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GLOSSARY

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Statistical Process Control. A set of problem-solving tools based on data that are used to improve a process. Statistical quality control. Statistical and engineering methods used to measure, monitor, control, and improve quality. Statistics. The science of collecting, analyzing, interpreting, and drawing conclusions from data. Stem and leaf display. A method of displaying data in which the stem corresponds to a range of data values and the leaf represents the next digit. It is an alternative to the histogram but displays the individual observations rather than sorting them into bins. Stepwise regression. A method of selecting variables for inclusion in a regression model. It operates by introducing the candidate variables one at a time (as in forward selection) and then attempting to remove variables following each forward step. Studentized range. The range of a sample divided by the sample standard deviation. Studentized residual. In regression, the studentized residual is calculated by dividing the ordinary residual by its exact standard deviation, producing a set of scaled residuals that have, exactly, unit standard deviation. Suf cient statistic. An estimator is said to be a suf cient statistic for an unknown parameter if the distribution of the sample given the statistic does not depend on the unknown parameter. This means that the distribution of the estimator contains all of the useful information about the unknown parameter. Tabular CUSUM. A numerical algorithm used to detect assignable causes on a cumulative sum control chart. See V mask. Tampering. Another name for overcontrol. t-distribution. The distribution of the random variable de ned as the ratio of two independent random variables. The numerator is a standard normal random variable and the denominator is the square root of a chisquare random variable divided by its number of degrees of freedom. Test statistic. A function of a sample of observations that provides the basis for testing a statistical hypothesis. Time series. A set of ordered observations taken at difference points in time. Tolerance interval. An interval that contains a speci ed proportion of a population with a stated level of con dence.

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Tolerance limits. A set of limits between which some stated proportion of the values of a population must fall with speci ed level of con dence. Total probability rule. Given a collection of mutually exclusive events whose union is the sample space, the probability of an event can be written as the sum of the probabilities of the intersections of the event with the members of this collection. Treatment. In experimental design, a treatment is a speci c level of a factor of interest. Thus if the factor is temperature, the treatments are the speci c temperature levels used in the experiment. Treatment sum of squares. In analysis of variance, this is the sum of squares that accounts for the variability in the response variable due to the different treatments that have been applied. t-test. Any test of signi cance based on the t distribution. The most common t-tests are (1) testing hypotheses about the mean of a normal distribution with unknown variance, (2) testing hypotheses about the means of two normal distributions and (3) testing hypotheses about individual regression coef cients. Type I error. In hypothesis testing, an error incurred by rejecting a null hypothesis when it is actually true (also called an -error). Type II error. In hypothesis testing, an error incurred by failing to reject a null hypothesis when it is actually false (also called a -error). U chart. An attribute control chart that plots the average number of defects per unit in a subgroup. Also called a defects-per-unit control chart. Similar to a C chart. Unbiased estimator. An estimator that has its expected value equal to the parameter that is being estimated is said to be unbiased. Uniform random variable. Refers to either a discrete or continuous uniform random variable. Uniqueness property of moment generating function. Refers to the fact that random variables with the same moment generating function have the same distribution. Universe. Another name for population. V mask. A geometrical gure used to detect assignable causes on a cumulative sum control chart. With appropriate values for parameters, identical conclusions can be made from a V mask and a tabular CUSUM. Variable selection. The problem of selecting a subset of variables for a model from a candidate list that

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