Professor Tathagata Bandyopadhyay, Indian Institute of Management, Ahmedabad, India

Testing Equality of Means from Paired Data When The Labels Are Missing

Suppose (Xi, Y9) i=1,..,n represent a random sample of size n from a bivariate normal population.  Suppose for some reason the labels in each pair are missing.  We consider the problem of testing the null hypothesis of equality of means based on such a messy data set.  We will cite a few practical instances when such a situation may arise.  Naturally, standard t- test cannot be applied here since one can not label the components of each pair by 'X' or 'Y'.  Instead, the observable pairs are (Mi, mi), i=1, ...n, where Mi = max(Xi, Yi) and mi = min(Xi, Yi).  We will talk about a number of large sample tests based on (Mi, mi) for testing the above hypothesis.