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I have been using the box-cox transformation to normalise data for input to an Ecological Niche Factor Analysis software, as recommended by the software creators.

However, it has occurred to me that the box-cox transformation method has (obviously!) been selecting different lambda values for each transformation. For example, I want to compare the influence of factors A,B and C on individual location over four sample dates. Each factor has been separately box-cox-ised (separately both from other factors and other dates). Does this mean that the results of each factor analysis will not be comparable (and that simple comparison of the transformed data, e.g. by ANOVA, will not be possible) because of the selection of different lambda values for each transformation?

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  • $\begingroup$ Could you please clarify what you mean by "separately both from other factors and other dates"? Are you saying each of A, B, and C has been separately transformed, using different parameters, or are you saying the transformation of (say) A has varied by date? The distinction is crucial, because the answer in the first case is that you can make the desired comparison while in the second case the conclusions you can draw are more limited. $\endgroup$
    – whuber ♦
    Jun 21, 2012 at 15:16
  • $\begingroup$ Each of A, B and C has been transformed separately from one another using a box-cox method. Within each factor, the transformation was performed separately for each of the four dates (so 12 transformations in total). I hope this helps. Also, thank you to Michael Chernick. $\endgroup$
    – JSnf2012
    Jun 21, 2012 at 15:20
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    $\begingroup$ Then Michael is correct (+1). The fix is to go back and transform all the A values in the same way, all the B values, etc., and re-do the analysis. $\endgroup$
    – whuber ♦
    Jun 21, 2012 at 15:36

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Yes, if they are on different scales you logically cannot compare them. Had the transformations all been the same you could, since the power transform is monotonic. However, the sample variance changes because of the transformation and that would need to be accounted for. But in your situation, you cannot compare them.

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  • $\begingroup$ Ah, this confirms my fears. Thanks for your help Michael and whuber! $\endgroup$
    – JSnf2012
    Jun 21, 2012 at 16:15
  • $\begingroup$ It would probably be better for you to find a compromise transformation! and then use the same boxcox transform power for all the data sets. $\endgroup$
    – kjetil b halvorsen ♦
    Feb 25, 2017 at 14:27

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