Testing for normality
Before setting out on a discussion of tests for normality, we must consider briefly the consequences of non-normality. Clearly, if we know that the distribution of the disturbances is, say gamma, then a different model, and different methods, should be used than those discussed in this volume. However, in many situations we may have at least ‘near’ normality, and we wish to know how serious the effect of deviation from normality might be. Box and Watson (1962) showed that this depends on the distribution of the explanatory variables. If the explanatory variables can be regarded as approximately normal, then the F-test for multiple regression is insensitive to non-normality. If the explanatory variables cannot be so regarded, then there can be a substantial effect on the ‘F-test’ distribution.
Unable to display preview. Download preview PDF.
- Barnett, F. C. Mullen, K. and Saw, J. G. (1967) Linear estimation of a population scale parameter. Biometrika, 54, 551–554.Google Scholar
- Bowman, K. O. and Shenton, L. R. (1975) Omnibus test contours for departures from normality based on (b1) and b2. Biometrika, 62, 243–250.Google Scholar
- Box, G. E. P. and Watson, G. S. (1962) Robustness to non-normality of regression tests. Biometrika, 49, 93–106.Google Scholar
- B.S.I. (1982) Draft BS2846: British Standard guide to statistical interpretation of data. Part 7: Tests for departure from normality (ISO/DIS 5479). Obtainable from British Standards Institution, Sales Department, Linfood Wood, Milton Keynes, MK14 6LR.Google Scholar
- Gurland, J. and Dahiya, R. C. (1972) Tests of fit for continuous distributions based on generalized minimum chi-squared, in Statistical Papers in Honour of George W. Snedcor (ed. T. A. Bancroft ). State University Press, Iowa, pp. 115–128.Google Scholar
- Hahn, G. J. and Shapiro, S. S. (1967) Statistical Models in Engineering. Wiley, New York.Google Scholar
- Harter, H. L. (1961) Expected values of normal order statistics. Biometrika, 48, 151–165.Google Scholar
- Hastings, C. (1955) Approximation for Digital Computers. Princeton University Press, Prinction, NJ.Google Scholar
- Kendall, M. G. and Stuart, A. (1969) The Advanced Theory of Statistics, Vol. I, 3rd edn. Griffin, London.Google Scholar
- Royston, J. P. (1983). A simple method for evaluating the Shapiro-Francia W’-test for non-normality. J. Inst. Statist., 32, 297–300.Google Scholar
- Seber, G. A. F. (1977) Linear Regression Analysis. Wiley, New York.Google Scholar
- Shapiro, S. S. and Wilk, M. B. (1965) An analysis of variance test for normality (complete samples). Biometrika, 52, 591–611.Google Scholar
- Kennard, K. V. C. (1978) A review of the literature on omnibus tests of normality with particular reference to tests based on sample moments. M.Sc. dissertation, University of Kent.Google Scholar