Transforming Response-Time Data for normal distribution?

Question

I am a psychology student and currently working on my master thesis. I have developed an experimental paradigm (Dot-Probe Paradigm) in which participants have to react to words, that are presented on their screen.

I have different trial types of words:

misophonic (e.g. smacking) - neutral (congruent: Dot appears on the side of the misophonic stimulus)

misophonic - neutral (incongruent: Dot appears on the side of the neutral stimulus)

negative - neutral (congruent)

negative - neutral (incongruent)

neutral - neutral (Baseline)

In order to test, if all participants have the tendency to react quicker to negative words, I calculated the means of the trials:

negative - neutral congruent and negative - neutral - incongruent

Then I subtracted them:

Attentional Bias(neg): (Mean: negative - neutral - inkongruent) - (Mean: negative - neutral congruent)

Now I would like to do a one-sample t-test, but my Attentional Bias (neg) is not normally distributed.

I have read that I could do a log-transformation of my variable but I am not sure if I have to log transform my raw data, the means or the calculated AttentionalBias(neg) component.

So my question is: At what step of my analysis do I have to log-transform my data?

Any advice would be very much appreciated!

Answer 1

First, it's your residuals that need to be normal, not your data. https://stats.stackexchange.com/search?q=normal+residuals

For example, if you are doing a two-sample t-test and your data are bimodally distributed, that could very well be just because your two groups have different means. For regression problems with more parameters, you may see a very non-normal distribution in the data but yet the residuals are perfectly normal once you account for all your predicting variables.

You're right, though, that reaction times are typically not normally distributed. I would log transform the original values. Once you've log-transformed the data, the meaning of all of your comparisons changes. Namely, subtractions on the log scale are equivalent to ratios. This works well for time intervals, because it changes your interpretation from "group A is XX seconds longer than group B" to "group A is XX times longer than group B". This contains an inherent normalization for the length of A.

Generally, I would favor some form of ANOVA rather than reducing your problem to a one-sample t-test on a subtraction; there are a lot of problems in data that you can catch this way that you wouldn't notice with the one-sample test. Once you've subtracted, it's less clear where the actual differences are across the different dimensions of your data.