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

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The formula:



cannot be used without modification since there is not one value of n but two: (n1 and n2). The solution is to use the harmonic mean of the two sample sizes. The harmonic mean (nh) of n1 and n2 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

n1 = 5, n2 = 4, M1 = 6, M2 = 5,

SSE1 = (3-6)² + (5-6)² + (7-6)² + (7-6)² + (8-6)² = 16,

SE2 = (3-5)² + (4-5)² + (6-5)² + (7-5)² = 10

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