is more extreme than the critical values
This “small fraction” is called α
Conventionally, α is usually set to .05, that is 5%
Directionality of a test
Is a test simply about whether there a difference, regardless of direction?
If so, it is a non-directed, or undirected, or two-tailed test
Your α must be evenly split between the two tails
For the conventional α = .05, that means each tail should have .025 or 2.5% of the total distribution
Is the test predicting one mean will be bigger than another? Or is it predicting one mean will be less than another?
If so, it a directional, or directed, or one-tailed test
Put all your α in a single tail
Special note on one-tailed tests
Step 3 of our procedure is a little awkward when we have one-tailed tests
How do you descr.
To p or not to p
This document discusses the appropriate use and interpretation of p-values. It defines what a p-value represents and outlines some common misuses, such as using p-values to describe the strength of an effect or double dipping in the data. Alternative approaches like confidence intervals and effect sizes are presented that provide more meaningful information about study results than p-values alone. Examples from clinical studies are provided where p-values were inappropriately emphasized over other important results.
Chi square test
The document discusses the chi-square test, which is used to determine if an observed frequency distribution differs from an expected theoretical distribution. It can be used as a test of independence to determine if two variables are associated, and as a test of goodness of fit to assess how well an expected distribution fits observed data. The steps of the chi-square test are outlined, including calculating the test statistic, determining degrees of freedom, and comparing the statistic to critical values to determine if the null hypothesis can be rejected. An example of a chi-square test of independence is shown to test if perceptions of fairness of performance evaluation methods are independent of each other.
2019 PMED Spring Course - SMARTs-Part I - Eric Laber, April 3, 2019
2019 PMED Spring Course - SMARTs-Part I - Eric Laber, April 3, 2019The Statistical and Applied Mathematical Sciences Institute
• Rationale and building blocks for a SMART
• Example SMARTs
• Primary analyses and power analyses
• Extensions and special topicsStatistical Analysis
is a lecture presentation covering various aspects of statistical analysis in research. It includes a case study on Barack Obama's 2008 homepage, focusing on multivariate testing to measure conversion rates of different homepage configurations. The lecture discusses statistical tests, the concept of a null hypothesis, p-values, and the chi-square (χ²) test. It also covers normal and binomial distributions, contingency tables, expected values, and how to compute and interpret χ² values. Python code for statistical analysis, particularly using the SciPy library, is also presented, demonstrating how to perform chi-square and t-tests in Python. This material is likely used in an educational setting, focusing on applying statistical methods in practical scenarios.
All content within this presentation is the property of Royal Holloway, University of London. Unauthorized use, duplication, or distribution of the materials contained herein is strictly prohibited.
T test
This document provides an overview of a presentation on statistical hypothesis testing using the t-test. It discusses what a t-test is, how to perform a t-test, and provides an example of a t-test comparing spelling test scores of two groups that received different teaching strategies. The document outlines the six steps for conducting statistical hypothesis testing using a t-test: 1) stating the hypotheses, 2) choosing the significance level, 3) determining the critical values, 4) calculating the test statistic, 5) comparing the test statistic to the critical values, and 6) writing a conclusion.
Statistical ProcessesCan descriptive statistical processes b.docx
Statistical Processes
Can descriptive statistical processes be used in determining relationships, differences, or effects in your research question and testable null hypothesis? Why or why not? Also, address the value of descriptive statistics for the forensic psychology research problem that you have identified for your course project. read an article for additional information on descriptive statistics and pictorial data presentations.
300 words APA rules for attributing sources.
Computing Descriptive Statistics
Computing Descriptive Statistics: “Ever Wonder What Secrets They Hold?” The Mean, Mode, Median, Variability, and Standard Deviation
Introduction
Before gaining an appreciation for the value of descriptive statistics in behavioral science environments, one must first become familiar with the type of measurement data these statistical processes use. Knowing the types of measurement data will aid the decision maker in making sure that the chosen statistical method will, indeed, produce the results needed and expected. Using the wrong type of measurement data with a selected statistic tool will result in erroneous results, errors, and ineffective decision making.
Measurement, or numerical, data is divided into four types: nominal, ordinal, interval, and ratio. The businessperson, because of administering questionnaires, taking polls, conducting surveys, administering tests, and counting events, products, and a host of other numerical data instrumentations, garners all the numerical values associated with these four types.
Nominal Data
Nominal data is the simplest of all four forms of numerical data. The mathematical values are assigned to that which is being assessed simply by arbitrarily assigning numerical values to a characteristic, event, occasion, or phenomenon. For example, a human resources (HR) manager wishes to determine the differences in leadership styles between managers who are at different geographical regions. To compute the differences, the HR manager might assign the following values: 1 = West, 2 = Midwest, 3 = North, and so on. The numerical values are not descriptive of anything other than the location and are not indicative of quantity.
Ordinal Data
In terms of ordinal data, the variables contained within the measurement instrument are ranked in order of importance. For example, a product-marketing specialist might be interested in how a consumer group would respond to a new product. To garner the information, the questionnaire administered to a group of consumers would include questions scaled as follows: 1 = Not Likely, 2 = Somewhat Likely, 3 = Likely, 4 = More Than Likely, and 5 = Most Likely. This creates a scale rank order from Not Likely to Most Likely with respect to acceptance of the new consumer product.
Interval Data
Oftentimes, in addition to being ordered, the differences (or intervals) between two adjacent measurement values on a measurement scale are identical. For example, the di ...
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