Question

1. An ANOVA was carried out on a set of data with 4 groups of 4 subjects each. The responses are presented in the following table:

Subject	A1	A2	A3	A4
S1	4	5	9	8
S2	5	5	10	8
S3	6	6	7	6
S4	5	4	6	6

1. Complete the ANOVA table (52 pts)

Source	SS		df		MS		F
Factor A	__		__		_		___
Subject	__		__		___
Within/error	__		__		___
Total	__		___

1. Find and report the critical value(s) and make a statistical decision for the F statistic and perform a post-hoc test, if applicable. (23 pts)

Answer 1

using excel>data>data analysis >two way anova without replication

we have

Anova: Two-Factor Without Replication
SUMMARY	Count	Sum	Average	Variance
S1	4	26	6.5	5.666667
S2	4	28	7	6
S3	4	25	6.25	0.25
S4	4	21	5.25	0.916667
A1	4	20	5	0.666667
A2	4	20	5	0.666667
A3	4	32	8	3.333333
A4	4	28	7	1.333333
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Factor A	6.5	3	2.166667	1.695652	0.236872	3.862548
Subject	27	3	9
Error	11.5	9	1.277778
Total	45	15

the table is

Source of Variation	SS	df	MS	F	P-value
Factor A	6.5	3	2.166667	1.695652	0.236872
Subject	27	3	9
Error	11.5	9	1.277778
Total	45	15

F = 1.69

critical value F(3,9) = 3.86

since F<3.86 so we do not reject Ho and so we cannot perform post hoc test