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F. Transformations                                                              

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.

 

  H I N T S :
  If you do run a transformation, you will need to interpret the transformed means.
  See the Examples tab for a fully worked example of transformations.

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