Minimum Sample Size Calculation Using Cumulative Distribution Function

Minimum sample size is a requirement in most experimental designs. Research in social science requires minimum sample size calculation in order to support the claim that the sample represents the population. If the sample does not adequately represent the population, generalizability could not be achieved. In this study, we present a minimum sample size calculation method by using the cumulative distribution function of the normal distribution. Since most quantitative data in social science research employ surveys with responses in the form of Likert or non-Likert scales, the CDF of the normal distribution curve is an appropriate tool for sample size determination. We use binary data in a form of (0,1), and continuous data, in a form of quantitative non-Likert (0,1,2,3), and Likert  (1,2,3,4,5), (1,2,3,4,5,6,7) and (1,2,3,4,5,6,7,8,9,10) scales as the bases for our modeling. We used Monte Carlo simulation to determine the number of repetition for each scale to achieve normality. The minimum sample size was determined by taking the natural log of the Monte Carlo repetition multiplied by pi. We found that in all cases, the minimum sample size is about 30 where we maintain the confidence interval at 95%. For non-parametric case, the new sample size calculation method may be used for discrete and continuous data. For parametric modeling, we employed the entropy function for common distribution as the basis for sample size determination. This proposed sample size determination method is a contribution to the field because it served as a unified method for all data types and is a practical tool in research methodology.