# Do t-test of two sample groups with variance 0 [duplicate]

I'm trying to do a Welch's t-test of two sample groups which turn to have estimated variance equal to 0.

As could be seen from wikipedia page of Welch's t-test: https://en.wikipedia.org/wiki/Welch%27s_t-test, the formula for calculating the t-stat:

$$t= \frac{\overline X_1 - \overline X_2}{\sqrt{\frac{s_1^2}{N_1} +\frac{s_2^2}{N_2}}}$$ contains 0 at the denominator and the t-stat could not be calculated (obviously my C++ program retuns me a NaN value...)

I need a way to handle this an calculate the t-test anyway, could you tell me how to proceed in these cases?