# The difference between means in t-test

When the sample size is large, the results tend to be statistically significant even when there is a small difference between the means of two groups. however, sometimes we see the results are not significant, despite the fact that the difference between the means of two groups is small with a large sample size. Can anyone describe its reason within a simple approach? Many thanks

• It also depends on the variability in the groups. – Sal Mangiafico Apr 21 at 21:17

$$t = \frac{m_a-m_b}{\sqrt{S^2/n_A + S^2/n_b}}$$