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 (r_adj)

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 which 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 (s_xy or cov_xy)

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 (F_c)

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.

df_error

Degrees of freedom associated with SS_error = k(n - 1).

df_group

Degrees of freedom associated with SS_group = k - 1.

df_total

Degrees of freedom associated with SS_total = 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.