Even though research interest is typically greatest for questions pertaining to central tendency and, to a lesser degree, variability, knowledge about the nature of a measure or variable is impoverished when information about the shape of the frequency distribution is ignored. This paper makes the point that descriptive and inferential measures of non-normality should be a routine part of research reporting, along with graphic displays of the frequency distribution of important variables. This point is especially true for research involving measures with non-arbitrary metrics where the shape of the distribution is not affected by measurement artifacts.
Get full access to this article
View all access options for this article.
References
1.
BMDP Statistical Software . (1988a). SOLO Statistical System: Version 2.0. Los Angeles: J. L. Hintze.
2.
BMDP Statistical Software . (1988b). BMDP statistical software manual: Volumes 1 and 2. Berkeley: University of California Press.
3.
Box, G. E. P. (1953). Non-normality and tests for variance. Biometrika, 40, 318-335.
4.
Box, G. E. P. , Hunter, W. G., and Hunter, J. S. (1978). Statistics for experimenters. New York: Wiley.
5.
Conover, W. J. (1980). Practical nonparametric statistics (2nd ed.). New York: Wiley.
6.
Cuneo, M. and Feldman, D. S. (1986). Stat View 512+ [manual]. Calabasas, CA: Brain Power, Inc.
7.
D'Agostino, R. B. (1982). Tests for departures from normality. In S. Kotz and N. L. Johnson (Eds.). Encyclopedia of Statistical Sciences. New York: Wiley.
8.
Elmore, P. B. and Woehlke, P. L. (1988). Statistical methods employed in AERJ, ER, and RER from 1978 to 1987. Educational Researcher, 17, 19-20.
9.
Ferguson, G. A. (1981). Statistical analysis in psychology and education (5th ed.). New York: McGraw-Hill.
10.
Glass, G. V. and Hopkins, K. D. (1984). Statistical methods in education and psychology (2nd ed.). Englewood Cliffs, NJ: Prentice Hall.
11.
Glass, G. V. , Peckham, P. D., and Sanders, J. R. (1972). Consequences of failure to meet assumptions underlying the fixed effects analysis of variance and covariance. Review of Educational Research, 42, 237-288.
12.
Goodwin, L. D. and Goodwin, W. L. (1985a). An analysis of statistical techniques used in the Journal of Educational Psychology, 1979-1983. Educational Psychologist, 20, 13-21.
13.
Goodwin, L. D. and Goodwin, W. L. (1985b). Statistical techniques in AERJ articles, 1979-1983: The preparation of graduate students to read educational research literature. Educational Researcher, 14, 5-11.
14.
Groeneveld, R. A. and Meeden, G. (1984). Measuring skewness and kurtosis. The Statistician, 33, 391-399.
15.
Hays, W. L. (1981). Statistics. New York: Holt, Rinehart, and Winston.
16.
Hilderbrand, D. K. (1986). Statistical thinking for behavioral scientists. Boston: Duxbury.
17.
Hogg, R. V. and Tanis, E. A. (1983). Probability and statistical inference. New York: Macmillan.
18.
Hopkins, K. D. and Durand, A. (1989). Robustness and power of variance tests of homogeneity of variance. Boulder: Laboratory of Educational Research, University of Colorado.
19.
Hopkins, K. D. , Glass, G. V., and Hopkins, B. R. (1988). Basic statistics for the behavioral sciences (2nd ed.). Englewood Cliffs, NJ: Prentice-Hall.
20.
Kendall, M. G. and Stuart, A. (1977). The advanced theory of statistics: Distribution theory. London: Charles Griffin.
21.
Kirk, R. (1984). Elementary statistics. Monterey: Brooks/Cole.
22.
Kotz, S. and Johnson, N. L. (Eds.). (1982). Kurtosis. Encyclopedia of statistical sciences: Vol. 4. New York: Wiley, 425-426.
23.
Lilliefors, H. W. (1967). On the Kolmogorov-Smirnov test for normality with mean and variance unknown. Journal of the American Statistical Association, 64, 399-402.
24.
MacGillivray, H. L. (1982). Mean, median, mode, and skewness. In S. Kotz and N. L. Johnson (Eds.). Encyclopedia of statistical sciences. New York: Wiley.
25.
Martinez, J. and Iglewicz, B. (1981). A test for departure from normality based on a biweight estimator of scale. Biometrika, 68, 331-333.
26.
Newell, K. M. and Hancock, P. A. (1984). Forgotten moments: A note on skewness and kurtosis as influential factors in inferences extrapolated from response distributions. Journal of Motor Behavior, 16, 320-335.
27.
Pearson, K. (1895). Contributions to the mathematical theory of evolution, II: Skew variation in homogeneous material. Philosophical Transactions of the Royal Society of London, 186, 343-414. [See Kendall and Stuart, 1977, p. 85.]
28.
Pearson, E. S. and Hartley, H. O. (1966). Biometric tables for statisticians (3rd ed.). Cambridge, England: Cambridge University Press.
29.
Rafferty, J. , Norling, R., McMath, C., Tamaru, R., and Morganstein, D. (1985). STATWORKS [manual]. Philadelphia, PA: Cricket Software, Inc.
30.
SAS Institute . (1988). SAS procedures (Release 6.03 ed.). Cary, NC: SAS Institute, Inc.
31.
SAS Institute . (1985). SAS user's guide: Basics. Cary, NC: SAS Institute, Inc.
32.
Shapiro, S. S. , Wilk, M. B., and Chen, H. J. (1968). A comparative study of various tests of normality. Journal of the American Statistical Association, 63, 591-611.
33.
Siegel, S. (1956). Non-parametric statistics for the behavioral sciences. New York: McGraw-Hill.
34.
Snedecor, G. W. and Cochran, W. G. (1980). Statistical methods (7th ed.). Ames, IA: The Iowa State University Press.
35.
SPSS Incorporated . (1988). SPSSIPC+ V2.0 base manual for the IBM PCIXTIAT and PS/2. New York: McGraw-Hill.
36.
Tukey, J. W. (1977). Exploratory data analysis. Reading, MA: Addison-Wesley.
37.
Wilkinson, L. (1988a). SYGRAPH. Evanston, IL: SYSTAT, Inc.
38.
Wilkinson, L. (1988b). SYSTAT. Evanston, IL: SYSTAT, Inc.
39.
Willson, V. L. (1980). Research techniques in AERJ articles: 1969 to 1978. Educational Researcher, 9, 5-10.
