3.5 General Two Sample Problem

For matched or paired sign and sign rank test the data consists of two samples but each element in one sample has linked with a particular element of the other sample by some unit association. This sampling situation can be described as a case of two dependent samples or as been sample of pairs from a bivariate population. During analysis differences of the paired observations are taken leaving a single set of observations. This type of data may be classified as a one sample problem.
Here we shall be concerned with data consisting of two mutually independent samples. i.e random samples drawn independently from each of the two populations. All the elements are independent of each other and between samples. This consists of two population \(X\) and \(Y\) population with edf \(F_X\) and \(F_Y\) respectively. We have a random sample of size \(m\) drawn from \(X\) population and other sample of size \(n\) drawn from \(Y\) population. \(X_1,X_2,\dots ,X_m\) and \(Y_1,Y_2,\dots ,Y_m\). The hypothesis of interest in the two sample problem is that the samples are drawn from identical populations. \(\text {i.e}\hspace {0.5cm} H_0:F_X(x)=F_Y(y)\hspace {0.4cm}\forall x\)

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