Confirming Increased Statistical Errors in Testing Correlations from Small Sample Sizes

Abstract

ABSTRACT Small sample sizes contribute to several problems in research and knowledge advancement. This conceptual replication study confirmed and extended the inflation of type II errors and confidence intervals in correlation analyses of small sample sizes common in kinesiology/exercise science. Current population data (N = 18, 230, & 464) on four mechanical variables of three kinds of tennis strings were used to study the effect of small randomly selected sample sizes. All small sample sizes (n = 10, 25, 50, & 100) had one to three type II errors in statistical tests of the six pairwise correlations and partial correlations but no type I errors. Correlation coefficients from these small sample sizes had imprecise mean confidence interval widths (.34 to 1.08) that limit accurate statistical inferences, sizes of associations, and are most vulnerable to not detecting small (ρ < .4) true associations in the population. These data confirm that there are likely numerous type II errors and imprecise correlation coefficients in KSES studies using small samples sizes that may slow the knowledge advancement of the field.