A Large Sample T-Statistic Which Is Insensitive to Non-Randomness

Published in: Journal of the American Statistical Association, v. 46, June 1951, p. 79-88

Posted on RAND.org on January 01, 1951

by J. E. Walsh

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Most of the well known significance tests and confidence intervals for the population mean are based on the assumption of a random sample. This paper considers how the significance levels and confidence coefficients of the commonly used class of tests and intervals based on the standard Student t-statistic are changed when the random sample requirement is violated and the number of observations is large. It is found that even a slight deviation from the random sample situation can result in a substantial significance level and confidence coefficient change. Thus this class of tests and confidence intervals would seem to be of questionable practical value for large sets of observations. Large sample tests and confidence intervals for the mean which are not sensitive to the random sample requirement are obtained for a situation of practical interest by development of a special type of t-statistic. These results are as efficient (asymptotically) as those based on the standard t-statistic for the case of a random sample.

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