What is the actual correlation between expressive and receptive measures of vocabulary? Approximating the sampling distribution of the correlation coefficient using the bootstrapping method.
Georgios D. Sideridis, Panagiotis G. Simos · 2010
The purpose of the present study was to evaluate the effects of sample size on the magnitude of the correlation coefficient between two measures and the actual distortion from true parameter estimates. The research theme emerged from the estimation of the correlation between expressive and receptive measures of vocabulary (i.e., WISC-III vs. PPVT-R). Using samples of 10 through 65 participants bootstrap distributions were created based on sample data. Each bootstrap distribution, based on 1000 replications, was tested for bias (inflation or underestimation) compared to the actual population estimate (based on a population-based study). It was concluded that with sample sizes of 65 participants the bootstrap distribution provided estimates that were very close to population estimates. It is concluded that small sample sizes have a devastating effect on the estimation of the correlation coefficient as they tend to reproduce idiosyncrasies of the samples (and those were reflected in the bootstrap distribution). On the contrary, when sample sizes are moderate-to-large it is highly unlikely that the bootstrap distribution will provide biased estimates of the correlation coefficient.