 # Statistics for the Behavioral Sciences 9th edition David C. Howell  # Glossary

This glossary is a compilation of the definitions of keywords found throughout Fundamental Statistics for the Behavioral Sciences, 7th edition  and Statistical Methods for Psychology; 7th edition. It was suggested by D.K. Bauman at Valdosta State University, and I will try to make it a regular part of future editions of the book. I have omitted a few technical terms that do not make much sense out of context.

There are several other glossaries on the web. I particularly like the one compiled by Keith Dear at https://surfstat.anu.edu.au/surfstat-home/glossary/glossary.html and the one compiled by Valerie J. Eastman and John H McColl at http://www .stats.gla.ac.uk/steps/glossary/

I would appreciate any additions, corrections, and clarification that are appropriate.

 2 X 5 factorial design A factorial design with one variable having two levels and the other having five levels. Alpha (a) The probability of a Type I error. Abscissa Horizontal axis. Additive law of probability The rule giving the probability of the occurrence of one or more mutually exclusive events. Adjacent values Actual data points that are no more extreme than the inner fences. Adjusted correlation (radj) A correction to the computed correlation coefficient to adjust for the number of predictors relative to the sample size. Adjusted means Means that have been adjusted for differences on a covariate. All subsets regression The result of a stepwise multiple regression when the program chooses that set of variables that has the best correlation with the critierion. Alternative hypothesis (H1) The hypothesis that is adopted when H0 is rejected. Usually the same as the research hypothesis. Analysis of variance (ANOVA) A statistical technique for testing for differences in the means of several groups. Analysis of covariance An analysis of variance in which the data are adjusted (or controlled) for the presence of one or more other variables. Analytic view Definition of probability in terms of analysis of possible outcomes. Array The set of Y values associated with a given X, or the set of X values associated with a given Y. Asymmetric relationships Log-linear models where at least one variable is treated as an independent variable and at least one variable is treated as a dependent variable. Backward elimination A stepwise regression procedure in which we start with all predictors and them eliminate those that do not contribute significantly or up to some predetermined standard. Behrens-Fisher problem An old name given to the problem of how to compare two independent means when we can not assume homogeneity of variance. Bernoulli trial A outcome with one of two mutually exclusive outcomes--such as pass/fail. b (Beta) The probability of a Type II error. Between­subjects designs Designs in which different subjects serve under the different treatment levels. Bimodal A distribution having two distinct peaks. Binomial distribution The distribution in which each of a number of independent trials results in one of two mutually exclusive outcomes. Biserial correlation The correlation between a continuous variable and a dichotomous variable, where we assume an underlying normality to the dichotomous variable. Rarely used. Bivariate normal model A regression model in which both X and Y are subject to random error. Bonferroni inequality An inequality on which the Bonferrone test is based. It states that the probability of the occurrence of one or more events can never exceed the sum of their individual probabilities. Bonferroni test A multiple comparison procedure in which the familywise error rate is divided by the number of comparisons. Box-and-whisker plot A graphical representation of the dispersion of a sample. Boxplot A graphical representation of the dispersion of a sample. Carry­over effect The effect of previous trials (conditions) on a subject's performance on subsequent trials. Categorical data Data representing counts or number of observations in each category. Cell The combination of a particular row and column; the set of observations obtained under identical treatment conditions. Censored data Data that have been categorized into two or more groups on the basis of a cutoff score on some criterion variable. Often a consideration in logistic regression. Centering The process of converting data to deviation scores. Central limit theorem The theorem that specifies the nature of the sampling distribution of the mean. Chi-square distribution The distribution of the chi-square (c2) statistic. Chi-square test A statistical test often used for analyzing categorical data. Coefficient of variation (CV) The standard deviation divided by the mean. Collinearity The condition in which the independent variables are (usually highly) correlated with each other. Column totals The total number of observations occurring in a column of a contingency table. Combinations The number of ways objects can be selected without regard to order. Combinatorics The branch of mathematics dealing with the number of different ways objects can be selected or arranged. Compound symmetry The condition with constant variances on the main diagonal of a matrix, and constant covariances off the main diagonal. Concordant pairs A pair of observations that are ordered in the same direction on two variables. Conditional distribution The distribution of Y for a fixed level of X. Conditional means The means for one variable at individual levels of a second variable. Conditional odds The odds of success given some level of another variable. Conditional probability The probability of one event given the occurrence of some other event. Confidence interval An interval, with limits at either end, with a specified probability of including the parameter being estimated. Confidence limits An interval, with limits at either end, with a specified probability of including the parameter being estimated. Confounded Two variables are said to be confounded when they are varied simultaneously and their effects cannot be separated. Constant A number that does not change in value in a given situation. Contingency table A two­dimensional table in which each observation is classified on the basis of two variables simultaneously. Contingency coefficient A coefficient, based on chi-square, reflecting the degree of relationship exhibited in a contingency table. Continuous variables Variables that take on any value. Contrast A comparison between two levels (or two sets of levels) of the independent variable following an analysis of variance. Cook's D A measure of the influence of an observation in multiple regression. Correlation (r) Relationship between variables. Correlation coefficient A measure of the relationship between variables. Correlational measures A measure of the degree of relationship between two variables that are each at least ordinal. Count data Data representing counts or number of observations in each category. Counter­balancing An arrangement of treatment conditions designed to balance out practice effects. Covariance (sxy or covxy) A statistic representing the degree to which two variables vary together. Covariance matrix (S) A matrix of variances and covariances among variables. Covariate A variable whose influence is controlled in the analysis of covariance. Cramér's phi (Fc) The extension of the phi coefficient to the case of larger contingency tables. Criterion variable The variable to be predicted. Critical value The value of a test statistic at or beyond which we will reject H0 . Cross- correlation The correlation between one predictor and all other predictors. Cross- validation The result of taking a regression equation from one set of data, applying it to a new set of data, and examining the correlation between the predicted and obtained values on the new set of data. Curvilinear relationship A situation that is best represented by something other than a straight line. Deciles Points that divide the distribution into tenths. Decision tree Graphical representation of decisions involved in the choice of statistical procedures. Decision making A procedure for making logical decisions on the basis of sample data. Degrees of freedom (df) The number of independent pieces of information remaining after estimating one or more parameters. Delta (d) A value used in referring to power tables that combines gamma and the sample size. Density Height of the curve for a given value of X- closely related to the probability of an observation in an interval around X. Dependent variables The variable being measured. The data or score. Depth Cumulative frequency counting in from the nearer end. Design matrix A matrix of coded or dummy variables representing group membership. dferror Degrees of freedom associated with SSerror = k(n - 1). dfgroup Degrees of freedom associated with SSgroup = k - 1. dftotal Degrees of freedom associated with SStotal = N - 1. Deviation scores Data in which the mean has been subtracted from each observation. Descriptive statistics Statistics which describe the sample data without drawing inferences about the larger population. Dichotomous variables Variables that can take on only two different values. Difference scores The set of scores representing the difference between the subjects' performance on two occasions. Also known as "gain scores." Directional test A test that rejects extreme outcomes in only one specified tail of the distribution. Discordant pairs A pair of observations that are ordered in opposite directions on two variables. Discriminant analysis A procedure for developing a procedure for optimally discriminating between two groups. This technique often being replaced with logistic regression. Discrete variables Variables that take on a small set of possible values. Disordinal interaction An interaction in which group differences reverse their sign at some level of the other variable. Dispersion The degree to which individual data points are distributed around the mean. Distance The vertical distance between a point and the regression line. Usually known as the "residual." Distribution­free tests Statistical tests that do not rely on parameter estimation or precise distributional assumptions. Dotplot A distribution that represents the frequencies of individual points by stacking dots about the axis--similar to a histogram. Dunn-Sidák test A test similar to the Bonferroni test which is based on a more precise inequality and has slightly more power. Dunnett's test A multiple comparison procedure for comparing each mean against a standard control group mean. Effect size (d) The difference between two population means divided by the standard deviation of either population. Effective sample size The sample size needed in equal-sized groups to achieve the power when we have groups of unequal sizes. It will generally be less than the total number of subjects in the unequal groups. Efficiency The degree to which repeated values for a statistic cluster around the parameter. Equally weighted means An analysis of variance in which cell means all carry the same weight in determining row and column means, regardless of the number of subjects in each cell. Error rate per comparison (PC) The probability of making a Type I error on any specific comparison when using multiple comparison procedures. Error variance The square of the standard error of estimate. Errors of prediction The differences between Y and Yhat. Eta squared (h2) A measure of the magnitude of effect. Also known as the correlation ratio. Event The outcome of a trial. Exhaustive A set of events that represents all possible outcomes. Expected value The average value calculated for a statistic over an infinite number of samples. Expected frequencies The expected value for the number of observations in a cell if H0 is true. Experimental hypothesis Another name for the research hypothesis. Exploratory data analysis (EDA) A set of techniques developed by Tukey for presenting data in visually meaningful ways. External validity The ability to generalize the results from this experiment to a larger population. Factorial design An experimental design in which every level of each variable is paired with every level of each other variable. Factors Another word for independent variables in the analysis of variance. Familywise error rate The probability that a family of comparisons contains at least one Type I error. Fisher's Least Significant Difference Test (LSD) A multiple comparison technique that requires a significant overall F, and that involves standard t tests between pairs of means. Also known as the "protected t test." First order interaction The interaction of two variables. Also known as a "simple interaction." Fixed marginal totals The situation in which the marginal totals in a contingency table are known before the data are collected and are not subject to sampling error. Fixed model Anova An analysis of variance model in which the levels of the independent variable are treated as fixed. Fixed variable A variable that takes on a specific set of values. An independent variable who levels are assigned by the experimenter. Fractiles A generic name for statistics such as deciles, percentiles, and quartiles. Frequency distribution A distribution in which the values of the dependent variable are tabled or plotted against their frequency of occurrence. Frequency data Data representing counts or number of observations in each category. Friedman's rank test for k correlated samples A nonparametric test analogous to a standard one-way repeated­measures analysis of variance. Gamma The symbol for the effect size. Gamma function (G) A statistical function closely related to factorials. General linear model The basic model underlying the analysis of variance and multiple regression. Geomteric mean A mean of n objects that is computed by taking the nth root of the product of the n terms. Goodness­of­fit test A test for comparing observed frequencies with theoretically predicted frequencies. Grand total (SX) The sum of all of the observations. H-spread The range between the two hinges. Harmonic mean The number of elements to be averaged divided by the sum of the reciprocals of the elements. Heavy tailed distribution A distribution with a higher percentage of scores in the tails than we would expect in a normal distribution. Heterogeneity of variance A situation in which samples are drawn from populations having different variances. Heterogeneous subsamples Data in which the sample of observations could be subdivided into two distinct sets on the basis of some other variable. Hierarchical log-linear model A model in which the presence of an interaction requires the inclusion of any main effects that comprise that interaction. Hierarchical (sequential) sums of squares Sums of squares in the analysis of variance where later terms in the model are adjusted only for terms that precede them. higher order interaction The interaction of three or more variables. Hinge location The location of the hinge in an ordered series. Hinges (Quartiles) Those points that cut off the bottom and top quarter of a distribution. Histogram Graph in which rectangles are used to represent frequencies of observations within each interval. Homogeneity of regression The assumption that the regression line expressing the dependent variable as a function of a covariate is constant across several groups or conditions. Homogeneity of variance The situation in which two or more populations have equal variances. Homogeneity of variance in arrays The requirement that the variance in Y associated with one value of X is the same as the variance in Y associated with other values of X. Hyperspace Multidimensional space beyond the three dimensions that we can easily represent. Hypothesis testing A process by which decisions are made concerning the values of parameters. Independent variables Those variables controlled by the experimenter. Independent events Events are independent when the occurrence of one has no effect on the probability of the occurrence of the other. Inferential statistics That branch of statistics that involves drawing inferences about parameters of the population(s) from which you have sampled. Influence A measure of the degree to which an individual data point can influence the obtained value of a regression coefficient. Inner fences Points that are 1.5 times the H-spread above and below the appropriate hinge. Interaction A situation in a factorial design in which the effects of one independent variable depend upon the level of another independent variable. Intercept The value of Y when X is 0. Intercorrelation matrix A matrix (table) showing the pairwise correlations between all variables. Interquartile range The range of the middle 50% of the observations. Internal validity The degree to which a study if logically sound and free of confounding variables. Interval scale Scale on which equal intervals between objects represent equal differences‹differences are meaningful. Interval estimate A range of values estimated to include the parameter. Intraclass correlation A measure of the degree of relationship between two variables. It is usually squared. Joint probability The probability of the co-occurrence of two or more events. Kappa (k) Cohen's measure of agreement based on a contingency table. Kendall's coefficient of concordance (W) A coefficient of agreement among two or more judges. Kendall's tau A correlation for ranked data which relies on the number of inversions of the rank order of one variable when the other variable is ranked in order. Kruskal­Wallis one-way analysis of variance A nonparametric test analogous to a standard one-way analysis of variance. Kurtosis A measure of the peakedness of a distribution. Latin square design A design which varies the order of presentation of stimuli in such a way as to distribute sequence effects across the design. Leading digits (most significant digits) Left-most digits of a number. Least significant difference test A technique in which we run t tests between pairs of means only if the analysis of variance was significant. Leaves Horizontal axis of display containing the trailing digits. Leptokurtic A distribution that has relatively more scores in the center and in the tails. Leverage The degree to which an observation is unusual with respect to the predictor variables.  Similar to an outlier. Likelihood ratio chi- square An alternative procedure for calculating the chi-square statistic--most commonly used in log-linear models Linear combination The sum of a weighted set of means. Linear contrast A linear combination where the sum of the squared weights sum to 0. Linear regression model A regression model in which the independent variable (X) is not subject to random error. Linear relationship A situation in which the best-fitting regression line is a straight line. Linear transformation A transformation involving addition, subtraction, multiplication, or division of or by a constant. Linear regression Regression in which the relationship is linear. Linearity of regression The assumption that the best fitting line for a bivariate set of data in linear (straight).. Log-linear models Models for handling multiple categorical variables, such as a contingency table with three or more variables. Logistic regression A variant of standard regression used when the dependent variable is a dichotomy, such as success/failure. Logit (transform) The natural log of the odds of success. Magnitude of effect A measure of the degree to which variability among observations can be attributed to treatments. Main diagonal The diagonal cells of a matrix from upper left to lower right. Main effect The effect of one independent variable averaged across the levels of the other independent variable(s). Mann­Whitney U test A nonparametric test for comparing the central tendency of two independent samples. Marginal distribution The distribution of Y across all values of X. In other words, the distribution of Y ignoring X. Marginal totals Totals for the levels of one variable summed across the levels of the other variable. Matched samples An experimental design in which the same subject is observed under more than one treatment. Matched-samples t test A t test comparing the means of matched (or repeated) samples. Matrix algebra Algebra in which you work with matrices of elements or variables instead of individual elements. Mean The sum of the scores divided by the number of scores. Mean absolute deviation (m.a.d.) Mean of the absolute deviations about the mean. Measurement The assignment of numbers to objects. Measurement data Data obtained by measuring objects or events. Measures of association Measures, often based on the chi-square statistic, that reflect the degree of relationship between two variables. The variables are often only nominal. Measures of central tendency Numerical values referring to the center of the distribution. Measures of location Another term for measures of central tendency. Median (Med) The score corresponding to the point having 50% of the observations below it when observations are arranged in numerical order. Median location The location of the median in an ordered series. Mesokurtic A distribution with a neutral degree of kurtosis. Midpoints Center of interval -- average of upper and lower limits. Mixed model designs Anova designs with one or more between subjects factors and one or more repeated measures factor. Also refers to designs with both fixed and random independent variables. Modality The term used to refer to the number of major peaks in a distribution. Mode (Mo) The most commonly occurring score. Monotonic relationship A relationship represented by a regression line that is continually increasing (or decreasing), but perhaps not in a straight line. MSbetween groups (MSgroup) Variability among group means. MSwithin (MSerror) Variability among subjects in the same treatment group. Multicategory case A situation in which data can be sorted into more that two categories. Multicollinearity A condition in which a set of predictor variables are highly correlated among themselves. Multinomial distribution The distribution in which each of a number of independent trials results in one of two or more mutually exclusive outcomes. Multiple comparison techniques Techniques for making comparisons between two or more group means subsequent to an analysis of variance. Multiple correlation coefficient (R0.123..p) The correlation between one variable (Y) and a set of p predictors. Multiple regression Regression with two or more independent variables. Multiplicative law of probability The rule giving the probability of the joint occurrence of independent events. Multivariate analysis of variance (Manova) An analysis of variance with two or more dependent variables. Multivariate outliers Observations that are outliers in some multivariate space. Multivariate procedures Procedures that deal with two or more dependent variables simultaneously. Multivariate normal distribution A generalization of the normal distribution to the joint distribution of two or more variables. Mutually exclusive Two events are mutually exclusive when the occurrence of one precludes the occurrence of the other. N factorial (!) N*(N- 1)*(N-2)*(N-3)*...*1 Negative relationship A relationship in which increases in one variable are associated with decreases in the other. Negatively skewed A distribution that trails off to the left. Newman-Keuls test A popular multiple comparison procedure for making pairwise comparisons among means. Nominal scale Numbers used only to distinguish among objects. Noncentrality parameter The degree to which the mean of the sampling distribution of the test statistic departs from its mean when the null hypothesis is true. Nondirectional test A test that rejects extreme outcomes in either tail of the distribution. Non-equivalent groups design A design in which the experimental groups differ on one or more important variables at the start of the experiment. Nonparametric tests Statistical tests that do not rely on parameter estimation or precise distributional assumptions. Normal distribution A specific distribution having a characteristic bell-shaped form. Normality Usually refers to the assumption behind most parametric tests that the data are normally distributed in the population. Normality in arrays The assumption that the Y values in any array of X are normally distributed. Null hypothesis (H0 ) The statistical hypothesis tested by the statistical procedure. Usually a hypothesis of no difference or no relationship. Observed frequencies The cell frequencies that were actually observed--as distinguished from expected frequencies. Odds The ratio of the probability (p) that an event occurs to the probability (1-p) that it does not: odds=p/(1-p). In a contingency table it is the ratio of the number of success to the number of failures. (As distinguished from a probability, which is the ratio of the number of success to the total number of events.) Odds ratio (W) The ratio of two odds. Off-diagonal elements The elements of a matrix that are not on the main diagonal. Omega squared (w2) A less biased measure of the magnitude of effect. One-tailed test A test that rejects extreme outcomes in only one specified tail of the distribution. One-way ANOVA An analysis of variance where the groups are defined on only one independent variable. Order effect The effect on performance attributable to the order in which treatments were administered. Ordinal interaction An interaction in which the group differences do not reverse their sign. Ordinal scale Numbers used only to place objects in order. Ordinate Vertical axis. Orthogonal contrasts A set of contrasts that are independent of one another. Outlier An extreme point that stands out from the rest of the distribution. p level The probability that a particular result would occur by chance if H0 is true. The exact probability of a Type I error. Parameters Numerical values summarizing population data. Parametric tests Statistical tests that involve assumptions about, or estimation of, population parameters. Partial correlation (r01.2) The correlation between the dependent and independent variables with the effects of one or more additional independent variables removed from both sides of the equation. Partialing To hold constant the effect of one variable when looking at the effects of two or more other variables. Partition To divide up a sum of squares--usually the SStreatment. Pearson product-moment correlation coefficient (r) The most common correlation coefficient. Pearson's chi-square (c2) The traditional chi-square statistic--as opposed to the likelihood ratio chi- square. Percentage of agreement The ratio of the number of times two judges agree, divided by the number of judgments. It is a measure that does not correct for chance agreement. Percentile The point below which a specified percentage of the observations fall. Permutations The number of ways objects can be arranged taking ordering into account. Phi (F) The correlation coefficient when both of the variables are measured as dichotomies. Platykurtic A distribution that is relatively thick in the "shoulders." Point biserial correlation (rpb) The correlation coefficient when one of the variables is measured as a dichotomy. Point estimate The specific value taken as the estimate of a parameter. Polynomial trend coefficient A set of coefficients used for testing for polynomial (e.g., linear, quadratic, ...) trend. Pooled variance A weighted average of the separate sample variances. Population variance Variance of the population‹usually estimated, rarely computed. Population Complete set of events in which you are interested. Positively skewed A distribution that trails off to the right. Power The probability of correctly rejecting a false H0 . Prediction The prediction of one variable (Y) on the basis of one or more predictor variables (Xi). Predictor variable The variable from which a prediction is made. Proportional improvement in prediction (PIP) The degree to which the prediction of Y is improved by using X. Proportional reduction in error (PRE) The degree to which the residual error is reduced after taking X into account, relative to the error without X. Proportionality A condition in a factorial analysis of variance where a certain proportionality exists among sample sizes. Protected t A technique in which we run t tests between pairs of means only if the analysis of variance was significant. Also known as Fisher's LSD test. Quadratic function A polynomial function of the 2nd order, which has one point of inflection. An equation of the form . Quantitative data Data obtained by measuring objects or events. Qualitative data Non-numerical data, often in the form of categorical data. Quantiles A generic name for statistics such as deciles, percentiles, and quartiles. Quartiles The points which break the distribution into fourths. Random marginal totals The situation in which the marginal totals in a contingency table are not known before the data are collected and are subject to sampling error. Random model Anova An analysis of variance model in which the levels of the independent variable are treated as a random variable. Random sample A sample in which each member of the population has an equal chance of inclusion. Random variable A random variable is a numerical value which is  determined by the outcomes or events of an experiment.A random independent variable is one who levels vary from one replication to another, and are not determined by the experimenter. Randomized blocks design A design in which subjects are matched against one another and put into "blocks" of subjects of the same size as the number of treatments. Members of each block are then randomly assigned to treatments. Range The distance from the lowest to the highest score. Range restrictions Refers to cases in which the range over which X or Y varies is artificially limited. Ranked data Data for which the observations have been replaced by their numerical ranks from lowest to highest. Rank­randomization tests A class of nonparametric tests based on the theoretical distribution of randomly assigned ranks. Ratio scale A scale with a true zero point -- ratios are meaningful. Real lower limit The points halfway between the top of one interval and the bottom of the next. Real upper limit The points halfway between the top of one interval and the bottom of the next. Rectangular distribution A distribution in which all outcomes are equally likely. Also known as a uniform distribution. Reflection The process of reversing the direction of scoring such that high values become low values and low values become high values. Regression surface The equivalent of the regression line in multidimensional space. Regression The prediction of one variable from knowledge of one or more other variables. Regression equation The equation that predicts Y from X. Regression coefficients The general name given to the slope and the intercept ‹most often refers just to the slope). Regression line The line of best fit drawn through a scatterplot. Regression surface The generalization of the regression line, or the regression plane, to multidimensional space. Rejection level The probability with which we are willing to reject H0 when it is in fact correct. Rejection region The set of outcomes of an experiment that will lead to rejection of H0 . Related samples An experimental design in which the same subject is observed under more than one treatment. Relative frequency view Definition of probability in terms of past performance. Repeated­measures designs An experimental design in which each subject receives all levels of at least one independent variable. Replicate The repeat an experiment. Research hypothesis The hypothesis that the experiment was designed to investigate. Residual The difference between the obtained and predicted values of Y. Residual error The error remaining after the predictor variable(s) has/have been considered. Another term for residual variance. Residual variance The square of the standard error of estimate. Resistance The degree to which an estimator is not influenced by the presence of outliers.. Rho (r) Correlation coefficient on the population. Also occasionally used for Spearman's rank-order correlation. Robust A test is robust if it is not seriously disturbed by the violation of underlying assumptions. Row totals The total number of observations occurring in a row of a contingency table. Ryan procedure (REGWQ) A multiple comparison procedure that holds the familywise error rate at a while having greater power than Tukey's test. Sample Set of actual observations. Subset of the population. Sample statistics Statistics calculated from a sample and used primarily to describe the sample. Sample variance (s2) Sum of the squared deviations about the mean divided by N ­ 1. Sample with replacement Sampling in which the item drawn on trial N is replaced before the drawing on trial N + 1. Sampling distributions The distribution of a statistic over repeated sampling from a specified population. Sampling distribution of differences between means The distribution of the differences between means over repeated sampling from the same population(s). Sampling distribution of the mean The distribution of sample means over repeated sampling from one population. Sampling error Variability of a statistic from sample to sample due to chance. Sampling fraction The fraction of the number of levels actually used in an experiment to the potential number of levels that could have been used. In a fixed model the sampling fraction is 1.0, and in a random model it approaches 0.0. Satterthwaite solution See Welch-Satterthwaite solution Saturated model A log-linear model having as many parameters as unknowns. Scalar algebra The plain old kind of algebra you learned in high school--as opposed to matrix algebra. Scales of measurement Characteristics of relations among numbers assigned to objects. Scatter plot A figure in which the individual data points are plotted in two-dimensional space. Scatter diagram A figure in which the individual data points are plotted in two-dimensional space. Scattergram A figure in which the individual data points are plotted in two-dimensional space. Scheffé test A relatively conservative multiple comparison procedure. Second order interaction The interaction of three variables. Semi-partial correlation (r0(1.2)) The correlation between the dependent and the independent variables with the effect of another variable or variables removed from just the independent variables. Also known as the part correlation. Sequence effect The situation in which the presentation of one level of the independent variable has an effect on response to another level of that variable. Sigma (S)--capital Symbol indicating summation. Sigma (s)--lower case Symbol designating the standard deviation of a population. Sign test A statistical test which looks at only the sign, not the magnitude, of the outcomes. (Often used with the set of difference scores.) Significance level The probability with which we are willing to reject H0 when it is in fact correct. Simple effect The effect of one independent variable at one level of another independent variable. (Also known as simple main effects.) Simple interaction The interaction of two variables at one level of a third variable. Singular matrix A matrix that does not have a unique inverse. Skewness A measure of the degree to which a distribution is asymmetrical. Slope The amount of change in Y for a one unit change in X. Spearman's correlation coefficient for ranked data (rs) A correlation coefficient on ranked data. Sphericity A condition very like compound symmetry that is required for repeated-measures designs. SScells The sum of squares assessing differences among cell totals. SSerror The sum of the squared residuals. SSerror The sum of the sums of squares within each group. SSgroup The sum of squares of group totals divided by the number of scores per group minus SX2/N.< /td> SSsubjects The sum of squares of subject totals. Usually calculated to remove those effects from the error term. SStotal The sum of squares of all of the scores, regardless of group membership. SSwithin subjects Variability within the scores from the same subject. SSY The sum of the squared deviations. Standard deviation Square root of the variance. Standard error The standard deviation of a sampling distribution. Standard error of differences between means The standard deviation of the sampling distribution of the differences between means. Standard error of estimate The average of the squared deviations about the regression line. Standard scores Scores with a predetermined mean and standard deviation. Standard normal distribution A normal distribution with a mean equal to 0 and variance equal to 1. Denoted N (0, 1). Standardized regression coefficient (b) The regression coefficient that results from data that have been standardized. Statistics Numerical values summarizing sample data. Stem Vertical axis of display containing the leading digits. Stem-and-leaf display Graphical display presenting original data arranged into a histogram. Stepwise procedures A set of rules for deriving a regression equation by adding or subtracting one variable at a time from the regression equation. Stepwise regression See "stepwise regression." Stratification The partitioning of subjects into subgroups that are matched on important variables. Structural model A theoretical model assumed to underlie the data that expresses the relationship between the dependent variable and the independent variables. Studentized range statistic (q) A test statistic for testing the difference between the largest and smallest means in a set. Studentized residual A statistic for evaluating the residual for an observation in multiple regression. Student's t distribution The sampling distribution of the t statistic. Subjective probability Definition of probability in terms of personal subjective belief in the likelihood of an outcome. Success/Failure An arbitrary designation of the two possible outcomes in Bernoulli trials. Sufficient statistic A statistic that uses all of the information in a sample. Sums of squares The sum of the squared deviations around some point (usually a mean or predicted value). Suppressor variable A variable whose correlation with the criterion is opposite in sign from its regression coefficient. Symmetric Having the same shape on both sides of the center. Symmetric relationships Log-linear models in which all variables are treated as dependent variables. T scores A set of scores with a mean of 50 and a standard deviation of 10. Tabled distribution of chi-square The table showing the critical values of chi-square for various degrees of freedom and levels of a when the null hypothesis is true. Test statistics The results of a statistical test. Tetrachoric correlation The correlation between two dichotomous variables when underlying normality of each variable is assumed. Rarely used. Tolerance One minus the squared correlation of a predictor with all other predictors. Trailing digits (least significant digits) Right-most digits of a number. Treatment effect The difference between the mean of one treatment (or condition) and the grand mean. Trimmed statistics Statistics calculated on trimmed samples. Trimmed samples Samples with a percentage of extreme scores removed. Tukey's HSD test A multiple comparison procedure for making pairwise comparisons among means while holding the familywise error rate at a. Two-Tailed test A test that rejects extreme outcomes in either tail of the distribution. Two­way factorial design An experimental design involving two independent variables in which every level of one variable is paired with every level of the other variable. Type I error The error of rejecting H0 when it is true. Type II error The error of not rejecting H0 when it is false. Unbiased estimator A statistic whose expected value is equal to the parameter to be estimated. Unconditional probability The probability of one event ignoring the occurrence or nonoccurrence of some other event. Unimodal A distribution having one distinct peak. Uniform distribution A distribution in which all possible outcomes have an equal chance of occurring. Also known as a rectangular distribution. Univariate design An experimental design having only one dependent variable. Unweighted means Row or column means based on the average of the cell means in that row or column--without giving greater weight to cells with more observations. Also known as equally weighted means. Validities The correlations of individual predictor variables with the criterion. Validity The degree to which a variable measures what it is intended to measure. Variables Properties of objects that can take on different values. Variance The sum of the squared deviations from the mean, divided by the degrees of freedom (N- 1). Variance inflation factor (VIF) The reciprocal of the tolerance--the degree to which the standard error of bj is incresed becuase of the degree to which Xj is correlated with the other predictors. Variance Sum Law The rule giving the variance of the sum (or difference) of two or more variables. Venn diagrams A way of representing shared and unshared variances by a set of overlapping circles. Weighted average The mean of the form: (a1X1 + a2X2)/(a1 + a2) where a1 and a2 are weighting factors and X1 and X2 are the values to be average. Weighted means Row or column means where the cell sizes are used to weight the cell means. Welch-Satterthwaite solution A solution to the problem of comparing means with heterogeneous variances-- independently arrived at by Welch and Satterthwaite. Whiskers Lines drawn in a boxplot from hinges to adjacent values. Wilcoxon's matched­pairs signed­ranks test A nonparametric test for comparing the central tendency of two matched (related) samples. Wilcoxon's rank-sum test A nonparametric test for comparing two independent groups. It is functionally equivalent to the Mann-Whitney U test. Winsorized samples Samples in which extreme values have been trimmed and replaced by the most extreme value(s) remaining in the distribution. Yates' correction for continuity An old correction to adjust chi-square for a 2 X 2 table for the fact that cell frequencies are integer, rather than continuous. Rarely recommended any longer. z score Number of standard deviations above or below the mean.  dch:

David C. Howell
University of Vermont
David.Howell@uvm.edu