Module 8: Correlations

Overview: Analyzing Correlational Data “Eyeballing” scatterplots Coming up with a number What does it tell you? Things to watch out for Hypothesis testing with correlations

“Eyeballing” Scatterplots Each individual is entered as a point on this plot; can see where that person falls on the two variables. As two variables get more closely related, plot more closely approximates a straight line. Note how direction of “line” tells you what kind of correlation you have.

Coming up with a Number Pearson’s r –Definitional formula –Heart is in the cross-product –Corrections for sample size, variability –Computational formula

What does the Number tell You? Sign Magnitude Variance accounted for

Things to Watch out For Correlation does not imply causation Problems interpreting size Captures only linear relationships Truncated range Problems with different subgroups Problems with skewed variables

So, you should: Check means, SDs of subgroups Check distributions of variables Eyeball your scatterplot Watch your interpretations

Other Correlation Coefficients Spearman’s rank coefficient Point biserial Phi Eta squared Bivariate regression (briefly)

Hypothesis Testing with Correlations Was your hypothesis supported? How big does a correlation have to be to be “real”? –Sampling distributions (how often do you see a number this big by chance) –What counts as chance? (setting alpha levels) –Critical values –P-levels –One-tailed vs. two-tailed tests