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Consider we have a one-way ANOVA, with 3 groups and 5 different participants each, and each solve 5 problems. If we measure the performance of solving each problem for each participant, would it be possible to do the following steps for normalizing the data?

1- Transforming the raw data values before computing the performances by method A

2- Obtaining the performance value from the transformed values of raw data

3- Transforming the obtained performance value by method B

(method A and B can be any methods in among of the transformation methods)

If it works for the test result, would the above steps be valid from the theory view? I mean this type of transforming both data and result.

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I FOUND THE ANSWER:

Actually, it really depends which kind of transformation we're going to use. If it's a non-linear transformation, the answer would be NO, IT'S NOT A VALID PRACTICE!

As doing two non-linear transformations, each on row data and performance values, can make the discussion of the ANOVA test results impossible, as it's nearly TOO HARD to convert the values back to the origin raw values.

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  • $\begingroup$ To what does "it" refer in "it's a non-linear transformation"? Your question mentions two transformations, not one. What distinction are you making between "row data" and "performance values"? The question is murky and this answer is impenetrable; together they are confusing. $\endgroup$
    – whuber ♦
    Commented Feb 16, 2015 at 18:49

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