Frequency Sampling and Type II Errors

Abstract

Probabilities of detecting frequency differences based on data obtained by random sampling were determined by computer simulation. Artificial, monotypic populations of known frequency were generated and sampled. Sample sizes of 100, 200, 500, and 1,000 plots were used to compare baseline populations of 20, 50, and 80% frequency to populations having progressively larger or smaller frequencies. Probabilities of detecting a difference in frequency from baseline populations were empirically estimated from 10,000 comparisons using a test of proportions (P<0.05). Results indicated that the power of the test was substantially reduced at lower sample sizes. Equating the probability of Type I and Type II errors at 0.05 resulted in sample sizes of approximately 500 plots being needed to statistically distinguish between differences of plus or minus 10% frequency.