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Using SAS Choose Design ANOVA Compare Means Regression Examples
ANOVA Diagnostics Start     3 of 8

B. Check for equal variance.

Just above the boxplot output, you should see the equal variance diagnostic:                                      

This lists standard deviations of the residuals for each treatment combination, along with the Levene Test for equal variance. Here the Levene Test has p-value=0.014, less than the usual 0.05 significance level, indicating potential problems with equal variance (reject Ho: variances are equal). However, this test (like most diagnostic tests) is overly sensitive, and can suggest there is a problem before the variances are unequal. Therefore it is recommended that more emphasis be placed on visually checking the standard deviations, and a common cutoff is that the variances are sufficiently equal as long as the standard deviations are within 5-fold of each other. Here we see a range in standard deviations of about 5 to 50, or 10-fold, so it appears there is a problem with equal variance.

Note that the unusually high variance treatment, Clover with No Supplement, is the treatment with outliers seen in Step A. This is an example of how the various diagnostics interrelate, and you need to keep in mind that fixing one problem is likely to fix all diagnostic problems.

In addition, the same boxplots as used in Step A provide equal variance information. The example here shows that standard deviations are displayed on the boxplots, and again check that the values are within 5-fold. Visually the width of the boxes also contains variance information, and can be used for a quick crude check of equal variance. Note that the boxplots are for treatment factors, whereas the table above is for treatment combinations.


 Verify that the stddev_y values are within 5-fold of each other, and that the Levene P is greater than 0.05.

    If so, treatment variances are sufficiently equal for the standard ANOVA to be valid.

    Even if the Levene P is less than 0.05, there still should not be any problem as long as the standard deviations are within 5-fold..

    If stddev_y values are not within 5-fold of each other and the Levene P is less than 0.05, then you will
      need to consider transformations described in Step D, but first see next screen to check normality.

 next >> ( Step C: Check for Normality )

  H I N T S :
  Why five-fold? Research has shown that ANOVA performs well even if variances are slightly unequal. Experience       suggests that up to five-fold is sufficiently equal.
  In your output, you will have as many standard deviations as treatments, but only one Levene P value for all      treatments.

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