# Degrees of freedom with small variances

I am running a two-sample t-test with unequal variances. However, my standard deviations are so small (as in .03 in some cases) that I cannot get a number greater than 0 for the degrees of freedom (despite sample sizes in the hundreds and sometimes thousands), which makes it impossible to compute the p value.

What do I do here? Is there a different way to compute the degrees of freedom, or is there a way to manipulate the data so that the degrees of freedom formula actually gives me an appropriate number?

Degrees of Freedom is calculated as (s1^2/n1 + s2^2/n2)^2/((1/(n1-1))*s1^2/n1 + (1/(n2-1))*s2^2/n2)

• Can you give a reference for your formula? Sep 16, 2015 at 12:53

The formula for degrees of freedom for Welch's t-test given by Wikipedia is

$$\nu \quad \approx \quad {{\left( \; {s_1^2 \over N_1} \; + \; {s_2^2 \over N_2} \; \right)^2 } \over { \quad {s_1^4 \over N_1^2 (N_1-1)} \; + \; {s_2^4 \over N_2^2 (N_2-1) } \quad }}$$

The formula you give has the same numerator but quite a different denominator; and as a result it isn't unitless (which it should definitely be!). This makes the formula you used get small when you have small variances, which is the cause of your problem.

Use the correct formula and your problem should disappear.