T ransformations and reporting results
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T ransformations and reporting results. more problem 3.26. The Box-Cox Transformation.

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T ransformations and reporting results

Transformations and reporting results

more problem 3.26


The box cox transformation
The Box-Cox Transformation

Sometimes a transformation on the response fits the model better than the original response. A commonly used transformation raises the response to some power. Box and Cox (1964) formalized and described this family of power transformations. (From JMP Help menu).


The functional form
The functional form

The transformed response variables are then:

when lambda is not zero and is ln(Y) if zero, and where

is the geometric mean.


What are common values of lambda
What are common values of lambda?

  • For Poisson data lambda=0, i.e. ln(Y)

  • For most growth data lambda=1/2

  • If variance decreases with the mean then lambda=-1.

  • For some percentage data, arcsin square root is the appropriate transformation.


Validity of statements of statistical significance
Validity of statements of Statistical significance

  • The validity of statements of significance depend on the validity (at least approximate validity) of the distributional assumptions.

  • If the raw data does not satisfy the assumptions, but the transformed data does, then report the significance for the transformed data.

  • This includes F-tests and tests of mean comparisons.

  • However, use the raw data in the report of the results.



Now the anova
Now the ANOVA



Report the untransformed mean values in the results
Report the untransformed mean valuesin the Results

Level Mean

4 5723.0000 A

3 2941.7500 A

1 159.7500 B

5 10.7500 C

2 6.2500 C


Why is this reasonable
Why is this reasonable?

  • The Box-Cox transformations are monotone, continuous functions.

  • Any ordered differences between means of Trt groups is therefore preserved.

  • Conclusions about Trt group mean differences are also therefore valid.


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