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Thread: a theorem about pwer transformation

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    a theorem about pwer transformation




    Hi,

    while studying on Montgomery's Design and Analysis of experiments, i saw a theorem without proof of which I don't find the correct references. While discussing on how to use power transformations to data that exhibit heteroskedasticity due to a dependance of the variance to the mean, it stated that if the standard deviation of the data is proportional to (E[y])^a, then the standard deviation of y^b is proportional to (E[y])^(a+b-1), therefore to eliminate heteroskedasticity in this case one should set b=1-a.

    How can I prove this, or where can I find the proof? I can't find it even in the supplemental text material....

    Thanks in advance!

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    You would probably use the delta method or something analogous to it to show that result. Delta method

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