Variance of a Weighted Mean

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Abstract
In many analyses of biological data observations of unequal accuracy must be combined to measure some overall effect. If the unequal variances are known exactly, the best method of combining the observations is to wt. each with the inverse of its variances. Since the variances are seldom known exactly, estimated variances are usually substituted. The author obtains an approx. unbiased estimate of the variance of a mean obtained in this fashion and shows that it is distributed approx. as an ordinary variance estimate with a number of degrees of freedom which may be also be estimated from the data. The method is applied to a plasma protein expt. taken from a standard text.