FAQ/Simon - CBU statistics Wiki

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High levels of skewness (symmetry) and kurtosis (peakedness) of regression/ANOVA model residuals (which may be saved in SPSS) are not desirable and can undermine these analyses. SPSS gives these values (see CBSU Stats methods talk on exploratory data analysis at [http://www.mrc-cbu.cam.ac.uk/Statistics/Resources/Lectures2005/2-eda-PW.ppt Exploratory Data Analysis]). [http://www.childrens-mercy.org/stats/ Steve Simon] gives some sound advice on checking normality assumptions including rules of thumb on just how large skew and kurtosis must be to start worrying about doing statistical analyses. His main points are reproduced below:

  • There are no official rules about cut-off criteria to decide just how large skew or kurtosis values must be to indicate non-normality.
  • Avoid using a test of significance, because it has too much power when the assumption of normality is least important and too little power when the assumption of normality is most important.
  • I generally don't get too excited about skewness unless it is larger than +/- 1 or so.

[Note: Hair Jr, JF, Anderson, RE, Tatham, RL, Black WC (1998) Multivariate Data Analysis Fifth Edition. Prentice-Hall:New Jersey give same cutoffs for skewness].

  • SPSS defines kurtosis in a truly evil way by subtracting 3 from the value of the fourth central standardized moment. A value of 6 or larger on the true kurtosis (or a value of 3 or more on the perverted definition of kurtosis that SPSS uses) indicates a large departure from normality. Very small values of kurtosis also indicate a deviation from normality, but it is a very benign deviation. This indicates very light tails, as might happen if the data is truncated or sharply bounded on both the low end and the high end.
  • Don't let skewness and kurtosis prevent you from also graphically examining normality. A histogram and/or a Q-Q plot are very helpful here.

[:FAQ/Simon/question: What about if most the variables that I have are normal and a few of them are not? In this case, is it possible to use the parametric tests?]