Question

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.

Use SPSS to compare the mean anxiety scores with a one-way ANOVA.

1. Before computing any analyses, state the null hypothesis and alternative hypothesis in words (not formulas).
2. Identify the factor and dependent variable.
3. Name the levels of the factor.
4. State the degrees of freedom between groups and explain how you calculated it by hand.
5. State the degrees of freedom within groups and explain how you calculated it by hand.
6. Identify the obtained F value using SPSS and report it in your answer document.
7. Identify the p value using SPSS and report it in your answer document.
8. Explain whether the F test is statistically significant. Explain how you know.
9. Explain what the psychologist can conclude about the relationship between different types of therapy and anxiety.
10. 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.

• Anxiety scores for 5 veterans who received behavioral therapy
108
109
107
105
106
• Anxiety scores for 5 veterans who received cognitive therapy
105
102
104
102
106
• Anxiety scores for 5 veterans who received biofeedback therapy
101
102
105
100
101
• Anxiety scores for 5 veterans who received medication therapy
101
104
103
105
103

Answer 1

1)

Null hypothesis: The mean anxiety scores between the 4 levels of therapy are the same.

Alternative Hypothesis: At least one level of therapy has different mean anxiety scores than remaining levels of therapy.

2) The factor and dependent variables are therapy and anxiety score respectively.

3) The levels of the factor are behavioral, cognitive, biofeedback and medication.

4. The degrees of freedom between groups= number of levels of factor-1=4-1=3.

5. The degrees of freedom within groups= number of observation-number of levels of factor=20-4=16.

ANOVA
Anxiety_scores
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	72.550	3	24.183	8.339	.001
Within Groups	46.400	16	2.900
Total	118.950	19

6. The obtained value of F using SPSS is 8.339.

7. The p-value using SPSS is 0.001.

8. The F test is statistically significant because the estimated p-value 0.001 is less than 0.05.

9. The psychologist can conclude about the relationship between different types of therapy and anxiety that is changing the type significantly affect the mean anxiety score.

10. The psychologist should conduct a post hoc test because the p-value is less than 0.05 and can reject the null hypothesis. Hence, at least one level of therapy has significant different mean anxiety scores than the remaining levels of therapy.

Multiple Comparisons
Anxiety_scores Tukey HSD
(I) Therapy	(J) Therapy	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
					Lower Bound	Upper Bound
behavioral	biofeedback	5.2000*	1.07703	.001	2.1186	8.2814
	cognitive	3.2000*	1.07703	.040	.1186	6.2814
	medication	3.8000*	1.07703	.013	.7186	6.8814
biofeedback	behavioral	-5.2000*	1.07703	.001	-8.2814	-2.1186
	cognitive	-2.0000	1.07703	.285	-5.0814	1.0814
	medication	-1.4000	1.07703	.576	-4.4814	1.6814
cognitive	behavioral	-3.2000*	1.07703	.040	-6.2814	-.1186
	biofeedback	2.0000	1.07703	.285	-1.0814	5.0814
	medication	.6000	1.07703	.943	-2.4814	3.6814
medication	behavioral	-3.8000*	1.07703	.013	-6.8814	-.7186
	biofeedback	1.4000	1.07703	.576	-1.6814	4.4814
	cognitive	-.6000	1.07703	.943	-3.6814	2.4814

From the above post-hoc test, the level behavioral has significant mean anxiety score than remaining levels cognitive, biofeedback and medication.