Sample size and the detection of means: a signal detection account

Using statistical theory as a basis, Kareev (e.g., 1995) claimed that people's ability to correctly infer the existence of a population correlation should be greater for small than for large samples. Simulations by R. B. Anderson, Doherty, Berg, and Friedrich (2005) identified conditions favoring small samples but could not determine whether such an advantage was due to sampling skew, variance, or central tendency displacement. In the present study, we investigated theoretical effects of sample size (n) on the detection of population means under circumstances in which sampling variance is unconfounded with skew or central tendency displacement. The results demonstrate an extremely limited, criterion-specific, small-sample advantage that was attributable to n-related sampling variance and that occurred only with highly conservative, suboptimal criterion placement.