# Tests of Differences between Means, Independent Groups, Standard Deviation
Estimated (6 of 8)

The formula:

cannot
be used without modification since there is not one value of n but two: (n

_{1} and n

_{2}). The
solution is to use the

harmonic mean of
the two sample sizes. The harmonic mean (n

_{h}) of
n

_{1} and n

_{2} is:

The formula for the estimated standard error of the difference
between means becomes:

The hypothetical data shown below are from an experimental group
and a control group.

Experimental |
Control |

3
5
7
7
8 |
3
4
6
7 |

n

_{1} = 5, n

_{2} = 4, M

_{1} = 6,
M

_{2} = 5,

SSE

_{1} = (3-6)² +
(5-6)² + (7-6)² + (7-6)² +
(8-6)² = 16,

SE

_{2} = (3-5)² +
(4-5)² + (6-5)² + (7-5)² = 10