Three tests are proposed based on F-distribution, Likelihood Ratio Test (LRT) and large sample Z-test for intraclass correlation coefficient under unequal family sizes based on a single multinormal sample. It has been found that the test based on F-distribution consistently and reliably produces results superior to those of Likelihood Ratio Test (LRT) and large sample Z-test in terms of size fo...

We cringe at the pervasive notion that a randomised trial needs to yield equal sample sizes in the comparison groups. Unfortunately, that conceptual misunderstanding can lead to bias by investigators who force equality, especially if by non-scientific means. In simple, unrestricted, randomised trials (analogous to repeated coin-tossing), the sizes of groups should indicate random variation. In ...

The three likelihood-based tests, namely, likelihood ratio test, Rao score test, and Wald test and two more asymptotic tests which use Srivastava’s estimator of intraclass correlation coefficient are considered to test the null hypothesis of equality of intraclass correlation coefficients when the families have unequal number of children. Methods are illustrated on Galton’s data set. Using simu...

Private set intersection (PSI) is a cryptographic technique that is applicable to many privacy-sensitive scenarios. For decades, researchers have been focusing on improving its efficiency in both communication and computation. However, most of the existing solutions are inefficient for an unequal number of inputs, which is common in conventional client-server settings. In this paper, we analyze...

Researchers occasionally have to work with an extremely small sample size, defined herein as N ≤ 5. Some methodologists have cautioned against using the t-test when the sample size is extremely small, whereas others have suggested that using the t-test is feasible in such a case. The present simulation study estimated the Type I error rate and statistical power of the oneand two-sample ttests f...