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170 2:57 Goodness-of-Fit Tests for Normality
level. Note, however, that this combined test is not recommended for samples of size
40 due to its poor power performance; it is given here for purposes of illustration only.
11.7 CONCLUSION
In this chapter, the generic concepts behind GOF tests together with several important
and popular GOF tests have been discussed. Such tests are essential for the appro-
priate statistical modeling of real-world data. This is a critical link in the Six Sigma
approach prior to any process of product optimization exercise which relies on rigor-
ous statistical models.
REFERENCES
1. Gao, Y., Lam, S.W. and Tang, L.C. (2002) A SWOT analysis to Six Sigma Strategy. Proceedings
of the 8th Asia Pacific Quality Organization Conference, pp. 197--207.
2. Goh, T.N., Tang, L.C., Lam, S.W. and Gao, Y. (2005) Core Six Sigma: a self assessment. 4th
Sino-Korea Bilateral Symposium on Quality, pp. 3--8.
3. Neyman, J. and Pearson, E.S. (1933) On the problem of the most efficient tests of statistical
hypothesis. Philosophical Transactions of the Royal Society, Series A, 231, 289--337.
4. Cochran, W. (1952) The chi square test of goodness of fit. Annals of Mathematical Statistics,
23, 315--345.
5. 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 risen from random sampling. Philosophical Magazine, Series 5, 50, 157--172.
6. Massey, F.J. (1951) The Kolmogorov--Smirnov test for goodness of fit. Journal of the American
Statistical Association, 46, 68--78.
7. Hahn, G.J. and Shapiro, S.S. (1967) Statistical Models in Engineering. New York: John Wiley
& Sons, Inc.
8. Box, G.E.P. and Liu, P.Y.T. (1999) Statistics as a catalyst to learning by scientific methods,
Part 1. An example. Journal of Quality Technology, 31, 1--15.
9. D’Agostino, R.B. and Stephens, M. (1986) Goodness-of-Fit Testing. New York: Marcel Dekker.
10. Watson, G.S. (1961) Goodness-of-fit tests on a circle. Biometrika, 48, 109--114.
11. Doob, J.L. (1949) Heuristic approach to the Kolmogorov--Smirnov theorems. Annals of Math-
ematical Statistics, 20, 393--403.
12. Feller, W. (1948) On the Kolmogorov--Smirnov limit theorems for empirical distributions.
Annals of Mathematical Statistics, 19, 177--189.
13. Kolmogorov, A. (1933) Sulla determinazione empirica di una legge disitribuzione. Giornale
dell’Istituto Italiano degli Attuari,4,1--11.
14. Murdoch, J. and Barnes, J.A. (1998) Statistical Tables. New York: Palgrave.
15. Stephens, M.A. (1974) EDF statistics for goodness of fit and some comparisons, Journal of
the American Statistical Association, 69, 347, 730--737.
16. Anderson, T.W. and Darling, D.A. (1952) Asymptotic theory of certain ‘goodness of fit’
criteria based on stochastic processes. Annals of Mathematical Statistics, 23, 193--212.
17. Shapiro, S.S. and Wilk, M.B. (1965) An analysis of variance test for normality (complete
samples). Biometrika, 52, 591--611.
18. Pearson, E.S. and Hartley, H.O. (1976) Biometrika Tables for Statisticians, Vol. 1. London:
Biometrika Trust.