## Quick Reference

An estimate obtained by combining information from two or more independent samples taken from populations believed to have the same mean. Observations *x*_{11}, *x*_{12},…, *x*_{1m} are randomly selected from a population. Their mean is *x¯*_{1}, given by Random observations from a second population are denoted by *x*_{21}, *x*_{22},…, *x*_{2n} and have mean *x¯*_{2}. If the two populations are believed to have the same mean, then a pooled estimate of the common mean is *x¯*, given by With *k* samples of sizes *n*_{1}, *n*_{2},…, *n** _{k}* and with means

*x¯*

_{1},

*x¯*

_{2},…

*x¯*

*, the pooled estimate is given by The unbiased estimate of the variance of the first population is*

_{k}*s*

^{2}

_{1}, given by The corresponding estimate for the second population is

*s*

^{2}

_{2}. If it is believed that the two populations have the same variance, but possibly different means, then the pooled estimate of common variance is

*s*

^{2}, given by In the case of

*k*samples, with the estimate from sample

*j*being

*s*

^{2}

*, the pooled estimate is given by See also hypothesis test.*

_{j}
*Subjects:*
Probability and Statistics.

## Related content in Oxford Index

##### Reference entries

Users without a subscription are not able to see the full content. Please, subscribe or login to access all content.