Standard Error of the Difference Between the Means of Two Samples

The logic and computational details of this
procedure are described in Chapter 9 of
Concepts and Applications.

The difference between the means of two samples, A and B, both randomly drawn from the same normally distributed source population, belongs to a normally distributed sampling distribution whose overall mean is equal to zero and whose standard deviation ("standard error") is equal to

  square.root[(sd2/na) + (sd2/nb)]


  sd2 = the variance of the source population (i.e., the square of the standard deviation);
  na = the size of sample A; and
  nb = the size of sample B.

To calculate the standard error of any particular sampling distribution of sample-mean differences, enter the mean and standard deviation (sd) of the source population, along with the values of na and nb, and then click the "Calculate" button.

-1sd mean +1sd
<== source
<== sampling
standard error of sample-mean differences = ±
sd of source
sd = ±


size of sample A =
size of sample B =

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