Final FAQ #3

Q11: In the names of factorial designs, does it matter what order the numbers go in (e.g., is a 2x2x3 design different from a 2x3x2 design)?

A: No. Order of the numbers doesn't matter, so 2x2x3 = 2x3x2 = 3x2x2. They all just say that there are 3 IV's, two with two levels each and one with 3 levels. (But obviously 2x3x3 is different from 2x2x3x2 and from 2x2x1.)


Q12: How do I graph 2x2 factorial designs to look for interaction effects?

A: The goal of the graph is to plot a dependent variable mean (the numbers in the boxes) for each of the levels of the independent variables. To create the graph, you basically just need to remember which variable goes where.

The dependent variable always goes on the vertical axis.
One of the IV's (it doesn't matter which) goes on the horizontal axis.
The other IV is plotted as separate lines on the graph.

Once you've labelled everything, you just need to match the numbers in the boxes (the DV values) with lines on the graph. (FYI, if you have a 2x2 factorial design, then you'll need to plot 2x2=4 points on the graph, and the 4 points will be joined by 2 lines.) Once you've plotted the two lines, imagine that the lines go on forever. If the lines would eventually cross, then there's an interaction effect (between the IV's), but if the lines are parallel, there's no interaction effect.


Q13: How do I graph the marginal means?

You don't. You only graph the numbers inside the "boxes" (cells). The marginal means don't tell you anything about interactions, but they do tell you about main effects. If the marginal means of different "rows" are different from each other, then there's a main effect of the variable whose levels are in different rows. If the marginal means of the different columns are different from each other, then there's a main effect of the variable whose levels are in different columns.


Q14: In practice final qu. 10, why is "a" the correct answer?

A: Here's the practice question:
If a study finds that a measure of “prejudicial attitudes” is correlated with a measure of “discriminatory behaviors” at r = .85, what would be appropriate to conclude?
a. The more discriminatory behaviors a person shows, the more prejudicial attitudes that person is likely to hold.
b. There is a weak relationship between prejudicial attitudes and discriminatory behaviors.
c. Prejudicial attitudes are likely to lead to discriminatory behaviors.
d. both a and c

This question is complicated because it's testing a few different areas of knowledge at once (particularly, knowledge about correlations and knowledge about causality) -- it requires thorough understanding of the course material. Here are the things you need to know in order to answer this question correctly:

1. r = .85 indicates a positive (direct) correlation, meaning that as one variable goes up, the other goes up. (If it were r = -.85, that would mean that as one variable goes up, the other goes down.)

2. r = .85 indicates a strong correlation; as a correlation gets farther from 0, it gets stronger. (If it were r = -.85, then the magnitude would be the same -- to tell how strong a correlation is, ignore the + or - in front of the number.)

3. If you have a simple correlation between variables, you can't rule out the possibility that instead of the "independent variable" causing the "dependent variable", the direction could be the reverse -- the DV could cause the IV. (Recall that the other main causality problem with correlations is the "3rd-variable problem" -- it could be a third, unmeasured variable that's changing both the IV and the DV.)

4. Causality cannot be established by correlational/survey research (see 3. above), so in correlational/survey research, you can't appropriately conclude that one of the variables has caused changes in another, even if the two variables are strongly correlated.

Answer choice (a) is really asking 2 things:
(I) Does r= .85 between prejudiced attitudes (PA) and discriminatory behavior (DB) mean there's a positive relationship between the variables (as one variable goes up, the other variable goes up)?
Answer: yes -- the sign is positive.
(II) Is it the same thing to say that PA is associated with DB as to say that DB is associated with PA?
Answer: yes -- directionality can't be established.

Answer choice (b) is asking:
Is r=.85 a weak correlation?
Answer: no -- the magnitude of .85 is far from 0 and close to 1, so it's a strong correlation.

Answer choice (c) is asking:
(I) Does r= .85 between PA and DB mean there's a positive relationship between the variables (as one goes up, the other goes up)?
Answer: yes -- the sign is positive.
(II) Based on correlational research, can you conclude that one variable causes ("leads to") the other?
Answer: NO -- correlation doesn't equal causation.

So the correct answer is (a).