# NUR 705 Assignment 9.1: ANOVA Analysis

## NUR 705 Assignment 9.1: ANOVA Analysis

### Assignment Guidelines

Part One

Using the NUR705 Week 9 dataset (Links to an external site.), conduct an ANOVA to see if there is a statistically significant difference in the Interval Depression Score among 3 groups of shift workers. (Conduct a one-way ANOVA. If the F-test is significant, use the Tukeys post-hoc test.) Assume a .05 level of significance. Complete the following:

1. Identify the independent and dependent variables.
2. Write a null hypothesis.
3. Write an alternative non-directional hypothesis.
4. Interpret your results. Guidelines for interpreting ANOVA results can be found in What to Include When Writing Up One-Way ANOVA Test Results (PDF) (Links to an external site.).

### JASP One-Way ANOVA Screencast

JASP One-Way ANOVA Transcript (Links to an external site.)

Note: Remember that the dependent variable needs to be measured on a continuous/interval level, not a categorical level. Be sure to select the correct dependent variable when conducting your analysis.

For part one of the assignment, submit screenshots of the items above. It is best to copy these and put them in a Word document.

Part Two

For part two of the assignment:

1. Prepare a short narrative to describe the ANOVA analysis. Your narrative should use of APA formatting.
2. This narrative should be approximately one paragraph, double-spaced.

### Submission

Submit your assignment and review full grading criteria on the Assignment 9.1: ANOVA Analysis page.

### Against All Odds: One-Way ANOVA

Review the presentation by Dr. Pardis Sabeti to learn about ANOVA:

Sabeti, P. (Host), & Villiger, M. (Writer/Producer/Director). (2014). One-way ANOVA (Links to an external site.) [Video Unit 31]. Against All Odds: Inside Statistics. Retrieved from Annenberg Learner (Links to an external site.). (Closed captioning is provided.)

One-Way ANOVA Transcript (Links to an external site.)

### Lecture: ANOVA

Lecture: ANOVA Transcript (Links to an external site.)

### Analysis of Variance (ANOVA)

Review the video on Analysis of Variance (ANOVA).

Analysis of Variance (ANOVA) Transcript (Links to an external site.)

### Introduction to One-Way ANOVA

Review the video on one-way ANOVA.

Introduction to One-Way ANOVA Transcript

## Lesson 1: Comparing Group Means—Analysis of Variance

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### Introduction

This week, you will learn more complex statistical testing. Most research studies need to compare more than two groups. For example, if you want to compare outcomes in three or four groups, you need a different statistical test.

Multiple-group comparison with a continuous variable measurement for categorical groups is done with an Analysis of Variance test, or ANOVA for short.

### Learning Outcomes

At the end of this lesson, you will be able to:

• Understand how the number of groups and variables impact the choice of statistical tests to compare differences.
• Understand the purpose of multiple comparison testing.
• Use JASP to compute a one-way ANOVA.
• Correctly report findings of statistical tests in APA style.

Before attempting to complete your learning activities for this week, review the following learning materials:

### Learning Materials

Read the following in your Kim, Mallory, & Vallerio (2022) Statistics for evidence-based practice in nursing textbook:

Chapter 11, “Tests for Comparing Group Means: Part I” pages 230–245

Read the following in your Polit & Beck (2021) Nursing research: Generating and assessing evidence for practice textbook:

Chapter 18, “Inferential Statistics” pages 396 (starting at “Testing Mean Differences with Three or More Groups”) through 400

# Introduction to One-Way ANOVA

Let’s look at an introduction to one-way analysis of variance, sometimes shortened to ANOVA. Here, I have plotted three box plots corresponding to three samples from three separate populations. A natural question that arises is, is there strong evidence against the null hypothesis that the population means are all equal? And this is what one-way analysis of variance is going to test. And the alternative hypothesis is simply going to be that the null hypothesis is wrong, or in other words, that the population means are not all equal. One-way ANOVA is a statistical method that tests the null hypothesis, that K populations all have the same mean by comparing the variability between groups to the variability within groups. Now, it might not be immediately obvious what this means, so let’s take a look at this visually. If we take a look at this plot on the left for a moment, we’ll see these three different box plots corresponding to these three different samples.

And we can see that the sample means are five, seven, and six. So there is some variability between these sample means. There is some variability here between these samples. Over here on the right, we have a very similar type of setting. And the sample means over here, five, seven, and six, are exactly the same as the plot on the left. So there is the same variability between the sample means, the same variability between the averages, and the sample sizes are the same for all groups here. The fundamental difference between these two scenarios is that the variability within groups on the plot on the right is much greater than the variability within groups on the plot on the left. So there is greater variability within groups here than over on the left. Let’s see what the end result of an analysis of variance on these two separate data sets looks like. We will learn how to carry out this test as we go along.

But if we know something about hypothesis testing and we know what the null hypothesis is and we can properly interpret a p-value, we should be able to see here that, for this null hypothesis, that mu A and mu B and mu C are equal, or in other words, that these three samples come from three populations that all have the same population mean. The p-value is very, very small over here, so there is very strong evidence against this null hypothesis. We’ll see this test statistic is an F-test statistic, and that F-test statistic is going to help us get this p-value. But for now, we can look at this p-value and say there is very strong evidence against that null hypothesis. But if we look at the other side corresponding to the plot on the right, we’d see that our F-statistic is rather small, yielding a large p-value.

So we get a large p-value here, meaning that there is not strong evidence against this null hypothesis. Note again that the only difference between these two scenarios is that the variability within groups on this side is much greater than over here. What happened then is that the variability within the groups over here swamped the variability between the groups, and we didn’t see a significant difference. And to summarize, the p-values tell us that there is strong evidence against the null hypothesis that mu A and mu B and mu C are equal, but there is no real evidence against the null hypothesis that mu D, E, and F are equal.

One-way analysis of variance can be viewed as a generalization of the pooled variance two-sample t-test to more than two groups. And as such, the assumptions of one-way analysis of variance are the same as those of the pooled variants two-sample t-test. Specifically, we are assuming that we have independent, simple, random samples, that the populations are normally distributed, and that the population variances are equal. Or in other words, sigma one squared through sigma K squared are all equal. And we sometimes say that that’s equal to some common variance sigma squared. The end result of the calculations will be in an ANOVA table, and our ANOVA table is going to look something like this. The names over here can change: treatment sometimes, maybe groups, different names for these over here. But overall, the gist is the same. And I look at all of these calculations in another video, so this is just the general idea. Over here in the end, we get this F-statistic, and this F-statistic is going to yield a p-value for us. And we’re going to use that p-value to reach an appropriate conclusion.

Although it’s possible to do the calculations by hand, it’s typically best to use a computer. If we look at our A, B, C example from earlier, the ANOVA table looks something like this. This is the output from the statistical computer package R, but other statistical computing packages have very similar output. As you can see, R calls this top line “Group” and this bottom line “Residuals,” where we called them “Treatment” and “Error” earlier. And the computer can do the brute force calculations for us and give us our end result of our F-statistic. And our F-statistic is going to yield this p-value, and our p-value will help us reach our conclusion. And since this p-value is very small, if you recall, we reached the conclusion that there is very strong evidence that these three samples come from populations that do not all have the same population mean. But we will learn how to carry out these calculations and look at another example in another video.

Assignment 9.1: ANOVA Analysis Rubric
CriteriaRatingsPts
Part 1: JASP Dataset
5 to >1 pts
Meets Expectations

Completed screenshots of statistical output for your ANOVA is present.

1 to >0 pts
Does Not Meet Expectations

Completed screenshots are not included.

4.5 / 5 pts
Part 2: Narrative
5 to >4 pts
Meets Expectations

Narrative includes a description of your sample and analysis. Narrative includes the identification of independent and dependent variables, a null hypothesis, an alternative non-directional hypothesis, and an interpretation of your results.

4 to >1 pts
Nearly Meets Expectations

Narrative includes a description of your sample and analysis. Narrative includes some of the following: • Identification of independent and dependent variables • A null hypothesis, an alternative non-directional hypothesis • An interpretation of your results

1 to >0 pts
Does Not Meet Expectations

Narrative does not include a description of your sample and analysis. Narrative does not include the identification of independent and dependent variables, a null hypothesis, an alternative non-directional hypothesis, and an interpretation of your results.

4 / 5 pts
Documentation and Mechanics
5 to >4 pts
Meets Expectations

No errors in grammar, spelling, punctuation, or sentence structure.

4 to >1 pts
Nearly Meets Expectations

Few errors in grammar, spelling, punctuation, or sentence structure.

1 to >0 pts
Does Not Meet Expectations

Numerous and distracting errors in grammar, spelling, punctuation, or sentence structure.

4.5 / 5 pts
Total Points: 13

APA Writing Checklist
Use this document as a checklist for each paper you will write throughout your GCU graduate program. Follow specific instructions indicated in the assignment and use this checklist to help ensure correct grammar and APA formatting. Refer to the APA resources available in the GCU Library and Student Success Center.
☐ APA paper template (located in the Student Success Center/Writing Center) is utilized for the correct format of the paper. APA style is applied, and format is correct throughout.
☐ The title page is present. APA format is applied correctly. There are no errors.
☐ The introduction is present. APA format is applied correctly. There are no errors.
☐ Topic is well defined.
☐ Strong thesis statement is included in the introduction of the paper.
☐ The thesis statement is consistently threaded throughout the paper and included in the conclusion.
☐ Paragraph development: Each paragraph has an introductory statement, two or three sentences as the body of the paragraph, and a transition sentence to facilitate the flow of information. The sections of the main body are organized to reflect the main points of the author. APA format is applied correctly. There are no errors.
☐ All sources are cited. APA style and format are correctly applied and are free from error.
☐ Sources are completely and correctly documented on a References page, as appropriate to assignment and APA style, and format is free of error.
Scholarly Resources: Scholarly resources are written with a focus on a specific subject discipline and usually written by an expert in the same subject field. Scholarly resources are written for an academic audience.
Examples of Scholarly Resources include: Academic journals, books written by experts in a field, and formally published encyclopedias and dictionaries.
Peer-Reviewed Journals: Peer-reviewed journals are evaluated prior to publication by experts in the journal’s subject discipline. This process ensures that the articles published within the journal are academically rigorous and meet the required expectations of an article in that subject discipline.
Empirical Journal Article: This type of scholarly resource is a subset of scholarly articles that reports the original finding of an observational or experimental research study. Common aspects found within an empirical article include: literature review, methodology, results, and discussion.
Adapted from “Evaluating Resources: Defining Scholarly Resources,” located in Research Guides in the GCU Library.
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