Deciding which t-test to choose for comparing two means from two sets of data I'm studying basic stats for a class I'm taking, and I have a question about t-tests.
So, say we have two sets of data, X and Y. We are trying to compare the means of the two sets, but say that X contains Nx of data points and Y has Ny of data points. The question is choosing whether a paired sample t-test or an independent sample t-test is better for the following situations:


*

*When Nx > Ny (or Nx < Ny, basically when they have diff. number of data points)

*When Nx == Ny


I've attempted to solve the question and here is my reasoning:


*

*Independent sample t-test, because the number of observations for each group is different, so the two groups have to be treated independently. The df would be (Nx + Ny) - 1.

*Paired sample t-test, because the number of observations is the same, and you can compare each pair of observations (X1 and Y1, X2 and Y2...). df would be Nx - 1 (or Ny - 1).


But I'm not very sure about number 2. The question does not give any more details about the two sets of data (doesn't say if they are related/dependent etc) so I'm not sure what I'm supposed to base my answer on. I understand that dependent (=paired) t-test is for repeated measures, for instance the same participants repeating the experiment and giving changed results. But I'm not sure how that concept relates to this question.
So, I want to clarify whether the type of t-test I choose is dependent on the number of data I have, since I can't find any information regarding this. This class doesn't cover stats in depth, so please do point me to any readings / resources if necessary. Thanks!
 A: You would use paired t-tests when the data are actually paired, not when the sample sizes merely happen coincidentally to be equal.
They can be paired in all manner of ways -- anything which would make the values within the pairing-condition even a little more alike than would be two random values (one from each of the two samples).
[If you happen to make a mistake and treat as paired values which are not paired or which are nominally paired but the pairing has no effect at all, this does not matter much -- so you might still do it in cases where you're unsure of whether the pairing condition produces an association or not, but you should not normally do it merely because the sample sizes are the same. If the samples are independent, you should use the independent test.]
Now imagine that you have sample sizes of 99 and 100. Are they unpaired? Well, it might instead be that there are 99 paired values and one extra value whose pair-partner was lost. It would be better to do a paired test in that case -- and potentially lose the stray observation, at least if the cause of the loss was "at random" -- unrelated to anything which would affect the inference you were performing. (Things would be much trickier if you had something more like 25 complete pairs and about 37 in each group that had lost a pair partner ... )
So just because the sample sizes aren't identical, it doesn't necessarily mean you couldn't have paired data either.
In the end you have to look at the situation, not the sample sizes.
