An estimate obtained by combining information from two or more independent samples taken from populations believed to have the same mean. Observations x11, x12,…, x1m are randomly selected from a population. Their mean is x¯1, given by Random observations from a second population are denoted by x21, x22,…, x2n 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 n1, n2,…, nk and with means x¯1, x¯2,… x¯k, the pooled estimate is given by The unbiased estimate of the variance of the first population is s21, given by The corresponding estimate for the second population is s22. If it is believed that the two populations have the same variance, but possibly different means, then the pooled estimate of common variance is s2, given by In the case of k samples, with the estimate from sample j being s2j, the pooled estimate is given by See also hypothesis test.
Subjects: Probability and Statistics.