Two‐sample problems in statistical data modelling

Abstract

A common problem in mathematical statistics is to check whether two samples differ from each other. From modelling point of view it is possible to make a statistical test for the equality of two means or alternatively two distribution functions. The second approach allows to represent the two‐sample test graphically. This can be done by adding simultaneous confidence bands to the probability‐probability (P — P) or quantile‐quantile (Q — Q) plots. In this paper we compare empirically the accuracy of the classical two‐sample t‐test, empirical likelihood method and several bootstrap methods. For a real data example both Q — Q and P — P plots with simultaneous confidence bands have been plotted using the smoothed empirical likelihood and smoothed bootstrap methods.

Keywords:

• two‐sample problem
• t‐test
• empirical likelihood
• quantile‐quantile plot
• probability‐probability plot
• simultaneous bands