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I currently have a experiment with a within subject design, where I repeatedly measure reaction times (RT). Reaction times for each category of reaction were measures multiple times. However now the problem is, that the mean of all reaction times for each subject may differ by quite a lot, as some person may react much slower altogether. The same goes for the standard deviation of each person.

Now I was thinking I could clean up the data by removing individual means and deviations. Removing the mean of each persons RT is quite simple by just substracting the mean for that person from each RT for that person. However this leaves the difference in personal deviation in the sample. I could reduce this by dividing by the personal deviation, thus getting z-scores based on individual man and deviation for all reaction times for each person. By calculating the means of each z-score for each category, I then could see if categories lie above the mean, or below it and how much they differ in terms of the individual standard-deviation from the mean.

Is this procedure acceptable to remove these individual factors from the analysis? Or is there another procedure, which should be used to clean up this kind of data?

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I'm not such a expert, but seems you can use standard score normalization
http://en.wikipedia.org/wiki/Normalization_%28statistics%29

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