Know for Quiz #4 on A&A Ch. 10, with one question on t-tests:

**T-tests:** Know what the answers were for quiz #3, and why. One of those questions will be back
in a new form.

Main focus will be ANOVA

1. Understand the basic logic of the ANOVA: you are making two estimates of the population
variance. One is based on variation of scores** within** the samples for each group; one is based on
variation **between** the **sample means** for the different groups. The ratio of these two estimated
variances S^{2}_{between}/ S^{2}_{within} is your F score. (Another way of writing this is _{ }MS-between/MS-within. MS is shorthand for variance, the mean square.)

If the ratio is 1, that means the estimated variances are equal, and you have no basis for
concluding that the population means for the different groups are different. If the ratio is
**significantly larger than 1** (according to the critical value you have defined on the F
distribution), this indicates that the sample means are spread farther apart (showing more
variation) than you would expect if the true population means were all the same.

2. Degrees of freedom for ANOVA. When you calculate the S^{2 } numbers for each group of
scores, remember to use n-1, the degrees of freedom for each group of scores. For the F
distribution, however, you have two separate degrees of freedom, one for **between groups**
estimate of population variance (the numerator), and one for **within groups **estimate of
population variance (the denominator). The df_{between} = the number of groups (or cells) minus 1.

The df_{within} = Ntotal - number of groups (or the df for each group of scores added up -- these give
the same result). For a design with 3 groups and 5 in each group, the df for each group of scores
will be 5-1 = 4. The df_{between} is 3-1 = 2. The df_{within} is 15 (total number of scores) - 3 = 12, or,
using the other method, 4 + 4 + 4 = 12. Why do we use up so many degrees of freedom? We
lose three by calculating the cell means, and one by calculating the **grand mean**, which is the
mean of all of the scores put together.

3. Understand the differences between one-way ANOVA and factorial ANOVA: Factorial has
more than one IV; you can investigate interactions in factorial ANOVAs.

4. Understand when you need to do an one-way ANOVA instead of a t-test: When you have more
than two levels of your independent variable.

5. Know what main effects and interaction effects are (see handout). Be able to look at a table
that shows cell means and marginal means and identify whether there are any main effects (see
your handouts, and book). Be able to look at a graph and identify whether there are any main
effects (lines not flat, lines separated) and whether there is an interaction (lines not parallel).

6. If a set of data is described in words, be able to identify what the research design is: it is a 2 x 3, or a 2 x 2 x 2? The numbers refer to the levels of each independent variable. Be careful!

A 2 x 2 x 2 has 3 variables, not 2 -- 2 refers to the two levels of each of these three variables.