Abstract

Determination of a valid sample size is a fundamental step in research. This paper explains how existing formulas are tied in a single thread by applying the concept of standard error, margin of error, Z and t scores, confidence interval and sampling distribution. Bringing the concept of sample control ratio, we suggest a unified formula which is n=(Nt²ρ²)/(N+t²ρ²) where n is the sample size, N is the population, t is the t-value at a desired level of probability with df = (N-1) and ρ is the sample control ratio to be estimated by 1/6ε for continuous variables and √(p(1-p))/ε for categorical variables where ε is the proportion of acceptable error and p is the proportion of presence of an attribute in the population. This formula does not need the finite population correction, and it has been derived from and consistent with existing formulas. A researcher does not need to calculate the error margin in absolute terms for this formula, and it is sufficient to provide only the proportion of error (e.g., 0.03 or 0.05). This paper should help social scientists, researchers, academicians and students determine the appropriate sample size for their research with greater confidence and clarity.

Key words: Research, Survey, Sample size, Sample control ratio, Sampling applet