## 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

Lecture Notes are here.

## Readings

**Text:**

Suggested background reading: the Chapter in your reference book describing complex designs, multiple independent variables or factorial designs

Focus Modules:

Statistics module 7: Correlations.

Mulltiple Independent Variables & Statistical Interactions.

For lecture & Discussion Group:

Computing and understanding the correlation coefficient.

Thinking about correlational versus experimental ways of testing your hypothesis.

Final feedback on your papers: they are due next week!

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, 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**

Your paper is due next week!

You should be writing away. Use this week's discussion group feedback to finish your paper off.

**Some paper writing hints:**

Begin with a rich (and interesting) description of your phenomenon; do not just jump right into your hypothesis, or begin describing a study in the literature. Give us the big picture first; what are you explaining, why is it important…

Be sure you well use the 2+ studies you cite. Do not just tell us that so-and-so’s paper addressed this topic also, and a general statement of what the study found. Tell us something about their theory, methods, or limitations on their results.

Make sure your paper is balanced. Do not spend pages describing your phenomenon and only a paragraph or two describing the methods, or visa-versa. Both the thought part (phenomenon à theory à hypothesis) and the methods section must be well developed

Make sure your hypotheses specific and concrete. Telling us that one variable will relate to some other variable is not a hypothesis. Make specific causal or ‘this leads to this’ –type statements. Your hypothesis must take into account your methods; I predict that people who are given the X (experimental) condition rather than the Y (control) condition will show higher scores on my scale of (describe dependent variable).

Shifting from outline mode to writing mode can be difficult. You cannot just scotch tape your paper sections together; you need to write a real narrative, with transition sentences and other way to make it flow.

- You need to show the integration of each step – Phenomenon à theory à hypothesis --. methods – not just list them.
- The Alcohol paper we read in Week 4 is a good example of writing; look it over to get a sense of style and “flow”; http://psp.sagepub.com/content/36/10/1301.full.pdf+html

Plagiarism, even when accidental, is very serious.

- You must cite a source for every finding or idea that comes from someone else. Look at the Paper Assignment page for a description of plagiarism: http://www.uic.edu/classes/psych/psych242/PaperRequirement.html
- Never simply lift text from a document and put it in your paper; that is clear plagiarism, and is grounds for flunking the paper.
- Avoid long quotes; learn to paraphrase or summarize, always cite sources.
- Look at the Research Citations page on the course web site: http://www.uic.edu/classes/psych/psych242/ResearchCitations.html
- You will submit your paper to Safe-assign. If your score is too high on that index (due to plagiarism, using another student’s or your own previous papers) you will receive a ‘0’ on the paper.