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 an α of 0.01?

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

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

Answer 1

a)

one-way ANOVA

b)

count, ni =	9	9	9
mean , x̅ i =	7.222	7.33	5.00
std. dev., si =	1.481	1.000	0.707
sample variances, si^2 =	2.194	1.000	0.500
total sum	65	66	45		176	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	6.52

square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	0.495	0.664	2.306
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	4.457	5.975	20.753		31.18519
SS(within ) = SSW = Σ(n-1)s² =	17.556	8.000	4.000		29.5556

	SS	df	MS	F	p-value	F-critical
Between:	31.19	2	15.59	12.66	0.0002	5.61
Within:	29.56	24	1.23
Total:	60.74	26

b)
critical value =  5.61

test statistic =  12.66

Decision:  ---Select--- Reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
η² = SSB/ SST

= 31.19/ 60.74

= 0.5134

large effect

d)

At least one of the sessions differ on anxiety.

e)

µ1-µ2	-0.11	1.68	-1.79	1.57	Not Significant means are not different
µ1-µ3	2.22	1.68	0.54	3.90	Significant means are different

Thanks in advance!

revert back for doubt

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