Transformations are mathematical functions applied to your dependent variable. The purpose is to "twist" the data such that the transformed variable has a normal distribution with equal variance. Do not use transformations unless you found problems in Steps B or C (and possibly D2).
To run transformations, you will be changing your SAS program. The %MMAOV macro has several common transformations that can be specified by TRANSTYPE= and TRANSVALUE= options.
For example, an analysis with transformation requested might be:
%MMAOV (one, fwt, CLASS=house age air, FIXED=age, RANDOM=house house*age, TRANSTYPE=log, TRANSVALUE=5);
Choose the transformation type based on the appearance of the normality diagnostic plots in C:
- Log. If distribution is strongly positively skewed, then use TRANSTYPE=log or log10 if you prefer base 10 logs. Use TRANSVALUE= a number that when added to your original dependent variable, makes all values greater than 0 (because log of a negative number is undefined).
- Square root. If distribution is moderately positively skewed, then use TRANSTYPE=sqrt, and again TRANSVALUE= should give values of at least 0 when added to your dependent variable.
- Arc sine. If your original data are percentages, TRANSTYPE=arcsinsqrt is commonly used, and TRANSTYPE= a value that when divided into your dependent variable, gives square roots that are between 0 and 1. Of course your dependent variable must be positive so a square root can be calculated.
- Power. If you have tried the transformations above, and none produce adequate normality and equal variance, then try TRANSTYPE=power, and TRANSVALUE= raises your dependent variable to that power. Try values between -3 and 3. Note that a value of .5 is equivalent to the SQRT transformation.
- Box-Cox. This is an alternative to Power, which automatically searches power transformations between -3 and 3, chooses the best value, and runs the analysis with that value. Note that experience suggests this often does not find a transformation that corrects diagnostic problems, so review diagnostics after this transformation carefully. You can request a wider search using the TRANSVALUE= option, for example TRANSVALUE=-5 to 5 by .1.
- Rank. If none of the above work, then use TRANSTYPE=rank. The rank transformation will produce a nonparametric test, that is relatively unaffected by normality and equal variance concerns. Use this as a last resort, since tests will have lower power, but ranks allow any diagnostic problems to be ignored.
You need to try one transformation at a time, typically working in order down the list above, re-running your SAS analysis each time. Attempt to find a transformation that gives both a high W value, and also gives sufficiently equal variances. If no transformation can be found, use the rank transformation.
Return to Step 7c in your analysis module, using your browser's Back button,
or clicking on the ANOVA or Choose Design tabs to start over.
Repeat all of the SAS steps but include in the % MMAOV statement the
appropriate TRANSTYPE= and TRANSVALUE= options as illustrated above.
Diagnostics will need to be re-checked on the new analysis.