Confidence Interval on Difference Between Means, Independent Groups, Standard Deviation Estimated (5 of 7)

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The solution is to use the harmonic mean of the two sample sizes for n. The harmonic mean (n_h) of n₁ and n₂ is:



Therefore the formula for the estimated standard error of the difference between means is:



For the example of the confidence interval on the difference between memory spans of seven-year olds and nine-year olds, assume that one more seven year old was tested and the resulting memory span score was 3.

For these data, M₁ = 3.6, M₂ = 6.0, and M_d = -2.4

SSE₁ = (3-3.6)²+(3-3.6)²+(3 - 3.6)² +
(4 - 3.6)² + (5 - 3.6)² = 3.2.

SSE₂ = (5-6)²+(6-6)²+(6-6)²+(7-6)²= 2.0.