Lets say I measure peoples reaction time across 2 manipulations (condition 1 and condition 2) within subjects (i.e. the same participant completes both conditions). My prediction is the RT measure in condition 2 is significantly more variable than it is in condition 1

A bit more detail about my setup...each person completes 5 trials per condition. Within each trial, they are pressing a button in response to a stimulus. They do this 20 times each trial, and I take the average of the 20, which is their mean reaction time for that trial. Over the course of the experiment, this means I would get 5 mean reaction times per condition (1 for each trial). I then average over these 5 to get a mean RT for that person, for that condition. Repeat for the second condition.

Ultimately, I end up with 2 numbers per participant (1 for each condition) which is the mean of (mean) RTs across all the sub trials. I want to see whether the variability of mean RT scores is greater in one condition vs. the other across all of my participants.

Here is an example of my data layout:

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What would be the correct way to test this?

Could it simply be an F test, with the Fvalue tested being var(1)/var(2)? Could Levene's test be used for this?

Given that condition is a within subjects factor, should I be averaging the sub trials the way that I am? Because if I calculate variance of condition 1, thats the variance across all participants, rather than for the individual subject. So I feel like I'm actually losing the benefit of using a within subjects/repeated measures design by doing this. The reason for doing it this way is due to concerns about violating independence if multiple rows correspond to the same subject


1 Answer 1


I think there are two ways of looking at this.

  1. You could an F test as you suggested on the two columns. If you want to do this using SPSS you would need to re-format the data so that it looked like between-subjects data, and look at the result of Levene's test (which relates to the difference in variances, not their proportion as your formula suggests).
  2. But I think what would be closer to what you have in mind is to go back to the original data on which you calculated the mean for each participant in each condition. Use the same figures to calculate a variance for each participant in each condition (or an SD, it wouldn't matter much), then do a within-subjects Anova on those variances.
  • $\begingroup$ I thought Levene's test is just an F test, both of which get an F value from the ratio of 2 variances? i.e. theyre not directly test the difference between 2 means? $\endgroup$
    – Simon
    Aug 16, 2016 at 22:50
  • $\begingroup$ Either way, are there any interpretation differences between the 2 approaches you mentioned? $\endgroup$
    – Simon
    Aug 16, 2016 at 22:51
  • $\begingroup$ Sorry, I put this aside so I don't know if this is water under the bridge now. Yes, Levene's is an F test on the variances, which tells you whether one variance is significantly different from another. Therefore method (1) looks at each subject's mean, and asks if those means are more variable between subjects in one condition than the other. Method (2) looks at each subject's variance (or SD) and asks whether those variances tend to be bigger in one condition than the other. $\endgroup$
    – MikeG
    Sep 14, 2016 at 16:50

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