Household expenditures (in Hong Kong dollars) of 20 single men and 20 single
women including fuel and light are reported in Table 2.5. This real data example is
taken from Hand et al. (1994, p. 44). We suspect that the distributions of the data
in the two groups have different locations as well as different scales. Moreover it is
suspected that the distribution functions associated with the populations behind the
samples may differ also in shape. Therefore this is a situation where a test for the
most general alternative hypothesis is more suitable than a test for the location-scale
problem (like the Lepage test or the Cucconi test, see Section 2.3).
A very familiar test for the general two-sample problem is the Kolmogorov–
Smirnov test which requires Assumptions A1 and A2 and it is based on the differences
between the empirical distribution functions (EDFs) of the two samples. If the random
variables X1 and X2 underlying the samples are continuous, the test is exact. In the
discrete case, or when in practice you have ties, the test is conservative (its significance
Table 2.5 Household expenditures (in Honk Kong dollars) of a group of men and a
group of women.