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which is also called the product moment correlation coef cient. It is a measure of the linear association between the two variables y and x. Correlation matrix. A square matrix that contains the correlations among a set of random variables, say X1, X2, p , Xk. The main diagonal elements of the matrix are unity and the off diagonal elements rij are the correlations between Xi and Xj. Counting techniques. Formulas used to determine the number of elements in sample spaces and events. Covariance. A measure of association between two random variables obtained as the expected value of the product of the two random variables around their means; that is, Cov(X, Y ) E[(X X)(Y Y)]. Covariance matrix. A square matrix that contains the variances and covariances among a set of random variables, say X1, X2, p , Xk. The main diagonal elements of the matrix are the variances of the random variables and the off diagonal elements are the covariances between Xi and Xj. Also called the variance-covariance matrix. When the random variables are standardized to have unit variances, the covariance matrix becomes the correlation matrix. Critical region. In hypothesis testing, this is the portion of the sample space of a test statistic that will lead to rejection of the null hypothesis. Critical value(s). The value of a statistic corresponding to a stated signi cance level as determined from the sampling distribution. For example, if P(Z z0.05) P(Z 1.96) 0.05, then z0.05 = 1.96 is the critical value of z at the 0.05 level of signi cance.

Dispersion The amount of variability exhibited by data Distribution free methods(s) Any method of inference (hypothesis testing or con dence interval construction) that does not depend on the form of the underlying distribution of the observations Sometimes called nonparametric method(s) Distribution function Another name for a cumulative distribution function Ef ciency A concept in parameter estimation that uses the variances of different estimators; essentially, an estimator is more ef cient than another estimator if it has smaller variance When estimators are biased, the concept requires modi cation Enumerative study A study in which a sample from a population is used to make inference to the population See Analytic study Erlang random variable A continuous random variable that is the sum of a xed number of independent, exponential random variables -error (or -risk).

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In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a type II error) -error (or -risk) In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called a type I error) Error mean square The error sum of squares divided by its number of degrees of freedom Error of estimation The difference between an estimated value and the true value Error sum of squares In analysis of variance, this is the portion of total variability that is due to the random component in the data It is usually based on replication of observations at certain treatment combinations in the experiment.

It is sometimes called the residual sum of squares, although this is really a better term to use only when the sum of squares is based on the remnants of a model fitting process and not on replication Error variance The variance of an error term or component in a model Estimate (or point estimate) The numerical value of a point estimator Estimator (or point estimator) A procedure for producing an estimate of a parameter of interest An estimator is usually a function of only sample data values, and when these data values are available, it results in an estimate of the parameter of interest..

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Event A subset of a sample space Exhaustive A property of a collection of events that indicates that their union equals the sample space Expected value The expected value of a random variable X is its long-term average or mean value In the continuous case, the expected value of X is xf 1x2 dx where f(x) is the density function E1X 2 of the random variable X Exponential random variable A continuous random variable that is the time between counts in a Poisson process Factorial experiment A type of experimental design in which every level of one factor is tested in combination with every level of another factor In general, in a factorial experiment, all possible combinations of factor levels are tested F-distribution The distribution of the random variable de ned as the ratio of two independent chi-square random variables each divided by their number of degrees of freedom.

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