On the Estimation of Power and Sample Size in Test of Independence

In this study, power and sample size estimations in the context of test of independent between categorical variables were examined. The required sample size in an experiment is a function of the alternative hypothesis, the size of type I error and the variability of the population. Power of a test is the probability of rejecting a false null hypothesis and it depends on the effect size, type I error and the sample size. A priori power analysis is determination of minimum sample size to obtain a required power while post-hoc power analysis is calculating power of a test. A test with small effect size requires large sample size to achieve a power 80% or more while effect size of medium or large size needs small sample size to achieve that. Test with small degrees of freedom will attain higher power than the same test with larger degrees of freedom.