Tables Describing Small Sample Properties Of The Mean Median Standard Deviation And Other Statistics In Sampling From Various Distributions

The note includes a collection of tables useful for study of the sampling distributions of some frequently-used statistics, with brief discussions of their construction and use: (1) The probability level P(epsilon, n) of any continuous parent distribution corresponding to level epsilon of the distribution of the median; (2) Probability points of certain sample statistics for samples from six distributions: normal and double-exponential (mean, median), rectangular (mean, median, midrange), Cauchy, Sech, Sech squared (median). In all the above tables, the sample size n = 3(2)15(10)95 and the probability levels are epsilon = .001, .005, .01, .025, .05, .10, .20, .25. Together with the tables listed under (2) are given the values of certain ratios useful for comparing the various statistics. (3) Probability that the standard deviation of a normal distribution will be underestimated by the sample standard deviation s and by unbiased estimators of sigma based on s, on the mean deviation, and on the sample range. Divisors are given for obtaining the corresponding 'median unbiased' estimators. (Author).