Question

Which of the following looks most like an F distribution?

Answer 1

Which of the following looks most like an F distribution?

1. T distribution.
2. F distribution
3. Normal distribution.
4. Another one.

Solution:

The first one looks like most an F distribution. Recognize that the test statistic for ANOVA, the F statistic, is calculated as the ratio of the mean square between groups (MSG, variability between groups) and mean square error (MSE, variability within errors).

Also recognize that the F statistic has a right skewed distribution with two different measures of degrees of freedom: one for the numerator (df_G=k-1

, where k is the number of groups), and one for the denominator (df_E=n−k

, where n is the total sample size).