Mathematics - Statistics Practice Homework

Module 3 Practice Homework Workbook

Your Name:

Purpose

This assignment is intended to help you learn to do the following:

· Explain the conditions for conducting a one-way analysis of variance with independent groups.

· Evaluate the assumptions for a one-way analysis of variance with independent groups.

· Interpret the results of the omnibus F test in ANOVA.

· Compute and interpret post hoc comparisons following a significant ANOVA result.

· Compute and interpret measures of effect size.

· Determine the minimum sample size for a one-way ANOVA.

Overview

This assignment requires you to apply the knowledge and skills you gained from the content of Module 3. In particular, the assignment is meant to allow you to practice your competencies in performing a one-way analysis of variance to test hypotheses about population means. The focus is on formulating appropriate null and alternative hypotheses, conducting the omnibus F test, interpreting measures of effect size, and performing post hoc comparisons. You will also determine the minimum sample size for a one-way ANOVA given various effect sizes. You are required to complete the following tasks:

Problem Set Up

· Explore the distribution of the job satisfaction measure separately for respondents from each sector

· Determine the minimum sample size required to detect effects of given sizes

· Evaluate the Research Question:

· State the null & alternative hypotheses

· State the decision rule for the test

· Evaluate the assumptions for the test

· Conduct the omnibus F test & interpret the result

· Calculate eta-squared & interpret it

· Describe the limitations inherent in this analysis

Report

· Write a report in APA format summarizing the results of the analysis.

Reflection

· Reflect on your experience working on this assignment.

Please review the grading rubric in Canvas before you begin so you have a clear idea of the expectations for your work.

Preparation

Begin by completing the following tasks:

· Read through this instruction sheet to get an overview of the assignment. There are helpful resources provided at the end of the document that can be used for additional support.

· Review the dataset and scenario document in Canvas. These are the same as for the last assignment.

· Import the data into your preferred analysis software. Remember that you are not permitted to have AI generate visualizations, statistics, interpretations or any text for the report.

Problem Set Up

Variables

For this assignment, we will focus on the following variables. You might want to review the variable type (categorical or quantitative) and scale of measurement for each.

· Sector

· JobSatis

Note: Be sure to use the cleansed data from Module 1 for these analyses.

Explore the Distribution

We are focusing on job satisfaction separately for the five sectors. Start by creating a boxplot for job satisfaction with separate plots for each sector on the same graph. Copy and paste the visualizations in the box below, and comment on the trends you observe.

In the next step, use statistical software to calculate descriptive statistics for job satisfaction separately for each sector. Include the most appropriate measure of central tendency and variability as well as statistics showing other qualities of each distribution. Copy and paste the results from software below, and comment on the trends you observe.

Research Question: Does the level of perceived job satisfaction differ for the five sectors?

Review the Power Analysis Results

Before you conduct a research study, it’s wise to do a power analysis. The purpose of this analysis is to determine the minimum sample size required to detect an effect. Review this video for an overview of the analysis: Power Analysis Explained

To run the analysis, I used G*Power, a free tool for that’s available for this purpose. I ran it four times entering different values for the effect size and level of power. The effect sizes are based on Cohen, 1992. Review the results below:

Minimum Sample Size Required for a One-Way Independent Samples ANOVA with 5 Groups for Various Effect Sizes and Levels of Power

	Model 1	Model 2	Model 3	Model 4
alpha level	.05	.05	.05	.05
Effect size	Medium .25	Medium .25	Large .40	Large .40
Power (1-β)	.8	.9	.8	.9
Minimum Total Sample Size	200	255	80	105

How does the minimum total sample size change as the effect size increases? How does the minimum total sample size change as the power level increases? Provide your response in the box below.

Fortunately, for this scenario, we have a sufficiently large sample. What would be the potential risks if our sample was smaller than the recommended minimum? Provide your response in the box below.

Run a One-Way ANOVA

Next, you will conduct a one-way ANOVA to address the research question. Specify the null and alternative hypotheses for this test in the box below.

Why is a one-way ANOVA better than conducting multiple t-tests? Provide your answer below.

If you use α = .05, what will be your decision rule for this test? Describe the specific circumstances in which you will reject the null hypothesis in the box below.

Before you proceed with the test, you need to determine if the assumptions have been met. In the box below, list the test assumptions and explain how you determined if they have or have not been met. Include test statistics when appropriate.

Assumption	How did you test the assumption? What did you conclude from the test?

Use statistical software to run the ANOVA and paste the results in the box below. What decision do you make about the null hypothesis? What does the decision mean in terms of the Research Question? Why did you make this decision?

In the table below, identify the value of eta-squared and describe the specific meaning of the value.

	Value	Interpretation
Eta-squared

Calculate Tukey’s or R-E-G-W-Q post hoc comparisons and provide the results below.

Comparison	Is the result statistically significant? If so, which group reported higher job satisfaction?
Business vs Healthcare
Business vs Education
Business vs. Government/ Public Administration
Business vs Nonprofit
Healthcare vs Education
Healthcare vs Government/ Public Administration
Healthcare vs Nonprofit
Education vs Government/ Public Administration
Education vs Nonprofit
Government/ Public Administration vs Nonprofit

Based on the results of the omnibus F test, should these post hoc comparisons be interpreted? Why or why not?

What are the limitations in using this research design and statistical test to address the Research Question?

Report

For the this part of the assignment, create a report of the results of the analysis of variance. As always, remember that good technical writing should be precise, concise and clear. You will need to use your judgment to determine which information is most important to report and which can be omitted.

Your report should begin with a table or figure in APA format that presents the mean, standard deviation and the sample size for job satisfaction separately for each sector. A figure could either be a bar graph or a line graph with the mean value on the y axis; give careful thought to which format is most appropriate for your data. Note that output from SPSS, Excel, and JAMOVI is often not organized in APA format. However, you may use AI to take information from statistical software and format it in APA style. You will need to guide the AI chat to format the information as you intend, and you will be responsible for ensuring that the final product follows APA guidelines, includes accurate information, and has readable labels for variables. Be sure to provide an appropriate title for your table or figure, and do not assume that readers will comprehend the variable names from the dataset. Review the following site for guidance on creating APA format tables: Reporting Research in APA Style/Tips and Examples.

Table or Figure of Descriptive Statistics ( Note: you can either paste an image of your table or figure into the box, or delete the box and paste in your own table):

Present your verbal report in the box below. Begin by directing the reader’s attention to your table or figure and highlighting the most important trends. Do not repeat all statistical values from the table or figure; only mention the value of a statistic if it’s something that stands out. Next, explain the results of the omnibus F test, including eta-squared. If appropriate, conclude with the results of the post hoc comparisons.

An example of an ANOVA result presented in APA format is given below.

A one-way independent samples analysis of variance was conducted to determine whether performance on the final training assessment differed by trainees’ experience level. As shown in Figure 1, experience had a significant effect on performance (F(2, 117) = 10.629, p < .001, η2 = .30). The eta-squared value represents a large effect size (Cohen, 1988). Tukey post hoc comparisons revealed that trainees with high experience performed better on the assessment than trainees with medium (p = .027) or low (p < .001) levels of experience. The performance of trainees with medium and low levels of experience did not differ significantly (p = .123).

All language should follow APA format. Enter your report in the box below.

Reflection

Finally, reflect on what you have learned by completing this assignment. In the box below, name two concepts you learned and two skills you have practiced. How might this conceptual knowledge and these skills be useful in your professional life? Complete the reflection with a critical thought question that identifies something you’d like to further understand about the Module 3 material.

Assignment Reflection:

What To Submit

Submit the following to Canvas:

· This workbook with all gray boxes completed.

· A copy of the data file from SPSS, Excel or JAMOVI.

· A copy of the output generated by the statistical software.

· For SPSS, submit the .spv file

· For Excel, be sure all results are on a single worksheet in the file

· For JAMOVI, export the output to a .pdf file

Helpful Resources

· Oneway ANOVA and Tukey’s Post Hoc Tests in SPSS

· One Way ANOVA with Post Hoc Test Using Jamovi

· Reporting Research in APA Style/Tips and Examples

· APA Style Numbers and Statistics

· Franklin’s APA Style Guide