Question

# 1. An ANOVA was carried out on a set of data with 4 groups of 4...

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)

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