Question

An educational psychologist has developed a meditation technique to reduce anxiety. The psychologist selected a sample of high anxiety students that are asked to do the meditation 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 = 0.05?

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

b) Obtain/compute the appropriate values 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
  
e) Regardless of the H₀ decision in b), conduct Tukey's post hoc test for the following comparisons:
2 vs. 3: difference = ______________ ; significant:  ---Select--- Yes No
1 vs. 3: difference = ______________ ; significant:  ---Select--- Yes No

f) Regardless of the H₀ decision in b), conduct Scheffe's post hoc test for the following comparisons:
1 vs. 3: test statistic =  ______________; significant:  ---Select--- Yes No
1 vs. 2: test statistic =  ______________; significant:  ---Select--- Yes No

Answer 1

Applying two way ANOVA: (use excel: data: data analysis: two way ANOVA: without replication select Array):

Source	SS	df	MS	F	P value
treatments	22.74	2	11.37	5.95	0.0117
Blocks	18.30	8	2.29	1.20	0.3603
Error	30.59	16	1.91
Total	71.63	26

b)

critical value = 3.6337 ; test statistic = 5.9467

Decision:    reject Ho

c) η² = SS(treatment)/SS(total) =0.3175 ; large effect

e) 2 vs. 3: difference = 2 : significant:    Yes

1 vs. 3: difference = 1.89 ; significant:    Yes

f)

1 vs. 3: test statistic = 2.8978 ; significant:   :yes

1 vs. 2: test statistic = -0.1705 ; significant:   :No