Lecture Series in Statistics and Probability |
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analysis of variance assumptions Bhapkar Binomial Biometrics Biometrika Biometrika 42 block chi-square distribution Chi-Square Tests Coefficient column confidence interval Contingency Tables convergence defined degrees of freedom denoted distribution function distribution-free tests equal error estimate example experiment experimental design exponential distribution Factorial Designs Fractional Factorials Frequencies gamma distribution given Goodman Haldane identically distributed independent random variables interactions Kastenbaum Kerrich's coin Kullback Kupperman Lancaster large numbers lecture linear main effects Markov chain Math mathematical matrix mean square Measures of Association method Multinomial n₁ normal distribution null hypothesis number of degrees observations outcome parameter Poisson process Prob probability density function procedure Psychometrika random interval rank ratio regression response sample space Significance STANFORD statistician stochastic process subset sum of squares Technometrics test statistic theory tion Total transition probability treatment values vector x₁ x2 Test zero Σ Σ
Popular passages
Page 24 - The rule for determining the number of degrees of freedom associated with any contingency table of whatever structure is: the number of degrees of freedom is equal to the total number of cells in the table, minus the number of independent linear constraints on the observations, minus the number of free parameters to be estimated from the data.
Page 151 - ... particle." A one-dimensional random walk is a Markov chain whose state space is a finite or infinite subset a, a + 1, ..., 6 of the integers, in which the particle, if it is in state i, can in a single transition either stay in i or move to one of the adjacent states i — 1, i + 1. If the state space is taken as the nonnegative integers, the transition matrix of a random walk has the form...
Page 144 - On the Experimental Attainment of Optimum Conditions,
Page 144 - A Basis for the Selection of a Response Surface Design,
Page 42 - Maximum entropy for hypothesis formulation, especially for multidimensional contingency tables.
Page 22 - A and B are collected in a common bin, each of the articles having a small marking specific to the shop from which it came. On the basis of a sample of size N we wish to determine if the percentage defective in shop A is the same as it is in shop B. The sample of size N is taken from a common bin containing a large number of articles from both shops. If the true proportion of articles in category AI is...
Page 151 - ... £0, otherwise. The physical interpretation of this model is as follows. Imagine two containers containing a total of 2a balls. Suppose the first container, labeled A, holds k balls and the second container B holds 2a — k balls. A ball is selected at random (all selections are equally likely) from among the totality of the 2a balls and moved to the other container. Each selection generates a transition of the process. Clearly the balls fluctuate between the two containers with a drift from...
Page 46 - A Simple Method of Calculating the Exact Probability in 2 x 2 Contingency Tables with Small Marginal Totals,
Page 30 - Tables with degrees of freedom between 2 and 60 and all expectations less than 5: For small N, use Fisher's exact test. Otherwise use X2, considering whether the continuity correction is needed.