What does the F-statistic test in ANOVA?

What does the F-statistic test in ANOVA?

• A. It tests whether the model explains more variance than would be expected by random error.
• B. It tests whether all regression coefficients are equal to zero.
• C. It tests the normality of residuals.
• D. It tests whether the variances of residuals are constant.

Answer: (A)

The F-statistic in ANOVA is about whether the model adds real explanatory power beyond what random error would produce. It does this by comparing two sources of variation: how much of the total variance the model explains (between-group/MSS or mean square due to the model) and how much variance remains unexplained (within-group/MS error). The F-value is the ratio of these two quantities. A large F means the model accounts for substantially more variance than would be expected by chance, so we conclude there are real differences among the group means or that the factor has an effect. Normality of residuals and constant variance are separate assumptions or diagnostics that aren’t what the F-test directly evaluates. The notion that all regression coefficients are zero is related to a broader regression context; in ANOVA, the relevant null is that the model does not explain more variance than random error, i.e., there are no real differences among the group means.

The F-statistic in ANOVA is about whether the model adds real explanatory power beyond what random error would produce. It does this by comparing two sources of variation: how much of the total variance the model explains (between-group/MSS or mean square due to the model) and how much variance remains unexplained (within-group/MS error). The F-value is the ratio of these two quantities. A large F means the model accounts for substantially more variance than would be expected by chance, so we conclude there are real differences among the group means or that the factor has an effect.

Normality of residuals and constant variance are separate assumptions or diagnostics that aren’t what the F-test directly evaluates. The notion that all regression coefficients are zero is related to a broader regression context; in ANOVA, the relevant null is that the model does not explain more variance than random error, i.e., there are no real differences among the group means.