A Topical Dictionary of Statistics by Gary L. Tietjen

By Gary L. Tietjen

Data is the authorised physique of equipment for summarizing or describing information and drawing conclusions from the precis measures. every person who has info to summarize therefore wishes a few wisdom of facts. step one in gaining that wisdom is to grasp the pro jargon. This dictionary is geared to provide greater than the standard string of remoted and self sustaining definitions: it presents additionally the context, purposes, and similar terminology. The meant viewers falls into 5 teams with relatively various wishes: (1) specialist statisticians who have to remember a definition, (2) scientists in disciplines except data who want to know the suitable equipment of summarizing info, (3) scholars of statistics who have to develop their knowl­ fringe of their subject material and make consistent connection with it, (4) managers who may be analyzing statistical studies written through their staff, and (5) newshounds who have to interpret govt or medical experiences and transmit the knowledge to the general public.

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If there are k such samples rather than 2, we pro~eed in the same way, letting R; be the sum of the ranks of observations in the i-th sample, with N = Ln;. The test statistic is T = 12(N(N + 1) - I L(R~/ nJ - 3(N + 1). If T exceeds the critical value, the population medians are not equal. That generalization of the MannWhitney test is called the Kruskal-Wallis Test for k samples. The Bell-Doksum Test is a modification of the Kruskal-Wallis test that uses tabled values of Estlmation and Hypothesis Testing 41 the normal order statistics instead of ranks.

If 0 increases as p increases, the fiducial interval is given by L :::; 0 :::; U such that G(L) - G(U) = 1- u. Under the correct conditions the likelihood function L(O), scaled by L(O)dO, may be called the fiducial density: In that case the fiducial interval is given by the L and U such that r-oo r L(O) dO / foo L(O)dO = 1 - u. Kendall and Stuart have stated that "the fiducial distribution is not a probability distribution in the sense of the frequency theory of probability. It may be regarded as a distribution of probability in the sense of degrees of belief.

A second desirable criterion is to want an estimator T of 6 that is close, in some sense, to 6. One measure of closeness is the bias of the estimator T, defined as 6 - E(1). If E(n = 6, Tis an unbiased estimator. Unbiasedness is only an average property, however, and a marksman aiming at a bull' s eye could put every mark in the outermost circle and still, on the average, be unbiased. However, a marksman who can place every shot within a I-inch circle but still miss the bull' s eye substantially is said to be precise because his marks are repeatable.

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