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I am a statistician and doing some data analysis in cognitive sciences. I noticed that the distribution of response time (RT) is chisq-squared-like, and I want to do Box-cox transformation to make it look normal distributed. Because before I did not think much for this transform, my question is:

  • Does a box-cox transformation need to be applied to response times?
  • If so, what do the results mean?
  • For t-test, ANOVA and other tests, will the result be valid for the original response time data?
  • If not, should we transform the data since analysis of these data is based on the normality hypothesis?
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    $\begingroup$ Welcom to CogSci! Your question is on topic here, but in case you don't get a suitable answer over the course of some time, you can ask for migration to CrossValidated which is a SE site specializing in statistics. $\endgroup$
    – Steven Jeuris
    Jul 7, 2014 at 9:50

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This article by Whelan (2010) is one of the best introductory papers I've found on the subject. Normalization is covered quite clearly and extensively, including the caveats and "gotchas".

References

  • Whelan, R. (2010). Effective analysis of reaction time data. The Psychological Record, 58(3), 9.
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You can transform RT, i.e., by log(1/RT). This makes the distribution roughly normal. The problem is that you don't usually run the ANOVA on the RT values collected at each trial, but on the average for each participant. So the distribution across participants need to be normal. A trick is to transform the single RT values, calculate the mean for each participant and condition, and then transform the value back with the inverse.

Alternatively, you can run ANOVAs without corrections if you use the appropriate one (i.e., normality not assumed... this will lead to oddly-looking DOF with decimal values).

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My impression is that, recently, a consensus began to form recently that RTs should be transformed to satisfy model assumptions. This is especially true when data is analyzed with mixed models instead of ANOVAs.

Concerning the stability of effects under different transformations, you may find this paper interesting: http://web.uvic.ca/psyc/masson/KMR10.pdf

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[ I realize that I am 7 years late, but I still think this is worth responding to in case anyone comes across this in the future]

No. As Max Di Luca pointed out, we perform our analyses on the mean (or median) RTs, not the underlying distributions of each individual's data (unless you are doing linear-mixed effects). Furthermore, transforming them tosses away information. What if the underlying effect is due to the effect only occurring on 10% of the trials? If the effect lengthens the RTs, it will increase the mean, but by transforming the RTs (e.g. 1/RT) then you've effectively compressed the right tail, reducing the influence of those trials. But, it might be those very trials that are driving the effect in the first place!

For outliers, I use a robust method such as MAD (e.g. +/- 3 MAD sds).

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  • $\begingroup$ Transformations that be inverted like a log transform do not cause a loss of information, but taking the mean or median of a distribution certainly does. If the information on the effect is in the tail than you need to analyze the whole distribution, not let it get lost in the mean. $\endgroup$
    – Bryan Krause
    Jun 24 at 6:18

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