## Week 13.

## Multiple Independent Variables, correlation exercise.

## Lecture notes

**Multiple independent variables, factorial designs, 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**- Testing
hypotheses about > 1
Independent Variable
*(Does genetics make people more likely to become depressed under stress...? See graphic for an illustration from lecture; click for article.)* - Adding
a "control variable" such as demographics to a study
*(Is the effect the same for men as for women...?).*

- Testing
hypotheses about > 1
Independent Variable

## Readings

The Chapter in your reference book describing complex designs, multiple independent variables or factorial designs.

We will discuss three articles in lecture and examples of complex designs:

- Stressful life events, genetic dispositions, and vulnerability for Depression (click here for full article),
- Gender differences in responses to alcohol,
- The effect of attitudes and drugs on Sexual risk.

## Discussion group Assignment

Correlation coefficients: Going beyond your paper statistics.

For this week you will compute a correlation. This is not for your paper: an 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.

Recall that for a **t-test** we asked how different two groups are (the difference between their Means, or** between group variance**), weighted by the amount of variance (error) within the groups, or

**. t = between group variance divided by within-group variance. So, t compares two groups of participants on one variable.**

*within group variance*For the correlation we do the opposite: We measure two variables among one group of participants, and we examine how much * shared variance* there is between the variables.

The tables below show two variables measured for each of eight students.

The first table contains scores on 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 combined.
- Sum the products of the Z scores, divide by n:

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).

- 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” - 2 as the df
*. Is this a statistically significant correlation?* - 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**