Population Comparison
Let X_1 and X_2 be the number of successes in variates taken from two populations. Define
p^^_1 = (x_1)/(n_1)
(1)
p^^_2 = (x_2)/(n_2).
(2)
The estimator of the difference is then p^^_1-p^^_2. Doing a so-called z-transform,
where
| sigma_(p^^_1-p^^_2)=sqrt(sigma_(p^^_1)^2-sigma_(p^^_2)^2). |
(4)
|
The standard error is
SE_(p^^_1-p^^_2) = [画像:sqrt((p^^_1(1-p^^_1))/(n_1)+(p^^_2(1-p^^_2))/(n_2))]
(5)
SE_(x^__1-x^__2) = [画像:sqrt((s_1^2)/(n_1)+(s_2^2)/(n_2))]
(6)
s_(pool)^2 = [画像:((n_1-1)s_1^2+(n_2-1)s_2^2)/(n_1+n_2-2).]
(7)
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References
Gonick, L. and Smith, W. The Cartoon Guide to Statistics. New York: Harper Perennial, pp. 162-171, 1993.Referenced on Wolfram|Alpha
Population ComparisonCite this as:
Weisstein, Eric W. "Population Comparison." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/PopulationComparison.html