Multiple Independent Variables, correlation exercise.
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
- 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...?).
Lecture Notes are here.
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 within group variance. t = between group variance divided by within-group variance. So, t compares two groups of participants on one variable.
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 critical ratio to your correlation analysis. What is being compared to what, and what do your statistical results tell you about that comparison?