The Standard Error of the Difference Between Sample Means $\bar { X } _ { 1 } - \bar { X } _ { 2 }$

The standard error of the difference between sample means, $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ ,is calculated by the formula $\sigma _ { \bar { x } _ { 1 } - \bar { x } _ { 2 } } = \sqrt { \sigma _ { 1 } ^ { 2 } / n _ { 1 } - \sigma _ { 2 } ^ { 2 } / n _ { 2 } }$ where $\sigma _ { i } ^ { 2 }$ is the variance of population i (i = 1,2).