Question

A researcher investigated the number of viral infections people contracted as a function of the amount of stress they experienced during a 6-month period. She obtained the following data:

Report the means which significantly differ from one another according to the Tukey post-hoc results?

Negligible Stress	Minimal Stress	Moderate Stress	Severe Stress
2	4	6	5
1	3	5	7
4	2	7	8
1	3	5	4

Answer 1

Anova: Single Factor
SUMMARY
Groups	Count	Sum	Average	Variance	std dev
Negligible Stress	4	8	2.000	2.0	1.4
Minimal Stress	4	12	3.000	0.7	0.8
Moderate Stress	4	23	5.750	0.9	1.0
	4	24	6.00	3.33
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	47.688	3	15.90	9.19	0.0020	3.49
Within Groups	20.750	12	1.73
Total	68.438	15

Level of significance	0.05
no. of treatments,k	4
DF error =N-k=	12
MSE =	1.7292
q-statistic value(α,k,N-k)	4.1985

critical value = q*√(MSE/n) = 2.76

if absolute difference of means > critical value,means are significnantly different ,otherwise not

population mean difference	critical value			result
µ1-µ2	1.00	2.76			means are not different
µ1-µ3	3.75	2.76			means are different
µ1-µ4	4.00	2.76			means are different
µ2-µ3	2.75	2.76			means are not different
µ2-µ4	3.00	2.76			means are different
µ3-µ4	0.25	2.76			means are not different