Keywords: Fisher’s method, combined inference, paired, independent, simulation
Comparison of independent groups using two sample t-test or comparison of dependent groups using paired t-test is a common practice. But there are situations where the data contains a combination of independent and paired data. This situation could arise as a result of missing observations in one or both the groups or plainly because of the design of the study. Dropping the paired or independent data and analyzing only one type could mean losing on a lot of information. Textbook solutions are not readily available to handle such a data. One way out is to analyze the entire data as independent samples, ignoring the dependency in the paired data. This could mean losing on power of the test. The proposal is to separately analyze the independent and paired data using the two sample test and paired test respectively. Then to make a unique inference for the entire data, combine the p-values from independent and paired data using the Fisher’s method of combining independent p-values. We also look at some methods discussed in the literature. Using simulations, we compare the empirical powers of these methods as the degree of correlation and proportion of paired data is varied.