Question

Problem 4

a) Fill in the missing squares in the one-way ANOVA table.

Source	df	SS	MS=SS/df	F-statistic	P-value
Treatment	4
Error	20		6.76
Total		173.04

b) What are the Null and Alternative hypotheses for ANOVA F-test?

c) How many independent populations are compared?

d) Conduct the ANOVA F-test at a significance level of α=0.05 and write your conclusion based on the results.

e) Suppose that you perform one-way ANOVA and reject the null hypothesis. You may want to know which means are different, which mean is largest, or, more generally, the relation among all the means. What methods for dealing with these problems should you use?

Answer 1

(a) The ANOVA Table

df Total = 20 + 4 = 24

SS error = MS error * df error = 6.76 * 20 = 135.2

SS Treatment = SS Total - SS error = 173.04 - 135.2 = 37.84

MS Treatment = SS treatment / df treatment = 37.84 / 4 = 9.46

F statistic = MS Treatment / SS treatment = 9.46 / 6.76 = 1.40

P value at F (1.40, 4, 20) = 0.270

Source	DF	Sum of Squares	Mean Square	F	p value
Groups	4	37.84	9.46	1.40	0.270
Error	20	135.20	6.76
Total	24	173.04

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(b) The Hypothesis:

H0: All means are equal

Ha: Not all the means are equal

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(c) The df groups = number of populations - 1 = 4

Therefore number of populations being compared = 4 + 1 = 5

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(d) Since p value is < (0.05), we Reject H0.

There is sufficient evidence at the 95% level of significance to conclude that not all the means are equal.

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(e) There are many post hoc test which are conducted after testing for equality of means.

These tests are Tukeys HSD, Fischers LSD, Bonferroni test and Scheffes test.

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