Abstract
The aim of this study was to investigate the effects of sample size on the results of statistical tests in epidemiological research. Two kinds of populations were examined. One was made up of two ordinal variables, HU-DBI score and ORI score of young mothers, and the size of the population was 2847. The correlation coefficient of the whole population (ρ) was 0.215 (p<0.001). The HU-DBI questionnaire was an instrument for assessing dental health behavior, and the ORI was an index of oral health status in adults. The other was made up of two interval variables, height and weight of university students, between which the correlation was well known. The size of this population was 2885. The correlation coefficient of the whole population (ρ) was 0.650 (p<0.001). The sample sizes were set at 25, 50, 100, 200, 300, and 400. One hundred random samplings of each sample size were performed in both populations, followed by calculation of correlation coefficients (r) between two variables. Then for each size, the distributions of the 100 correlation coefficients (r) were recorded. The results were as follows. 1. Population with a low ρ 1) When the sample size was 100, 51 values of r were statistically significant. Then the β probability of rejecting the true hypothesis, ρ≠O, was 0.49. 2) When the size was 400, 99 values of r were significant. Then the β probability of rejecting the true hypothesis was 0.01. 2. Population with a high ρ 1) When the size was over 50, all values of r were significant. Then the β probability of rejecting the true hypothesis was zero. These results suggest that the smaller size of a sample taken at random from a population with a low ρ may induce the lower reproductivity of r. Therefore we need to be careful about the size of a sample.
