Psychology 202a Advanced Psychological Statistics November 19, 2015

The Plan for Today Visualizing ANOVA (continued) ANOVA as a special case of regression Post hoc comparisons Contrasts Orthogonal contrasts and contrast coding

Visualizing ANOVA Parallel boxplots Bar plots of means Line graphs of means Rules for choice of bar plots or line graphs –Grouping variable’s level of measurement technically should be interval or ratio for line graph –Often violated (without particularly dire consequences)

Reviewing ANOVA in SAS the easy way The “class” statement. “class” tells SAS “Figure out how to code this classification variable so that we can handle it using regression.” Let’s see how such coding works. Examples in SAS

An outlier test Sometimes we can use creative coding to do clever things in regression. Recall that our regression of Peabody on Raven had one observation that disturbed us. Create a dummy code for that observation. (Example in SAS.) Also known as the “externally Studentized residual”

Results of dummy coding GroupD1 D2 Massed Practice 1 0 Spaced Practice 0 1 No Practice 0 0

Other forms of coding Any coding system that uses two variables to identify the three groups will produce the same ANOVA This idea will turn out to be profoundly useful Example: effects coding

Example of effects coding GroupD1 D2 Massed Practice 1 0 Spaced Practice 0 1 No Practice -1 -1

Asking more detailed questions So far, we haven’t really learned anything interesting about these means. Post hoc procedures –Illustration in SAS

Asking more detailed questions When possible, if we can plan our questions in advance, we will be more likely to find effects.

A priori contrasts A contrast is a question about a linear combination of means. Example: Shorthand notation: 1/2 1/2 -1 Equivalent: Another question that might interest us is

Contrasts (continued) Once a contrast is specified, its sum of squares is calculated: Contrasts always have 1 df, so the sum of squares is a mean square. Division by the error mean square provides an F statistic that tests the contrast.