## Analysis Of Variance Assignment

• Anxiety scores for 5 veterans who received behavioral therapy: 104, 108, 107, 106, 103 • Anxiety scores for 5 veterans who received cognitive therapy: 99, 98, 101, 100, 99 • Anxiety scores for 5 veterans who received biofeedback therapy: 103, 104, 105, 107, 101 • Anxiety scores for 5 veterans who received medication therapy: 101, 100, 101, 103, 100.

**Assignment: Analysis of Variance (ANOVA)**

In Week 4, you explored t-tests, which allowed you to compare a sample to a population or compare two groups to one another. For example, you might want to compare the effectiveness of two types of treatment for insomnia, but what if you want to compare the effectiveness of more than two groups? A one-way analysis of variance, or ANOVA, allows you to do just that—compare multiple groups (called levels) of one independent variable (called a factor). For example, in a study about insomnia treatments, you might compare a level that receives muscle relaxation training to a second level that receives visualization training and, finally, to a third level that receives deep-breathing training. An ANOVA allows you to compare all of the levels at once to see if, in general, the type of treatment influences how long it takes to fall sleep. If results are statistically significant, post hoc analyses then provide even more information by identifying which specific levels differ from one another, ultimately showing you which specific treatments are more effective than others.

This application will allow you to continue your practice with hypothesis testing by comparing scores with ANOVA in order to determine if results are statistically significant. Download the data set that you will use for this Assignment from the Weekly Data Set forum. Be sure to watch this week’s instructional video in the introduction or Learning Resources folder before beginning your Assignment.

Scenario: Imagine that a psychologist working with veterans with post-traumatic stress disorder wants to compare the effectiveness of several therapies focused on reducing symptoms of anxiety. The psychologist randomly sampled 20 veterans who recently returned from combat and randomly assigned each of them to receive one of four interventions for 8 weeks. A survey was used to measure the participants’ anxiety at the end of the 8 weeks. Higher anxiety scores indicate more anxiety. You can find the data for this Assignment in the Weekly Data Set forum found on the course navigation menu.

**By Day 7**

**To complete this Assignment, submit** 7 answers to the following. Use SPSS to compare the mean anxiety scores with a one-way ANOVA.

- Before computing any analyses, state the null hypothesis and alternative hypothesis in words (not formulas).
- Identify the factor and the dependent variable.
- Name the levels of the factor.
- State the degrees of freedom between groups and explain how you calculated it by hand.
- State the degrees of freedom within groups and explain how you calculated it by hand.
- Identify the obtained F value using SPSS.
- Identify the p-value using SPSS.
- Explain whether the F test is statistically significant. Explain how you know.
- Explain what the psychologist can conclude about the relationship between different types of therapy and anxiety.
- Should the psychologist conduct a post hoc test? Why or why not? If post hoc testing is needed, conduct a Tukey HSD post hoc analysis in SPSS. Explain what the results tell you.

Be sure to fully explain the rationale for your answer to each question, including evidence from the text and Learning Resources.

Provide an APA reference list.

Submit three documents for grading:

- Your text (Word) document with your answers and explanations to the assignment questions, your SPSS Data file, and your SPSS Output file, your SPSS Data file, and your SPSS Output file. Get
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