t-Test for Independent Samples

This statistical test is used when examining the relationship between two independent samples, such as comparing average income among high school graduates to college graduates.

[latexpage]$t = \cfrac{\overline{X}_1 – \overline{X}_2}{\sigma _{\overline{X}_{1}-\overline{X}_{2}}} \:  \: = \cfrac{\overline{X}_1 – \overline{X}_2}{\sqrt{ \cfrac{s_{1}^{2}}{n_1} + \cfrac{s_{2}^{2}}{n_2} }}$