ANOVA

The total length of the videos in this section is approximately 19 minutes. You will also spend time answering short questions while completing this section.

You can also view all the videos in this section at the YouTube playlist linked here.

Sums of squares between and within - reviewing intuition

ANOVA.1.SumsOfSquares.mp4

Question 1: Is ANOVA a different method than an F-test?

Show answer

Nope. ANOVA is a way of organizing the information used in an F-test. You will hear people talk about "running and ANOVA." They mean that they will run an F-test and view the results in an ANOVA table. (Note that ANOVA is also the same thing as linear regression. I've posted a separate lecture about that idea.)

ANOVA table

ANOVA.2.Table Sum Squares 2.mp4

Question 2: Check all of the quantities that are equal to MSW (mean square within).

  • MSE

  • s_p^2 (pooled sample variance)

  • estimated residual variance

  • sigma-hat^2

Show answer

All of these options are labels for the same quantity.

Explaining the ANOVA table

ANOVA.3.Table Sums of Squares 3.mp4

Question 3: Is there such a thing as a one-sided v. two-sided p-value for an F-test?

Show answer

No. The F-distribution is not symmetric. Large values of F are evidence against the null, but small values of F suggest that the population means are quite similar. So, your p-value is always the probability that an F-distribution would be larger than your observed F-statistic.

F-distribution

ANOVA.4.F Distribution Sums of Squares 4.mp4

Question 4: Suppose that you ran a pooled t-test and obtained a t-statistic of 1.5. If you ran an extra sum of squares F-test on the same data, what would the F-statistic be equal to?

Show answer

The F-statistic is the t-statistic squared, in cases where there are only two groups.1.5^2 = 2.25.

Note that there is no similar statement if there are more than two groups, because then we don't have a t-test to compare our F-test to.

This folder contains an ANOVA table summarizing the data from the Spock example (only Wellesley affiliates will be able to open this link, due to copyrights). This image is taken from the Statistical Sleuth.

Question 5: What does this ANOVA table tell us about Spock's judge?

Show answer

The p-value is tiny. We have very strong evidence that Spock's venires do not have the same mean proportion of women as the other judges' venires. Spock's judge is doing something funny to his potential jurors. Of course, we knew this from looking at the boxplots in the first place, no test needed! But it is nice to quantify our observation that it is extremely unlikely that Spock's judge's venires would have so few women just by chance.

That's all.