## Week 13.

Multiple Independent Variables.

## Lecture notes

**Multiple independent variables, factorial designs, interactions.**

.Key topic: *Main effects* v. *Additive* effects v. Statistical *interactions*.

**Main effects**: simple effect of one variable on another- Independent variable Dependent variable
- Predictor Criterion

**Additive effects**: 2 (or more) separate variables each "add to" an effect.

**Interaction effects**

Lecture notes are here.

## Readings

Chapter 8 and articles on studies addressing multiple variables: Stressful
life events, genetic dispositions, and vulnerability for Depression (click here for
full article), Gender
differences in responses to alcohol, and the effect of attitudes
and drugs on Sexual
risk, .

## Discussion group Assignment

(Click for a Word copy of Week 13 assignment).

Correlation coefficients: Going beyond your paper statistics.

For this week you will do a correlation. This is not actually your statistics for your paper: doing an experiment (or quasi-experiment) calls for a t-test, and you did that last week. We want you to compute a correlation so you really understand how this approach asks a different question than the t-test does.

Here is another version of the data we have been using as an example:
these data tables show two variables measured for each of eight students. The
question here concerns how the two variables relate to each other *within** participants*;
do participants who ended up with a lower score on* Fear and Loathing
of Statistics* actually do better on a quiz later on? Your
t-test assignment last week examined differences ** between** different
groups of participants.

The first table contains scores attitudes toward statistics; the second table gives grades on a statistics quiz, both as a letter and a number. The participants are the same in each table. Recall how to compute a correlation:

- Calculate the mean [M] and standard deviation [S] for each variable;
- Use those to compute a Z score for each participant on each variable, showing how far each person is from the M on that variable;
- Multiply each person’s Z score on Variable 1 by their Z score on Variable 2 to show how far they are from the M on the two variables
- Sum the products of the Z scores, divide by df:

The tables on the next page show calculations for the Z scores for each participant on each variable (the actual Z scores are given in the last column). __For this assignment:__

- Draw a scattergram of the two variables against each other (see examples in Statistics 2 Notes), using the Z scores. Draw lines where the M is for each variable, as in the statistics lecture.
- Calculate the correlation between these variables, using the Z score formula. Show all your calculations. What is the correlation coefficient?
- Compare your correlation ('r' value) to the table of critical values for the Pearson Correlation. Here use “number of pairs” (number of subjects who have values on each of the variables you are correlating) rather than the
. Is this a statistically significant correlation?*df* - Apply the concept of the
to your correlation analysis. What is being compared to what, and what do your statistical results tell you about that comparison?**critical ratio**