Detecting significant reduction in reaction times

This gave me a mean difference of -0.04775 and a 95% CI of -0.05332.

-0.05332 is not a confidence interval, it is a single number! Did you mean standard error?

Sorry I meant -0.05332 is the bound of the confidence interval.

What's the other bound?

If the mean difference is about -0.048 and one bound of the 95% confidence interval is about -0.053, then I can guess that the other bound is going to be roughly -0.043. So your confidence interval is going to be something like (-0.053, -0.043) which excludes the value of zero difference. The correct interpretation is that there is evidence that there is a difference between the average reaction times for the random task and the repeated task.

We ran a one sided test as the hypothesis was one sided so only the one bound. I've concluded there is significant evidence to say repeated task had a lower reaction time as our p was <0.001.

However we were also asked to say how many individual participants exhibited the effect and it seems wrong to say anyone who had a decrease in times did. So I was wondering if it would be all the individuals whose difference was outside the CI bound so less than -0.05332.

Ok, that is fair enough, you have a one sided p-value upon which to base your conclusion. But note that one-sided confidence intervals do not really make sense. Confidence intervals give a sort of bound on the precision of an effect size estimate.



No, you can't use a confidence interval that way. I would encourage plotting a histogram of the raw differences and simply report how many differences were positive and how many negative.