On Increasing Confidence in Confidence Intervals

A set of N data elements (xI +•.• + X~)/N and variance of the th The r moment of the data elements elements is used to estimate E(xr ). th r x1' •.•• xN has r moment E(x)= th r 2r 2 r r moment Var(x ) = E(x )-E (x ). in an arbitrary subset of k Over all the choices of the sample, the mean error is zero and the mean squared error N-k r k(N-I) Var(x). A little-known theorem by Marlow shows that the frequency distribution of values of the estimator is approximately normal with mean E(xr ) and variance var(xr ). All these results arc proved without assuming statistical independence among sampled datu elements. The conclusion is that confidence-interval calculators based on the normal distribution actually applies in more cases than is commonly believed. Work reported herein supported in part by NSF Grant MCS78-01729 at Purdue.University.