Simplified Sample Size Formulas for Detecting a Medically Important Effect

The sample size is just about the most common question in the minds of many medical researchers. This size determines the reliability of the results and helps to detect a medically important effect when present. Some studies miss an important effect due to inappropriate sample size. Many postgraduate students and established researchers often contact a statistician to help them determine an appropriate sample size for their study. More than 80 formulas are available to calculate sample size for different settings and the choice requires some expertise. Their use is even more difficult because most exact formulas are quite complex. An added difficulty is that different books, software, and websites use different formulas for the same problem. Such discrepancy in the published formulas confounds a biostatistician also. The objective of this communication is to present uniformly looking formulas for many situations together at one place in their simple but correct form, along with the setting where they are applicable. This will help in choosing an appropriate formula for the kind of research one is proposing to do and use it with confidence. This communication is restricted to the sample size required to detect a medically important effect when present - known to the statisticians as the test of hypothesis situation. Such a collection is not available anywhere, not even in any book. The sample size formulas for estimation are different and not discussed here.