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12.14 Calculating the ANOVA F test P-value. For each of the following situations, find the degrees...

12.14 Calculating the ANOVA F test P-value. For each of the following situations, find the degrees of freedom for the F statistic and then use R to calculate the P-value.

   (a) Six groups are being compared with five observations per group. The value of the F statistic is 2.47.

   (b) Four groups are being compared with 11 observations per group. The value of the F statistic is 5.03.

   (c) Five groups are being compared using 65 total observations. The value of the F statistic is 3.11.

Solutions

Expert Solution

(a) Six groups are being compared with five observations per group.

k=6 and n=6*5 = 30

Degree of freedom for numerator = k - 1 = 6 -1 =5

Degree of freedom for demominator = n- k = 30 - 6 = 24

The value of the F statistic is 2.47.

pf(2.47,5,24,lower.tail=FALSE).......................using r command for p value

=0.0611

   (b) Four groups are being compared with 11 observations per group.

k=4 and n=11*4 = 44

Degree of freedom for numerator = k - 1 = 3

Degree of freedom for demominator = n- k = 44-4=40

The value of the F statistic is 5.03.

pf(5.03,3,40,lower.tail=FALSE).......................using r command for p value

=0.0047

   (c) Five groups are being compared using 65 total observations.

k=5 and n=65

Degree of freedom for numerator = k - 1 = 4

Degree of freedom for demominator = n- k = 65-5=60

The value of the F statistic is 3.11.

pf(3.11,4,60,lower.tail=FALSE).......................using r command for p value

=0.0216

orchestra answered 2 years ago
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