Would a paired t-test be appropriate if the variables had a range between 0 and 1? Suppose I have paired data $(X_1, \ldots, X_n)$ and $(Y_1, \ldots, Y_n)$ and I would like to compare if the means $\bar{X} = \frac{1}{n}\sum_{i=1}^nX_i$ and $\bar{Y} = \frac{1}{n}\sum_{i=1}^nY_i$ are significantly different.
The range of each variable is between 0 and 1: $X_i \in (0,1)$ and $Y_i \in (0,1)$.
In this case, would a paired t-test be appropriate due to the fact they range from 0 to 1?

Possibly appropriate, but not necessarily. There's two things to worry about: significance level, and power.

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*If the distribution is sufficiently skew (for example), the actual significance level might not be reasonably close to the desired one at some given sample size.


*The power properties of a t-test might be relatively poor compared to one based on a more suitable choice of distributional model.
