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Finite population corrections for the Kolmogorov-Smirnov tests. (English) Zbl 1239.62051

Summary: We examine the standard Kolmogorov-Smirnov test for assessing the goodness of fit for an assumed distribution, as well as the associated test of the equality of two distributions, in the case of a sample drawn without replacement from a finite population. In particular, we calculate an appropriate finite population adjustment factor for correcting the usual test statistics and numerically assess its properties. In addition, we provide an example of the use of the adjustment factor in sample size calculations which demonstrates the importance of incorporating the finite population effects in circumstances where the desired accuracy requires a very high sampling fraction.

MSC:

62G10 Nonparametric hypothesis testing
62D05 Sampling theory, sample surveys
62G30 Order statistics; empirical distribution functions
65C60 Computational problems in statistics (MSC2010)
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References:

[1] DOI: 10.1111/1467-9892.00194 · Zbl 0971.62044 · doi:10.1111/1467-9892.00194
[2] DOI: 10.1081/STA-120002653 · Zbl 1008.62667 · doi:10.1081/STA-120002653
[3] DOI: 10.1080/01621459.1951.10500769 · doi:10.1080/01621459.1951.10500769
[4] DOI: 10.1214/aos/1017938922 · Zbl 0961.62041 · doi:10.1214/aos/1017938922
[5] DOI: 10.1016/S0167-9473(96)00077-1 · Zbl 0900.62232 · doi:10.1016/S0167-9473(96)00077-1
[6] DOI: 10.1111/1467-9469.00234 · Zbl 04564870 · doi:10.1111/1467-9469.00234
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