Introduction to Tests for Statistical Equality of Two or More Populations:
Two random variables X and Y having distribution F
X
(x) and F
Y
(y) respectively, are said to be
equivalent, or equal in rule, or equal in distribution, if and only if they have the same distribution
function. That is,
F
X
(z) = F
Y
(z), for all z,
There are different tests depending on the intended applications. The widely used tests for
statistical equality of populations are as follow:
1.
Equality of Two Normal Populations:
One may use the Ztest and Ftest to
check the equality of the means, and the equality of variances, respectively.
2.
Testing a Shift in Normal Populations:
Often we are interested in testing
for a given shift in a given population distribution, that is testing if a random
variable Y is equal in distribution to another X + c for some constant c. In other
words, the distribution of Y is the distribution of X shifted. In testing any shift in
distribution one needs to test for normality first, and then testing the difference in
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 Spring '08
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