Question

1. The following data were obtained in a four-group study: Group1 Group 2 Group 3 Group...

1. The following data were obtained in a four-group study:

Group1 Group 2 Group 3 Group 4
6 6 3 5
5 9 7 3
7 9 6 1
5 4 3 4
3 5 4 3
4 6 7 5

(a) Are the four group means significantly different from each other?

(b) Suppose all pairwise comparisons were investigated. If the αΣ is maintained at the level of 0.05, is the difference between the means of groups 2 and 4 significant?

(c) Use the SNK method to test all pairwise contrasts. Consider the per comparison error rate α = 0.05. Does the result agree for the difference between the means of groups 2 and 4 with the result in (b).

Math   Statistics-And-Probability   
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Answer #1

Are the four group means significantly different from each other.

Here we have to test the null hypothesis,

Ho=The mean of the four groups are equals.

V/s:

Ha=The mean of four are significantly different from each other.

For testing the above hypothesis, we can use ANOVA,

The R function aov() can be used to answer to this question. The function summary.aov() is used to summarize the analysis of variance model.

Source

Df

Sum Sq

Mean Sq

F value

Pr(>F)

group

3

27

9.00

9.251

0.0575

residual

20

61

3.05

Interpret the result of one-way ANOVA tests

As the p-value is greater than the significance level 0.05, So we accept the null hypothesis Ho

and we can conclude that there are no significant differences between the groups. It means that the mean of the four groups are equals.

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