Question

The following questions are based on Chapter 12 (One-Way Analysis of Variance).

1. A researcher wishes to test the differences among five population means, using the .05 criterion of significance. Why is it a bad idea to perform 10 t tests for the 10 possible pairs of means?

2. In one-way analysis of variance, what can cause the group means to vary?

3. In a one-way analysis of variance, the degrees of freedom for the numerator is equal to…?

4. In one-way analysis of variance, the F ratio is computed by…?

5. The smallest and largest possible values of F are…?

6. When testing a Kruskal-Wallis H for statistical significance, the critical value can be found in the…?

Answer 1

(1)

It is a bad idea to perform 10 t tests for the 10 possible pairs of means because every time we conduct a t test, there is a chance that we will make a Type I Error. Thus,each t test increasesType I Error, whereas ANOVA controls Type I Error.

(2)

In one-way analysis of variance, the group means vary because of the variation among the means of the various groups.

(3)

In a one-way analysis of variance, the degrees of freedom for the numerator is equal to = k - 1,

wherek is the number of groups.

(4)

In one-way analysis of variance, the F ratio is computed as follows

,

where MSbetween is the Mean Square for Between Groups and MSwithin    is the Mean Square for Within Groups

(5)

The smallest and largest possible values of F are 0 and infinity respectively.

(6)

When testing a Kruskal-Wallis H for statistical significance, the critical value can be found in the Table of Critical Values of the Distribution.