Question

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 α = 0.05?

past	present	future
22 24 27 26 28	27 28 29 30 30	24 27 30 28 29

Compute the corresponding effect size(s) and indicate magnitude(s).
η² =  

Conduct Tukey's Post Hoc Test for the following comparisons:
1 vs. 3: difference =   
2 vs. 3: difference =   

f) Conduct Scheffe's Post Hoc Test for the following comparisons:
1 vs. 2: test statistic =   
2 vs. 3: test statistic =  

Answer 1

Treatment →	A	B	C	Pooled Total
observations N	5	5	5	15
sum ∑xi	127	144	138	409
mean ¯x	25.4	28.8	27.6	27.2667
the sum of squares ∑x2i	3,249.00	4,154.00	3,830.00	11,233.00
sample variance s2	5.8	1.7	5.3	5.781
sample std. dev. S	2.4083	1.3038	2.3022	2.4044
std. dev. of mean SEx¯	1.077	0.5831	1.0296	0.6208

source	sum of	degrees of	mean square	F statistic	p-value
	squares SS	freedom νν	MS
treatment	29.7333	2	14.8667	3.4844	0.0641
error	51.2	12	4.2667
total	80.9333	14