GLOSSARY

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Correlation. In the most general usage, a measure of the interdependence among data. The concept may include more than two variables. The term is most commonly used in a narrow sense to express the relationship between quantitative variables or ranks. Correlation coef cient. A dimensionless measure of the interdependence between two variables, usually lying in the interval from 1 to 1, with zero indicating the absence of correlation (but not necessarily the independence of the two variables). The most common form of the correlation coef cient used in practice is r a i 1 3 1yi

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Crossed factors. Another name for factors that are arranged in a factorial experiment. Cumulative distribution function. For a random variable X, the function of X de ned as P(X x) that is used to specify the probability distribution. Cumulative normal distribution function. The cumulative distribution of the standard normal distribution, often denoted as (x) and tabulated in Appendix Table II. Cumulative sum control chart (CUSUM). A control chart in which the point plotted at time t is the sum of the measured deviations from target for all statistics up to time t. Curvilinear regression. An expression sometimes used for nonlinear regression models or polynomial regression models. Decision interval. A parameter set in a Tabular CUSUM algorithm that is determined from a trade-off between false alarms and the detection of assignable causes. Defect. Used in statistical quality control, a defect is a particular type of nonconformance to speci cations or requirements. Sometimes defects are classi ed into types, such as appearance defects and functional defects. Defects-per-unit control chart. See U chart. Degrees of freedom. The number of independent comparisons that can be made among the elements of a sample. The term is analogous to the number of degrees of freedom for an object in a dynamic system, which is the number of independent coordinates required to determine the motion of the object. Deming. W. Edwards Deming (1900 1993) was a leader in the use of statistical quality control. Deming s 14 points. A management philosophy promoted by W. Edwards Deming that emphasizes the importance of change and quality. Density function. Another name for a probability density function. Dependent variable. The response variable in regression or a designed experiment. Discrete distribution. A probability distribution for a discrete random variable. Discrete random variable. A random variable with a nite (or countably in nite) range. Discrete uniform random variable. A discrete random variable with a nite range and constant probability mass function.

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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.

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