Is a paired samples t-test suitable in this case? I have 3 tasks and want to find out which one is more effective (that is, to find which task people performed better in).
Just over 30 people have participated in all 3 tasks, and their performance gives a numerical score in each.
Would it be appropriate to use a paired samples t test to compare performance between tasks A and B, A and C and B and C? What would be the best way of approaching data analysis in this instance?
Thank you so much.
 A: I would recommend a linear mixed model, the participants representing the random effects. Then you would be able to get all three comparisons at once, with a pooled variance.
A: There are two options, which are appropriate in different scenarios:

*

*perform t-tests for each pair and use a multiple comparisons adjustment to correct for family-wise error rate


*perform a random-effects ANOVA test to compare all 3 groups, and if you get a significant finding, do pairwise t-test comparisons using the pooled variance and a multiple comparisons adjustment
In both cases, you end up doing pairwise t-test comparisons. The difference is whether you're using the individual-group variances in those t-tests or using the pooled variance from the ANOVA calculation. #1 would be more appropriate if you have reason to believe that the groups don't have the same variances. #2 would be appropriate if you believe there is a single variance, and information from the groups should be aggregated to estimate the pooled variance.
If you end up taking approach #1, then you'd use the unequal variances t-test (Welch's t-test).
There are other assumptions to satisfy, like normality of the data--or a large enough sample size for the central limit theorem to apply, such that the sample means are normally distributed. If you're doing this in a classroom setting, then n≥30 is a common threshold for assuming that the CLT applies. If you're in a research setting, then it's entirely possible n=30 is far too small; it depends on the underlying distribution. If you have information about that distribution, you can run simulations where you draw random samples from the underlying distribution with n=30, compute the mean for each, and look at the sampling distribution of the mean to evaluate whether it's normal.
There are many ways to correct for multiple comparisons. I think Tukey and Bonferroni's method are the most common, but someone with more experience could weigh in here.
