Question

Application Exercise: A social psychologist is interested in how optimism is related to life satisfaction. A sample of individuals categorized as optimistic were asked about past, present, and projected future satisfaction with their lives. Higher scores on the life satisfaction measure indicate more satisfaction. Below are the data. What can the psychologist conclude with an a of 0.01? past present future 22 24 27 26 28 27 28 29 30 30 26 27 26 28 29 a) What is the appropriate test statistic? -Select--- b) Obtain/compute the appropriate values to make a decision about Ho. critical value = ; test statistic = Decision: --Select-- c) Compute the corresponding effect size(s) and indicate magnitude(s). n2 = ---Select-- d) Make an interpretation based on the results. O At least one of the temporal means is different on life satisfaction. None of the temporal means is different on life satisfaction. e) Regardless of the Ho decision in b), conduct Tukey's post hoc test for the following comparisons: 1 vs. 2: difference i significant: --Select--- 2 vs. 3: difference ; significant: --Select--- f) Regardless of the Ho decision in b), conduct Scheffe's post hoc test for the following comparisons: 1 vs. 3: test statistic = ; significant: --Select- 1 vs. 2: test statistic = i significant: ---Select--- Submit Answer

Answer 1

one way anova

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treatment	G1	G2	G3	L4
count, ni =	5	5	5
mean , x̅ i =	25.400	28.80	27.20
std. dev., si =	2.4	1.3	1.3
sample variances, si^2 =	5.800	1.700	1.700
total sum	127	144	136				407	(grand sum)
grand mean , x̅̅ =	Σni*x̅i/Σni =	27.13
( x̅ - x̅̅ )²	3.004	2.778	0.004
							TOTAL
SS(between)= SSB = Σn( x̅ - x̅̅)² =	15.022	13.889	0.022				28.93333333
SS(within ) = SSW = Σ(n-1)s² =	23.200	6.800	6.800				36.8000

no. of treatment , k =   3  
df between = k-1 =    2  
N = Σn =   15  
df within = N-k =   12  
      
mean square between groups , MSB = SSB/k-1 =    28.9333/2=   14.4667
mean square within groups , MSW = SSW/N-k =    36.8/12=   3.0667
      
F-stat = MSB/MSW =    14.4667/3.0667=   4.72
      
F-critical = 6.927

anova table
	SS	df	MS	F	p-value	F-critical
Between:	28.9	2	14.5	4.7	0.031	6.927
Within:	36.8	12	3.1
Total:	65.7	14
					α =	0.01

Decision: , do not reject null hypothesis    
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eta square ,effect size = SSbet/SST=   0.44 mediumeffect
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None of the temporal means is different on life satisfaction.

TUKEY HSD/KRAMER
Level of significance	0.01
no. of treatments,k	3
DF error =N-k=	12
MSE =	3.0667
q-critical value(0.01,3,12)=	5.0459

					confidence interval
	mean difference	absolute mean difference		critical value	lower limit	upper limit			result
µ1-µ2	-3.40	3.40		3.95	-7.35	0.55			no, means are not different
µ2-µ3	1.60	1.60		3.95	-2.35	5.55			no, means are not different

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