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	6 5 3 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. 2: 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

(a) one-way ANOVA

(b) critical value = 3.4028, test statistic = 12.6857 (please round these numbers to the required number of decimal places).
Reject H0.

(c) = 0.5139 (please round this number to the required number of decimal places)
medium effect.

(d) At least one of the sessions differ on anxiety.

(e) 1 vs. 2: difference = 0.2222; significant: No.
2 vs. 3: difference = 2.2222; significant: Yes.

(f) 1 vs. 3: test statistic = 2.4444; significant: Yes.
2 vs. 3: test statistic = 2.2222; significant: Yes.