Lecture 6- 30 January 2013
1. More about correlations
a. Effect size is how big a difference is between independent variables. It is
measured in standard deviations. It uses an average SD from SD of mean 1 and 2.
b. If you have an effect size of 0.5 is considered moderate. Its called Cohen’s d.
c. Correlation coefficient can be thought of as the relationship between the cosine
between those things and as you move along one arm of that geometric representation, you
move less far along the other arm.
d. If you change 1 SD in X it will lead to change in r times SD of Y
e. Correlation is the relationship between two variables. But we want to see you
multiple variables predict something
2. Multiple regression
a. Is a linear relationship. If you have an economic model, you could 100 predictors.
But science needs parsimony so you want useful predictors.
b. Regression coefficients can be thought of as correlational coefficients.
c. You want there to be something independent about the predictors.
d. You start with the best predictor then add predictors and see whether or not they
improve the prediction. You want to find the most compact model. If new factors are only
adding 2% to the model then you stop
3. The devil is in the details
a. (Read first sentence here). But if a predictor variable is perfectly correlated with
another predictor variable, its not going to add anything (height in meters and in inches)
b. (He read the rest of the slide). These are things to think about before adding
4. A simple minded example
a. Virus is the cause and green is the effect
b. Because load and green are perfectly correlated we can say that green and
suppression have a 0.5 correlation. Even if it weren’t perfect and was still high, green and
suppression would still be correlated.
5. Lets consider the Regression analysis
a. We are interested in immunosuppression, which is the beta load.
b. There could be 2 models that come from this (on the slide)
c. Because we know the cause, the model works well. But if you have SES, IQ, race
and so on, most of these factors are already correlated with some but not the other or you
could not have included some factors. This is the problem.
6. Self selection
a. The true solution of a multiple regression conclusion is to do an experiment to see
if it happens. You could take islanders and dye them green and see that it has no effect. Or
you could give them the virus and see its effects on the immune system.
b. (Read the rest of the slide)
7. Does class size make a difference?
a. Krueger in 1999 did a study where they randomly assigned students to different
class size. And they found smaller classes improved performance by 0.25. There could also
be a self-selection going on and we just don’t know what it is. b. Be careful because all of this has to do with correlation. This does not mean
cause. People that are really emotional about their point of view (eg. Nativists) would go
along with the data supporting their view and you have to keep an eye out for these things.
8. Back to processing speed
a. In the radex model they had all the subcomponents that were centered on general
intelligence with fluid in the middle and processing speed being in the corner. So its odd that
processing speed is important to IQ when the correlation was weak for g.
b. By cognitive factor we mean a specific ability (not critical for intelligence.
Intelligence isn’t a cognitive ability but it’s what drives all cognitive abilities.)
c. Ravens require more g because they correlate with it. There is nothing in g that is
ravens. Ravens use g and other perceptual things.
d. Rather they thought t