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A DISTRIBUTION‐FREE TWO‐SAMPLE GOODNESS‐OF‐FIT TEST FOR GENERAL ALTERNATIVES
Author(s) -
Gibbons Jean D.
Publication year - 1972
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1972.tb00480.x
Subject(s) - mathematics , statistics , f test of equality of variances , chi square test , test statistic , pearson's chi squared test , categorical variable , null distribution , kolmogorov–smirnov test , z test , null hypothesis , goodness of fit , sample size determination , sampling distribution , f test , statistic , conditional probability distribution , exact test , population , statistical hypothesis testing , demography , sociology
This paper presents a distribution‐free test of the null hypothesis that two independent samples are drawn from identical but completely unspecified populations. The test is a group randomization test, and the test statistic is a function of the sum of squared deviations between group relative frequencies in the samples. As its sampling distribution is conditional only upon the size of the groups formed and not on the individual observed values, the test is completely general and free of population distribution assumptions. It is applicable to categorical, discrete or continuous data, where the alternative does not specify the type of difference between populations. The complete exact null distribution of the test statistic is given for equal‐sized groups and equal sample sizes up to 12 each. The chi‐square approximation is investigated and seems sufficiently accurate for practical use in larger samples. Recommendations are made for the optimal number of groups to use. The merits of this test in comparison with the Kolmogorov‐Smirnov two‐sample maximum deviation test are fully explored.