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

d) Make an interpretation based on the results.

1)At least one of the sessions differ on anxiety.

2)None of the sessions differ on anxiety.    

e) Regardless of the H₀ decision, 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

Answer 1

treatment	A	B	C	D
count, ni =	9	9	9
mean , x̅ i =	6.889	7.00	5.000
std. dev., si =	2.205	0.866	0.707
sample variances, si^2 =	4.861	0.750	0.500
total sum	62	63	45		170	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	6.30
square of deviation of sample mean from grand mean,( x̅ - x̅̅)²	0.351	0.495	1.680
					TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	3.160	4.457	15.123		22.74074074
SS(within ) = SSW = Σ(n-1)s² =	38.889	6.000	4.000		48.8889

no. of treatment , k =   3
df between = k-1 =    2
N = Σn =   27
df within = N-k =   24
  
mean square between groups , MSB = SSB/k-1 =    11.3704
  
mean square within groups , MSW = SSW/N-k =    2.0370
  
F-stat = MSB/MSW =    5.5818

anova table
	SS	df	MS	F	p-value	F-critical
Between:	22.7407	2	11.370	5.582	0.0102	3.403
Within:	48.8889	24	2.037
Total:	71.6296	26

       α =    0.05

F stat = 5.582

critical = .3.403
Decision: F stat > critical , reject null hypothesis        

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eta square ,effect size = SSR/SST   0.32

medium

.............

d)

1)At least one of the sessions differ on anxiety.

...............

e)

Level of significance	0.05
no. of treatments,k	3
DF error =N-k=	24
MSE =	2.0370
q-statistic value(α,k,N-k)	3.53

			confidence interval
population mean difference	critical value	lower limit	upper limit	result
µ1-µ3	1.889	1.68	0.21	3.57	means are different
µ2-µ3	2.00	1.68	0.32	3.68	means are different

.............

thanks

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