Abstract
Goodness-of-fit tests are batteries of tests that test that the distribution of a sample is equal to some fixed-in-advance distribution. We already saw Q–Q plots in Chap. 5 where the samples were compared to some theoretical distributions but in a descriptive fashion, without formal inference. In this chapter we discuss the celebrated Pearson's χ 2-test and the Kolmogorov–Smirnov (KS) test.
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Chapter References
Benford, F. (1938). The law of anomalous numbers. Proc. Am. Philos. Soc., 78, 551–572.
Hill, T. (1998). The first digit phenomenon. Am. Sci., 86, 358–363.
Hoaglin, D. C. (1980). A poissonness plot. Am. Stat., 34, 146–149.
Jarque, C. and Bera, A. (1980). Efficient tests for normality, homoscedasticity and serial independence of regression residuals. Econ. Lett., 6, 3, 255–259.
Kemp, W. A. and Kemp, D. C. (1991). Weldon's dice data revisited. Am. Stat., 45, 3, 216–222.
Kolmogorov, A. N. (1933). Sulla determinazione empirica di una legge di distributione. Gior. Ist. Ital. Attuari, 4, 83–91.
Kvam, P. and Vidakovic, B. (2007). Nonparametric Statistics with Applications to Science and Engineering. Wiley, Hoboken.
Lilliefors, H. W. (1967). On the Komogorov-Smirnov test for normality with mean and variance unknown. J. Am. Stat. Assoc., 62, 399–402.
Pearl, R. (1907). Variation and differentiation in Ceratophyllum. Carnegie Inst. Wash. Publ., 58, 1–136.
Pearse, G. E. (1928). On corrections for the moment-coefficients of frequency distributions. Biometrika, 20 A, 314–355.
Pearson, K. (1900). On the criterion that a given system of deviations from the probable in the case of a correlated system of variables is such that it can be reasonably supposed to have arisen from random sampling. Philos. Mag. Ser., 5, 50, 157–175.
Phillips, D. P. (1972). Deathday and birthday: an unexpected connection. In: Tanur, J. M. ed. Statistics: a guide to the unknown. Holden-Day, San Francisco, 52–65.
Risebrough, R.W. (1972). Effects of environmental pollutants upon animals other than man. Proc. Sixth Berkeley Symp. on Math. Statist. and Prob., vol. 6, 443–453.
Smirnov, N. (1939). On the estimation of the discrepancy between empirical curves of distribution for two independent samples. Bull. Math. Univ. Moscou, 2, 3–14.
Stansfield, W. D. and Carlton, M. A. (2007). Human sex ratios and sex distribution in sibships of size 2. Hum. Biol., 79, 255–260.
Struhsaker, T. T. (1965). Behavior of the vervet monkey (Cercopithecus aethiops). Ph.D. dissertation, University of California-Berkeley.
von Bortkiewicz, L. (1898). Das Gesetz der kleinen Zahlen. Teubner, Leipzig.
Yates, F. (1934). Contingency table involving small numbers and the Â2 test. J. R. Stat. Soc., 1 (suppl.), 2, 217–235.
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Vidakovic, B. (2011). Goodness-of-Fit Tests. In: Statistics for Bioengineering Sciences. Springer Texts in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0394-4_13
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DOI: https://doi.org/10.1007/978-1-4614-0394-4_13
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