# Performing a t-test with discrete (currency) data

I want to perform a 2 sample t-test assuming unequal variances, however my variable is currency. Currency is discrete, however when checking the assumptions of the t-test, I see that the data should be continuous.

Technically, they aren't continuous, but I guess it's closer to a ratio scale (maybe interval). Is this assumption violated? What else should I check?

• How much data do you have? Jun 12 '16 at 15:52
• n=24 for both variables. Jun 12 '16 at 15:53
• What do they look like (within the groups)? Are they vaguely normal looking? Jun 12 '16 at 15:54
• I ran a JB test, they both appear normal. Jun 12 '16 at 15:55
• What do you precisely mean by your "variable is currency." As in, your variable is measured in dollars and there cannot be fractions of a cent (discrete units are $1/100$ of a dollar)? And you're trying to compare the mean of two samples? Jun 12 '16 at 17:32

Discrete isn't continuous, so technically the assumption of the t-test is not met, and that's that. However, the t-test is fairly robust and having $N=48$ with equal groups is a decent sample, so it might be OK. After all, in practice all data are discrete at some level because we don't record data to infinite decimal places.
• Worth pointing out too that with more data, he could lean on asymptotic arguments. Under certain regularity conditions, the sample mean $\frac{1}{n}\sum_i x_i$ would converge to a normally distributed random variable even if $x$ were discrete. Jun 12 '16 at 17:44