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Using SAS Choose Design ANOVA Compare Means Regression Examples
ANOVA Transformed Means      

Interpret transformed means.

You have done a statistical analysis using a transformation. The means produced by this analysis are on the transformed scale. For example, if your dependent variable had cm units and a log transformation was done, then the means are in log cm.

These are difficult to interpret. Two alternatives are widely used:

Alternative 1: Report the original means.

Alternative 2: The reverse transformation can be applied to the transformed means to convert them back to the original scale. This is referred to as back-transformation. %MMAOV does this for you, and reports the results on the page following the transformed means.


For example, here is least squares means output from a log transformed analysis. Untransformed means and back-transformed (BT) means are included along with the Estimates, which are the least squares means on the log scale. As you can see, the transformed means are meaningless, or at best difficult to interpret. Thus researchers report either untransformed results, or back-transformed.


The back-transformed means are not equivalent to means of the original variable, due to the mathematical "twisting" that has been done. For example, the log transformation will produce geometric means, not the usual arithmetic means . Geometric means are generally smaller, as they place less weight on large observations (necessary to reduce the influence of skewed data, the original reason for applying the transformation).

Choose the alternative that you are most comfortable with (probably the original means), or provides the fairest measure of treatment means. With either choice, all statistical test results must come from the transformed analysis, represented by the letter grouping, and ANOVA table tests.

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  H I N T S :
  The examples above are based on the CRD-Single-None example dataset.

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