Pooled sample estimate
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Pooling samples
Suppose we take two random samples from a population with unknown mean, [Equation goes here &- download the original to see it.], and unknown variance [Equation goes here &- download the original to see it.], then estimates for the joint mean and joint variance of the two samples are [Equation goes here &- download the original to see it.] where [Equation goes here &- download the original to see it.] is the unbiased estimator for the population mean [Equation goes here &- download the original to see it.] ; and [Equation goes here &- download the original to see it.] where, [Equation goes here &- download the original to see it.] is an unbiased estimator for the population variance [Equation goes here &- download the original to see it.] and [Equation goes here &- download the original to see it.] are the sample variances. Note, here, [Equation goes here &- download the original to see it.] are the sample variances, that is the biased estimators of the population variance; however [Equation goes here &- download the original to see it.] is an unbiased estimator of the population variance because of the subtraction of 2 from the divisor of the fraction (from the bottom of the fraction). So be begin by calculating the sample variances in the normal way, and then substitute into the formula for the pooled sample estimate, as will be illustrated below.
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Contents of
Pooled sample estimate
1 Pooled sample estimate &- Population and sample
2 Pooling samples
3 Example of pooled sample estimate
4 Pooled estimator of the population proportion
5 Second Example of pooled sample estimate
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