Correlations, Proportions, and Further Effect Size Measures
In earlier chapters, means and Cohen’s d are almost the only ESs I’ve discussed. Here I’ll go further and consider other measures we can use for the point estimates we want. Correlations and proportions are the main focus, and then I’ll briefly mention some other ESs. As usual, I’ll emphasize variation with replication, and the value of CIs. Here’s the agenda:
• Pictures of correlations • CIs on Pearson’s r • CIs on r, and replication • Comparing two correlations • The ESCI Effect sizes software for effect sizes and CIs • Proportions and their CIs • Further effect size measures
Suppose you read, for a group of N = 50 children, that the correlation between reading scores at age 6 and scores 3 years later was r = .56. That’s Pearson’s r, which measures the linear component of the relationship between two variables, traditionally labeled X and Y. In our case, X and Y are the two reading scores. Correlation r is a units-free measure, which means simply that it has no units of measurement. It can range between –1 and 1. I’m not going to attempt a full introduction to r, with formulas, but will focus on pictures and CIs. As usual, I’m interested in intuitions about the extent of sampling variability, and the insights CIs can give. Correlation r is worth our attention because it’s so widely used, is interestingly different from means, and is a favored ES for meta-analysis.