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# Detecting significant reduction in reaction times watch

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1. Hi all,

So I have been given data sets of people's reaction times to a random task and their reaction times to a repeated task. I have been asked to say how many showed an improvement in reaction time on the repeated task.

I first ran a paired t-test for repeated reaction time - random reaction time. This gave me a mean difference of -0.04775 and a 95% CI of -0.05332. Would I be correct in saying from this that any participants whose: repeated reaction time - their random reaction time<-0.05332 showed a significant improvement?
2. (Original post by jamiep151)
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?
3. (Original post by Gregorius)
-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.
4. (Original post by jamiep151)
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.
5. (Original post by Gregorius)
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.
6. (Original post by jamiep151)
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.
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.

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.
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.
7. (Original post by Gregorius)
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.
Ok thanks!

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