Question

In: Statistics and Probability

Which of the following statements about the one-way ANOVA are correct? (Select all that apply.) a....

Which of the following statements about the one-way ANOVA are correct? (Select all that apply.)

a. The results of the ANOVA F test does not tell us which groups are different or how different they are.

b. The larger the variability within groups relative to the variability between groups, the larger the F test statistic tends to be.

c. In one-way ANOVA, the mean square for error (MSE) gives a measure of the variation within the samples, while the mean square for groups (MSG) gives a measure of variation among the sample means.

d. An F-distribution is symmetrical about 0 and extends indefinitely in both directions.

e. A random variable with an F-distribution can take non-negative values only.

f. In a one-way ANOVA,if the null hypothesis is rejected, we conclude that the population means are all different (i.e. no two of the population means are equal).

Solutions

Expert Solution

a: The results of the ANOVA F test does not tell us which groups are different or how different they are. Correct.

b. The larger the variability within groups relative to the variability between groups, the larger the F test statistic tends to be. False (Since F-statistic=[SSgroups/(k-1)]/[SSerror/(n-k)] where n=total no. of observations, k=no. of groups and since for given n observations and k groups SSTotal=SSgroups+SSerror is fixed so as SSgroups increases SSerror decreases and hence value of F increases.)

c. In one-way ANOVA, the mean square for error (MSE) gives a measure of the variation within the samples, while the mean square for groups (MSG) gives a measure of variation among the sample means. Correct

d. An F-distribution is symmetrical about 0 and extends indefinitely in both directions. False (since pdf of F-distribution>0 for x>0, where, x=realization of r.v. X where X follows F distribution and pdf of F-distribution=0 for x<0 and F-distribution is positively skewed).

e. A random variable with an F-distribution can take non-negative values only.True.

f. In a one-way ANOVA,if the null hypothesis is rejected, we conclude that the population means are all different (i.e. no two of the population means are equal). False (if the null hypothesis is rejected, we conclude that the population means are all not equal).

Correct options are: a, c, e.

orchestra answered 1 year ago
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