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unfortunately I'm a statistics beginner. I am trying to transform my data. Here, according to Boxcox, a transformation with negative lambda has resulted ( L =-0.25).

But If I now run a T-tests with the transformed data, the results are exactly the other way around than expected --> that makes sense, because of the minus in the variable --> higher values are lower afterwards. But does anyone have an idea how I can interpret or transform the results, to get it right?

kjetil b halvorsen
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Sophia H
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  • Could you clarify what you mean by "other way around than expected"? There is, after all, no reason to suppose that the averages of the $-1/4$ powers of data will have any determinate relationship to the averages of the original data. What, then, do you mean by "get it right"?? – whuber Nov 12 '21 at 14:34
  • Data was previously transformed with L=-0.25. Consequently, a value such as 400 --> 0.224; a value such as 200 -->0.265. I want to compare these two. Thus, the second value is larger in the transformed form, although it was smaller before. If I now do a T-test of the transformed data it shows me a significant difference, but in the opposite way. Consequently, I cannot interpret the result directly and would have to transform it back or I don't know (?) Or did I do something wrong? – Sophia H Nov 12 '21 at 16:13
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    You aren't describing a Box-Cox transformation. Those are constructed to preserve the order of the data. See https://stats.stackexchange.com/a/467525/919 for instance. (The plots near the end include graphs of the $\lambda=-1/2$ transform, which will behave much like $\lambda=-1/4.$) Regardless, a t-test (or any test) comparing the means of the transformed data is not equivalent to a comparison of the means of the untransformed data. Thus, you have to decide what test you really need to perform. – whuber Nov 12 '21 at 16:27
  • What do you mean with I not describe a BoxCox-Transformation? Pages told me, that I can use a L=-0,25. Also the BoxCox-Powertransformation told me to use L=-0,25 – Sophia H Nov 15 '21 at 10:40

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