Editing Student's t-test (section)

====Equal sample sizes and variance====
Given two groups (1, 2), this test is only applicable when:
* the two sample sizes are equal,
* it can be assumed that the two distributions have the same variance.
Violations of these assumptions are discussed below.

The {{math|''t''}} statistic to test whether the means are different can be calculated as follows:

: <math> t = \frac{\bar{X}_1 - \bar{X}_2}{s_p \sqrt\frac{2}{n}}, </math>

where
: <math> s_p = \sqrt{\frac{s_{X_1}^2 + s_{X_2}^2}{2}}.</math>

Here {{math|''s<sub>p</sub>''}} is the [[pooled standard deviation]] for {{math|1=''n'' = ''n''<sub>1</sub> = ''n''<sub>2</sub>}}, and {{math|''s''{{su|b=''X''<sub>1</sub>|p=&nbsp;2}}}} and {{math|''s''{{su|b=''X''<sub>2</sub>|p=&nbsp;2}}}} are the [[unbiased estimator]]s of the population variance. The denominator of {{math|''t''}} is the [[Standard error (statistics)|standard error]] of the difference between two means.

For significance testing, the [[Degrees of freedom (statistics)|degrees of freedom]] for this test is {{math|2''n'' − 2}}, where {{math|''n''}} is sample size.