Question

An educational psychologist has developed a mediation technique to reduce anxiety. The psychologist selected a sample of high anxiety students that are asked to do the mediation at two therapy sessions a week apart. The participants' anxiety is measured the week before the first session and at each subsequent session. Below are the anxiety scores for the participants. What can the psychologist conclude with α = 0.01?

before	session 1	session 2
9 6 8 5 8 6 9 6 8	7 7 6 7 6 9 7 7 7	9 5 5 4 5 6 5 5 4

a) What is the appropriate test statistic?
---Select--- na one-way ANOVA within-subjects ANOVA two-way ANOVA

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  ;  ---Select--- na trivial effect small effect medium effect large effect

d) Make an interpretation based on the results.

At least one of the sessions differ on anxiety.None of the sessions differ on anxiety.    

e) Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =  ; significant:  ---Select--- Yes No
2 vs. 3: difference =  ; significant:  ---Select--- Yes No

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 3: test statistic =  ; significant:  ---Select--- Yes No
2 vs. 3: test statistic =  ; significant:  ---Select--- Yes No

Answer 1

Using Minitab software, (Stat -> ANOVA -> One way), we get the following output :

a) The appropriate test statistic - one-way ANOVA

b) The value of test statistic Fobs = 5.54 and critical value = 5.61359

Since F_obs  F_critical = 5.61359, so we fail to reject H₀ at 1% level of significance.

Decicion - Fail to reject H0

c) effect size

large effect

d) Conclusion : None of the sessions differ on anxiety.    

e)

1 vs 3 : value of test statistic = 0.36, significant - No, since confidence interval includes 0

2 vs 3 : : value of test statistic = 2.69, significant - No, since confidence interval includes 0