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Could really do with some help from someone with more stats expertise than I have.

I have some data relating to a customer survey along a range of measures which are consolidated into a number of scales. Participants rated the company and its competitor along all measures.

I transformed the raw data by squaring it to reduce skew and kurtosis. I now want to analyze the differences between the measures by the company and its competitor using the delta. I used the delats from the transformed variables, but as I have skew in the delta scores do I transform the data again or should I have taken the difference on the raw, untransformed scores, and then transformed the deltas to reduce skew and kurtosis?

Also, given that I’ve got negative and positive deltas, could you recommend an appropriate method to transform the data?
Thanks in advance for any help you can give.

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What do you mean by "using the deltas"? Why not a set of paired t-tests? – Peter Flom Oct 14 '12 at 15:04
Were the original data positively skewed or negatively skewed, and how much? What was their level of kurtosis? Was it too peaked or too flat? Same questions for deltas, which I am guessing are differences. – Peter Flom Oct 14 '12 at 15:05
Hi Peter, The data was negatively skewed and peaked. Squaring the variables did the job nicely. I've done the paired T tests and that tells me something about the variances between customer pereceptions of the two companies. What I'm intereested in is understanding how the competitive position effects overall performance rating. I'm making an assumption that ratings of performance along a range of variables is relative to the competition each customer experiences. I was planning to use the differences between the customer and competitor scales to do a regression analysis. – Confuser Oct 14 '12 at 15:50
How well will your colleagues or clients who are interested in these customer survey results be able to interpret findings if the data are transformed? Sometimes it's better to sacrifice a little bit of validity when it comes to hypothesis testing in order to enhance interpretability. – rolando2 Oct 14 '12 at 15:54
Hi Rolando2, Yes that is a problem. The advantage I have is that all of the variables are consistently squared, so the explanation is fairly simple. – Confuser Oct 14 '12 at 15:56
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