Checks assumptions for an
ANOVA analysis (R.W. Payne).
|Controls printed output (
||Which assumptions to test (
||Critical value for the test probabilities to decide whether to generate warning messages; default 0.025|
||Specifies the analysis to be checked; by default this will be the most recent
ACHECK checks some of the assumptions for an analysis of variance that has been performed by the
ANOVA directive. By default, the most recent
ANOVA analysis is checked. However, you can check an earlier analysis, by using the
SAVE option of
ACHECK to specify its save structure (saved using the
SAVE parameter of the earlier
The assumptions to check are controlled by the
ASSUMPTIONS option, with the following settings.
||performs Levene tests to check whether the residual variance seems to be affected by any of the terms in the analysis. With stratified designs it will make similar checks for the residual variation in the higher strata (e.g. for the whole-plot variation in a split-plot design).|
||performs a Shapiro-Wilk test to check for evidence that the residuals do not come from a Normal distribution.|
||performs two Levene tests to check whether the residual variance differs according to the size of the response. The data are divided into three groups (small, intermediate and large) according to the sizes of their fitted values. The tests compare the variance of the residuals in the first (small) group with those in the third (large) group, and the variance of the second (intermediate) group with the variance of other two groups combined.|
By default, they are all tested.
ACHECK produces warning messages if any of the tests generates a test probability less than or equal to the value specified by the
PROBABILITY option. The default value is 0.025 (i.e. 2.5%), which is the same as the value used for the similar messages that may occur with the summary of analysis in regression. It is important to realise that the estimated residuals (from either regression or analysis of variance) will be correlated. The Levene and Shapiro-Wilk tests assume that the residuals are independent Normally-distributed observations. Their test probabilities may therefore be too low – and generate too many significant results. So the use of a smaller critical probability value provides some protection against spurious messages.
Other output is controlled by the
||prints the detailed test results, and|
||prints a confirmatory message if there are no problems.|
Details about Levene tests can be found in Snedecor & Cochran (1989); also see O’Neill & Mathews (2002) for further information about the issues that arise in their use in balanced analysis of variance.
The Shapiro-Wilk test is performed by the
WSTATISTIC procedure, which uses the methods of Royston (1993, 1995).
If the y-variate in the
ANOVA was restricted, only the units not excluded by the restriction will be included in the checks.
O’Neill, M.E. & Mathews, K.L. (2002) Levene tests of homogeneity of variance for general block and treatment designs. Biometrics, 58, 216-224.
Royston, P. (1993). A toolkit for testing for non-normality in complete and censored samples. The Statistician, 42, 37-43.
Royston, P. (1995). A remark on Algorithm AS 181: the W-test for Normality. Applied Statistics, 44, 547-551.
Snedecor, G.W. & Cochran, W.G. (1989). Statistical Methods (eighth edition). Iowa State University Press, Ames.
Commands for: Analysis of variance.
CAPTION 'ACHECK example',!t('Plankton example from Snedecor & Cochran',\ '(1967, Statistical Methods, 6th Edition, p. 329);',\ 'also see Section 4.5 of the Analysis of Variance Guide.');\ STYLE=meta,plain SPLOAD '%gendir%/data/Plankton.gsh' BLOCKSTRUCTURE Haul TREATMENTSTRUCTURE Type ANOVA Number ACHECK [PRINT=tests; PROBABILITY=0.05]