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#### ilacatd

I ran a Box Cox on Group 1 and got an optimum lambda of 0.171, and on Group 2 I got an optimum lambda of 0.231. I need to use only one lambda. So do I use the average of 0.171 and 0.231 = 0.201? The resulting A-D p-values are 0.470 and 0.262, which is a lot better than the raw data, but I?m not sure whether it?s optimal.

With Johnson Transformation, it?s much more complicated to find one optimum equation because there are so many factors in the equation. For Group 1, I got 2.79632 + 1.50848 * Log( ( X - 17.2401 ) / ( 2265.63 - X ) ), and for Group 2 I got -0.0969158 + 1.32128 * Asinh( ( X - 190.918 ) / 121.167 ). The A-D p-values are 0.534 and 0.431 respectively, which is better than the Box-Cox transformation. But I can?t figure out how to find the optimum Johnson Transformation for both groups ? the equations are so different.

Does anyone have any suggestions?

I?m also aware that transformations can be tricky, and that it?s best to use a single type of transformation which fits the type of data in question and then stick with it, rather than finding the ?optimum? equation for every data set. For example, break strength of round cables varies with the square of the diameter of the cable, so SQRT(X) is probably the best transformation equation. Bacteria multiplying in a Petri dish would have exponential growth, so would that be log(X)?, survival time to failure might be Weibull, etc. My test is burst pressure of a vessel, so I?m not sure which transformation is best ? I generally get good results with natural log, but it?s not that clear. Does there need to be a further justification for doing a transformation besides simply to improve normality for purposes of doing a t-test? Any comments on transformations in general and in choosing the most appropriate transformation for an ongoing series of tests would be appreciated.

Thanks.

Ari Goldberg