Is there a minimum number of subjects required for a t-test?

#1
Hi everyone,

I am carrying out a piece of research on the effects of heel pain on the way we walk. I have two groups, 8 in the heel pain group and 15 in the non-heel pain group and am looking at data such as step length, foot angles and amount of steps per minute.

The plan was to carry out a unpaired t-test on the results gained however someone has commented that we may not have enough subjects to carry this out. Is there a minimum number of subjects needed to carry out a t-test? Also because people have two feet we have two sets of data for each subject will this make our t-tests more accurate?

Any help would be appreciated
 
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CowboyBear

Super Moderator
#2
There isn't an exact minimum per se - the problem is that when you have small samples you have low statistical power, and a higher chance of failing to reject the null hypothesis (equal group means on your outcome variables) even if the population means are not equal - i.e. higher chances of Type 2 error.

What you probably need to is a power analysis - this site has an online calculator you can use. This'll require estimating the mean values and standard deviations for each population (heel pain/normal), which you can do based on the existing literature in the area or informed guesstimates. The calculator then spits out a statistical power figure that indicates the chance of rejecting the null hypothesis given that the null hypothesis is false (or more accurately, that the alternative hypothesis is true at the specified level).

If you find you have statistical power under around 80% for any of the analyses, you probably have a problem. The power depends heavily on the mean difference and standard deviations of the groups - so if you expect large differences between the groups and small standard deviations within them, you might be ok. If not... :( - 8 is definitely a rather small sample sub-group, I'm afraid.
 
#3
Thanks

Have done the power test as recommended. The results showed that we cannot reject the null hypothesis. With probiblility set at 5% our results for the different measurement categories averaged about 16%. I was expecting this to be the case but just needed to use some sort of statistical analysis to prove it.
 
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