Do Larger Samples Really Lead to More Precise Estimates? A Simulation Study

Abstract

In this paper, we use simulated data to find out if larger samples support estimation of population parameters by examining whether or not higher samples give rise to more precise estimates of population parameters. We simulated a normally distributed dataset and randomly drew 73 samples from it. Some basic statistics, namely the mean, standard deviation, standard error of the mean, confidence interval and the one-sample t-test significance were computed under some conditions for all samples. The correlation between sample size and each of these statistics was computed, among other statistical treatments. Our analysis suggests that larger samples produce estimates that better approximate the population parameters. The correlation between sample size and standard error of the mean is even stronger. We therefore conclude that larger samples lead to more precise estimates.