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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). 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. Finite population correction factor. A term in the formula for the variance of a hypergeometric random variable. First-order model. A model that contains only rstorder terms. For example, the first-order response surface model in two variables is y 0 1x1 x2 . A first-order model is also called a main 2 effects model. Fixed factor (or xed effect). In analysis of variance, a factor or effect is considered xed if all the levels of interest for that factor are included in the experiment. Conclusions are then valid about this set of levels only, although when the factor is quantitative, it is customary to t a model to the data for interpolating between these levels. Forward selection. A method of variable selection in regression, where variables are inserted one at a time into the model until no other variables that contribute signi cantly to the model can be found. Fraction defective control chart. See P chart. Fraction defective. In statistical quality control, that portion of a number of units or the output of a process that is defective. Fractional factorial. A type of factorial experiment in which not all possible treatment combinations are run. This is usually done to reduce the size of an experiment with several factors.
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