The standard error of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is equal to the standard error of the difference $\bar { X } _ { 2 } - \bar { X } _ { 1 }$ .

Question

Quizplus · Accepted Answer

The standard error of the difference $\bar { X } _ { 1 } - \bar { X } _ { 2 }$ is computed using the standard deviations and sample sizes of both samples. Similarly, the standard error of the difference $\bar { X } _ { 2 } - \bar { X } _ { 1 }$ is also computed using the same values. Since the formula for both is the same, and the values used in the formula are the same, the standard error of the difference is the same regardless of the order of the averages. Therefore, the statement is true.

The Standard Error of the Difference Xˉ1−Xˉ2\bar { X } _ { 1 } - \bar { X } _ { 2 }Xˉ1​−Xˉ2​

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