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?

## Best Answer

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

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.