A Topical Dictionary of Statistics by Gary L. Tietjen

By Gary L. Tietjen

Statistics is the authorised physique of tools for summarizing or describing information and drawing conclusions from the precis measures. everybody who has facts to summarize hence wishes a few wisdom of data. 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 sufficient definitions: it presents additionally the context, functions, and comparable terminology. The meant viewers falls into 5 teams with relatively diverse wishes: (1) specialist statisticians who have to remember a definition, (2) scientists in disciplines except facts who want to know the appropriate equipment of summarizing information, (3) scholars of information who have to develop their knowl­ fringe of their subject material and make consistent connection with it, (4) managers who should be interpreting statistical experiences written by way of their staff, and (5) newshounds who have to interpret govt or clinical studies and transmit the knowledge to the public.

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Johnson and S. Y. ), and Continuous Multivariate Distributions (1972). 4 Estimation and Hypothesis Testing Estimation If a layman were given the task of describing the average height of the population of white male college students at a certain university, he would no doubt take a sample from the population, measure the heights, and average the results. A quicker estimate would be the average of the smallest and largest heights in the sample. Another estimate would be the sample median (a number smaller than half the measurements and larger than the other half of them).

In certain circumstances the procedure can be varied. A randomized test is one in which a statistic, 0 ~ (x) ~ 1, depending on the outcome s, is calculated. A Bernoulli trial (such as a coin toss) is then performed, which has (x) as a probability of success. If the Bernoulli trial results in a success, Ho is rejected. (All the tests we discuss will be of the nonrandomized type). When testing a hypothesis, the experimenter may make the correct decision or commit 1 of 2 errors: (a) reject the null hypothesis when it is true (referred to as an error of the first kind or a Type I error) or (b) accept the null hypothesis when it is false (called an error of the second kind or a Type II error).

Ek • Let k increase until Sk ~ 1 and Sk+ I > 1. The value of k then has a Poisson distribution with parameter A. In general, if we know the cdf F(x), we can generate variates from it by usingX = F-I(U), where U ~ U(O,I). We do that by setting U = F(x) and solving for x. That is the inversion method. For discrete random variables, we can frequently use the table look-up method. If X takes the values 0, 1, 2, ... with probabilities PI> P2 ... , we form a table of integers 1,2, ... N so that numbers 1 to kl correspond to X = 0, those from kl + 1 to k2 to X = 1, etc.

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