alpha The Greek letter a, which symbolizes the criterion, the size of the region of rejection of a sampling distribution, and the theoretical probability of making a Type I error

alternative hypothesis The statistical hypothesis describing the population parameters that the sample data represent if the predicted relationship does exist

analysis of variance The parametric procedure for determining whether significant differences exists in an experiment containing two or more sample means

ANOVA Abbreviation of analysis of variance

as a function of A way to describe a relationship using the format "changes in Y as a function of changes in X"






bar graph A graph in which a free-standing vertical bar is centered over each score on the X axis; used with nominal or ordinal scores

bar graph A graph in which a free-standing vertical bar is centered over each score on the X axis; used with nominal or ordinal scores

beta The Greek letter ß, which symbolizes the theoretical probability of making a Type II error

between-subjects ANOVA The type of ANOVA that is performed when a study involves between-subjects factors

between-subjects factor An independent variable that is studied using independent samples in all conditions

biased estimator A fomula for a sample's variability that involves dividing by N is biased toward underestimating the corresponding population variability

bimodal distribution A symmetrical frequency polygon with two distinct humps where there are relatively high-frequency scores and with center scores that have the same frequency

biomodal distribution A symmetrical frequency polygon with two distinct humps where there are relatively high-frequency scores and with center scores that have the same frequency






C The symbol for contingency coefficient

cell In a two-way ANOVA, the combination of one level of one factor with one level of the other factor

central limit theorem A statistical principle that defines the mean, standard deviation, and shape of a theoretical sampling distribution

chi square procedure The nonparametric inferential procedure for testing whether the frequencies of category membership in the sample represent the predicted frequencies in the population

coefficient of alienation The proportion of variance not accounted for by a relationship; computed by subtracting the squared correlation coefficient from 1

coefficient of determination The proportion of variance accounted for by a relationship; computed by squaring the correlation coefficient

collapsing In a two-way ANOVA, averaging together all scores from all levels of one factor in order to calculate the main effect means for the other factor

complete factorial design A two-way ANOVA design in which all levels of one factor are combined with all levels of the other factor

condition An amount or category of the independent variable that creates the specific situation under which subjects' scores on the dependent variable are measured

confidence interval for a single m A range of values of m, one of which is likely to be represented by the sample mean

confidence interval for the difference between two ms A range of differences between two population ms, one of which is likely to be represented by the difference between the two sample means

m confidence interval for m A range of values of m, one of which is likely to be represented by the sample mean () in a related-samples test

confounded comparison In a two-way ANOVA, a comparison of two cells that differ along more than one factor

contingency coefficient The statistic that describes the strength of the relationship in a two-way chi square when there are more than two categories for either variable

continuous scale A measurement scale that allows for fractional amounts of the variable being measured

correlation coefficient A number that describes the type and the strength of the relationship present in a set of data

correlational study A procedure in which subjects' scores on two variables are measured, without manipulation of either variable, to determine whether they form a relationship

criterion The probability that defines whether a sample is too unlikely to have occurred by chance and thus is unrepresentative of a particular population

criterion variable The variable in a relationship whose unknown scores are predicted through use of the known scores on the predictor variable

critical value The value of the sample statistic that marks the edge of the region of rejection in a sampling distribution; values that fall beyond it lie in the region of rejection

cumulative frequency The frequency of the scores at or below a particular score; symbolized by cf

curvilinear relationship Another way of saying nonlinear relationship






data Scores obtained in research

data point A dot plotted on a graph to represent a pair of X and Y scores

data point A dot plotted on a graph to represent a pair of X and Y scores

degrees of freedom The number of scores in a sample that are free to vary, and thus the number that is used to calculate an estimate of the population variability

dependent events Events for which the probability of one is influenced by the occurrence of the other

dependent variable In an experiment, the variable that is measured under each condition of the independent variable

descriptive statistics Procedures for organizing and summarizing data so that the important characteristics can be described and communicated

design The way in which a study is laid out so as to demonstrate a relationship

deviation The distance that separates a score from the mean and thus indicates how much the score differs from the mean

df The symbol for degrees of freedom

df The symbol for degrees of freedom

dichotomous variable A discrete variable that has only two possible amounts or categories

discrete scale A measurement scale that allows for measurement only in whole-number amounts

distribution An organized set of data






effect size A measure of the amount of influence that changing the conditions of the independent variable had on dependent scores; may be computed as the proportion of variance accounted for

error variance The inherent variability within a population, estimated in ANOVA by the mean square within groups

estimated population standard deviation The unbiased estimate of the population standard deviation calculated from sample data using degrees of freedom (N - 1)

estimated standard error of the mean An estimate of the standard deviation of the sampling distribution of means, used in calculting the one-sample t-test

eta The correlation coefficient used to describe a linear or nonlinear relationship containing two or more levels of a factor

eta squared The proportion of variance in the dependent variable that is accounted for by changing the levels of a factor, and thus a measurement of effect size

expected frequency In chi square, the frequency expected in a category if the sample data perfectly represent the distribution of frequencies in the population described by the null hypothesis

experiment A research procedure in which one variable is actively changed or manipulated, the scores on another variable are measured, and all other variables are kept constant, to determine whether there is a relationship

experimental hypothesis Two statements made before a study is begun, describing the predicted relationship that may or may not be demonstrated by the study

experiment-wise error rate The probability of making a Type I error when comparing all means in an experiment






factor In ANOVA, an independent variable

F-distribution The sampling distribution of all possible values of F that occur when the null hypothesis is true and all conditions represent one population µ

Fisher's protected t-test The post hoc procedure performed with ANOVA to compare means from a factor in which all levels do not have equal n

F-ratio In ANOVA, the ratio of the mean square between groups to the mean square within groups

frequency The number of times each score occurs within a set of data; also called simple frequency; symbolized by f

frequency polygon A graph that shows interval or ratio scores (X axis) and their frequencies (Y axis), using data points connected by straight lines

Friedman X² text The nonparametric version of the one-way, repeated measures ANOVA for ranked scores






goodness-of-fit test A name for the one-way chi square, because it tests how "good" the "fit" is between the data and H0

grouped distribution A distribution formed by combining different scores to make small groups whose total frequencies, relative frequencies, or cumulative frequencies can then be manageably reported






H₀ The symbol for the null hypothesis

H₀ The symbol for the null hypothesis

heteroscedasticity An unequal spread of Y scores around the regression line (that is, around the values of Y'

histogram A graph similar to a bar graph but with adjacent bars touching, used to plot the frequency distribution of a small range of interval or ratio scores

homogeneity of variance A characteristic of data describing populations represented by samples in a study that have the same variance

homoscedasticity An equal spread of Y scores around the regression line and around the values of Y'

HSD Stands for the honestly significant difference






incomplete factorial design A two-way ANOVA design in which not all levels of the two factors are combined

independent events Events for which the probability of one is not influenced by the occurrence of the other

independent samples Samples created by selecting each participant for one sample, without regard to the participants selected for any other sample

independent samples t-test The t-test used with data from two independent samples

independent variable In an experiment, a variable that is changed or manipulated by the experimenter; a variable hypothesized to cause a change in the dependent variable

individual differences Variations in individuals' traits, backgrounds, genetic makeup, etc., that influence their behavior in a given stiuation and thus the strength of a relationship

inferential statistics Procedures for determining whether sample data represent a particular relationship in the population

inferential statistics Procedures for determining whether sample data represent a particular relationship in the population

inferential statistics Procedures for determining whether sample data represent a particular relationship in the population

interaction effect The effect produced by the manipulation of two independent variables such that the influence of changing the levels of one factor depends on which level of the other factor is present

interval estimation A way to estimate a population parameter by describing an interval within which the population parameter is expected to fall

interval scale A measurement scale in which each score indicates an actual amount and there is an equal unit of measurement between consecutive scores but in which zero is simply another point on the scale (not zero amount)






Kruskal-Wallis H test The nonparametric version of the one-way, between-subjects ANOVA for ranked scores






level In ANOVA, each condition of the factor (independent variable); also called treatment

level In ANOVA, each condition of the factor (independent variable); also called treatment

line graph A graph of an experiment when the independent variable is an interval or ratio variable; plotted by connecting the data points with straight lines

linear regression equation The equation that defines the straight line summarizing a linear relationship by describing the values of Y' at each X

linear regression line The straight line that summarizes the scatterplot of a linear relationship by, on average, passing through the center of all Y scores

linear relationship A correlation between the X scores and Y scores in a set of data in which the Y scores tend to change in only one direction as the X scores increase, forming a slanted straight regression line on a scatterplot






main effect In a two-way ANOVA, the effect on the dependent scores of changing the levels of one factor while ignoring (collapsing over) the other factor

main effect mean The overall mean of one level of a factor while ignoring (collapsing over) the influence of the other factor

Mann-Whitney U test The nonparametric version of the independent samples t-test for ranked scores when n is less than or equal to 20

margin of error Expressing the expected error when estimating a population parameter as plus or minus some amount

matched-samples design An experiment in which each participant in one sample is matched on an extraneous variable with a participant in the other sample

Mdn Abbreviation for the term median

mean The score located at the mathematical center of a distribution

mean square between groups In ANOVA, the variability in scores that occurs between the levels in a factor or the cells in an interaction

mean square within groups In ANOVA, the variability in scores that occurs in the conditions or cells; also known as the error term

measure of central tendency A score that summarizes the location of a distribution on a variable by indicating where the center of the distribution tends to be located

measures of variability Measures that summarize the extent to which scores in a distribution differ from one another

median The score located at the 50th percentile; symbolized by Mdn

mode The most frequently occurring score in a sample

multiple correlation coefficient The correlation that describes the relationship between multiple predictor (X) variables and one criterion (Y) variable

multiple regression equation The procedure for simultaneously using multiple predictor (X) variables to predict scores on one criterion (Y) variable

multivariate statistics Procedures applied to studies that measure two or more dependent variables






negative linear relationship A linear relationship in which the Y scores tend to decrease as the X scores increase

negatively skewed distribution A frequency polygon with low-frequency, exteme low scores but without corresponding low-frequency, extreme high ones so that its only pronounced tail is in the direction of the lower scores

Nemenyi's procedure The post hoc procedure performed with the Friedman X2 test

nominal scale A measurement scale in which each score is used simply for identification and does not indicate an amount

nonlinear relationship A relationship in which the Y scores change their direction of change as the X scores change; also called a curvilinear relationship

nonparametric statistics Inferential procedures that do not require stringent assumptions about the parameters of the raw score population represented by the sample data; usually used with scores most appropriately described by the median or the mode

nonparametric statistics Inferential procedures that do not require stringent assumptions about the parameters of the raw score population represented by the sample data; usually used with scores most appropriately described by the median or the mode

nonsignificant Describes results that are considered likely to result from chance sampling error when the predicted relationship does not exist; it indicates failure to reject the null hypothesis

normal curve The symmetric, bell-shaped curve produced by graphing a normal distribution

normal distribution A set of scores in which the middle score has the highest frequency, aand proceeding toward higher or lower scores the frequencies at first decrease slightly but then decrease drastically, with the highest and lowest scores having very low frequency

null hypothesis The statistical hypothesis describing the population parameters that the sample data represent if the predicted relationship does not exist






observed frequency In chi square, the frequency with which participants fall into a category of a variable

one-sample t-test The parametric procedure for a one-sample experiment when the standard deviation of the raw score population must be estimated

one-tailed text The test used to evaluate a statistical hypothesis that predicts that scores will only increase or only decrease

one-way ANOVA The analysis of variance performed when an experiment has only one independent variable

one-way chi square The chi square procedure for testing whether the sample frequencies of category membership on one variable represent the predicted distribution of frequencies in the population

ordinal scale A measurement scale in which scores indicate rank order






parameter A number that describes a characteristic of a population of scores, symbolized by a letter from the Greek alphabet

parametric statistics Inferential procedures that require certain assumptions about the parameters of the raw score population represented by the sample data; usually used with scores most appropriately described by the mean

participant An individual who is measured in a sample

Pearson correlation coefficient The correlation coefficient that describes the linear relationship between two interval or ratio variables

percent A proportion multiplied times 100

percentile The percentage of all scores in the sample that are at or below a particular score

phi coefficient The statistic that describes the strength of the relationship in a two-way chi square when there are only two categories for each variable

point estimation A way to estimate a population parameter by describing a point on the variable at which the population parameter is expected to fall

point-biserial correlation coefficient The correlation coefficient that describes the linear relationship between scores from one continuous interval or ratio variable and one dichotomous variable

pooled variance The weighted average of the sample variances in a two-sample experiment

population The infinitely large group of all possible scores that would be obtained if the behavior of every individual of interest in a particular situation could be measured

population parameter A number that describes a characteristic of a population of scores, symbolized by a letter from the Greek alphabet; also called parameter

population standard deviation The square root of the population variance, or the square root of the average squared deviation of scores around the population mean

population variance The average squared deviation of scores around the population mean

positive linear relationship A linear relationship in which the Y scores tend to increase as the X scores increase

positively skewed distribution A frequency polygon with low-frequency, exteme high scores but without corresponding low-frequency, extreme low ones so that its only pronounced tail is in the direction of the higher scores

post hoc comparisons In ANOVA, statistical procedures used to compare all possible pairs of sample means in a significant effect, to determine which means differ signficantly from each other

power The probability that a statistical test will detect a true relationship and allow the rejection of a false null hypothesis

predicted Y score In linear regression, the best prediction of the Y scores ata particular X, based on the linear relationship summarized by the regression line

predictor variable The variable for which known scores in a relationship are used to predict unknown scores on another variable

probability A mathematical statement indicating the likelihood that an event will occur when a particular population is randomly sampled

probability distribution The probability of every event in a population, derived from the relative frequency of every event in that population

proportion A decimal number between 0 and 1 that indicates a fraction of a total

proportion of the total area under the curve The proportion of the total area beneath the normal curve at certain scores, which represents the relative frequency of those scores

proportion of variance accounted for The proportion of the error in predicting scores that is eliminated when, instead of using the mean of Y, we use the relationship with the X variable to predict Y scores; the proportional improvement in predicting Y scores thus achieved

proportion of variance accounted for The proportion of the error in predicting scores that is eliminated when, instead of using the mean of Y, we use the relationship with the X variable to predict Y scores; the proportional improvement in predicting Y scores thus achieved

proportion of variance accounted for The proportion of the error in predicting scores that is eliminated when, instead of using the mean of Y, we use the relationship with the X variable to predict Y scores; the proportional improvement in predicting Y scores thus achieved






r They symbol for the Pearson correlation coefficient

r² The proportion of variance accounted for in a 2x2 chi square design.

r²_pb The symbol for point-biserial correlation coefficient

random sampling A method of selecting samples so that all members of the population have the same chance of being selected for a sample

range The distance between highest and lowest scores in a set of data

rank sums test The nonparametric version of the independent-samples t-test for ranked scores when n is greater than 20; also, the post hoc procedure performed with the Kruskal-Wallis H test

ratio scale A measurement scale in which each score indicates an actual amount, there is an equal unit of measurement, and there is a true zero

rectangular distribution A symmetric frequency polygon shaped like a rectangle; it has no discernible tails because its extreme scores do not have relatively low frequencies

region of rejection That portion of a sampling distribution containing values considered too unlikely to occur by chance, found in the tail or tails of the distribution

regression line The line drawn through the long dimension of a scatterplot that best fits the center of the scatterplot, thereby visually summarizing the scatterplot and indicating the type of relationship that is present

related samples Samples created by matching each participant in one sample with a participant in the other sample or by repeatedly measuring the same participant under all conditions; also called dependent samples

relationship A correlation between two variables whereby a change in one variable is accompanied by a consistent change in the other

relative frequency The proportion of time a score occurs in a distribution, equal to the proportion of the total number of scores that is made up by the score's simple frequency; symbolized by rel. f

relative frequency distribution A distribution of scores, organized to show the proportion of time each score occurs in a set of data

relative standing A description of a particular score derived from a systematic evaluation of the score using the characteristics of the sample or population in which it occurs

repeated-measures design A related-samples design in which the same subjects are measured repeatedly under all conditions of an independent variable

representative sample A sample whose characteristics accurately reflect those of the population

restriction of range In correlation, improper limitation of the range of scores obtained on one or both variables, leading to an underestimate of the strength of the relationship between the two variables

robust procedure A procedure that results in only a negligible amount of error in estimating the probability of a Type I error, even if the assumptions of the procedure are not perfectly met; describes parametric procedures






sample A relatively small subset of a population, intended to represent the population; a subset of the complete group of scores found in any particular situation

sample standard deviation The square root of the sample variance or the square root of the average squared deviation of sample scores around the sample mean

sample variance The average squared deviation of a sample of scores around the sample mean

sampling distribution of differences between the means A frequency distribution showing all possible differences between two means that occur when two independent samples of a particular size are drawn from the population of scores described by the null hypothesis

sampling distribution of mean differences A frequency distribution showing all possible mean differences that occur when the difference scores from two related samples of a particular size are drawn from the population of difference scores described by the null hypothesis

sampling distribution of means A frequency distribution showing all possible sample means that occur when samples of a particular size are drawn from the raw score population described by the null hypothesis

sampling distribution of r A frequency distribution showing all possible values of r that occur when samples are drawn from a population in which ? is zero

sampling distribution of r_s A frequency distribution showing all possible values of rs that occur when samples are drawn from a population in which rs is zero

sampling error The variation, due to random chance, between a sample statistic and the population parameter it represents

sampling with replacement A sampling procedure in which previously selected individuals or events are returned to the population before any additional samples are selected

sampling without replacement A sampling procedure in which previously selected individuals or events are not returned to the population before additional samples are selected

scatterplot A graph of the individual data points from a set of X-Y pairs

s The symbol for the standard error of the mean difference

significant Describes the results that are too likely to accept as resulting from chance sampling error when the predicted relationship does not exist; it indicates rejection of the null hypothesis

simple frequency The number of times that a score occurs in data

simple frequency distribution A distribution of scores, organized to show the number of times each score occurs in a set of data

slope A number that indicates how much a linear regression line slants and in which direction it slants; used in computing predicted Y scores

Spearman rank-order correlation coefficient The correlation coefficient that describes the linear relationship between pairs of ranked scores

standard error of the difference The estimated standard deviation of the sampling distribution of differences between the means of independent samples in a two-sample experiment

standard error of the estimate A standard deviation indicating the amount that the actual Y scores in a sample differ from, or are spread out around, their corresponding Y' scores

standard error of the mean The standard deviation of the sampling distribution of means; used in the z-test and estimated in the one-sample t-test

standard error of the mean difference The standard deviation of the sampling distribution of means differences between related samples in a two-sample experiment

standard normal curve A theoretical perfect normal curve, which serves as a model of the perfect normal z-distribution

standard score What z-scores are often referred to

statistic A number that describes a characteristic of a sample of scores, symbolized by a letter from the English alphabet

statistical hypothesis Two statements (H0 and Ha) that describe the population parameters the sample statistics will represent if the predicted relationship exists or does not exist

statistical notation The standardized code for the mathematical operations performed in formulas and for the answers obtained

strength of a relationship The extent to which one value of Y within a relationship is consistently associated with one and only one value of X; also called the degree of association

strength of a relationship The extent to which one value of Y within a relationship is consistently associated with one and only one value of X; also called the degree of association

sum of squares The sum of the squared deviations of a set of scores around the mean of those scores

sum of the deviations around the mean The sum of all differences between the scores and the mean; symbolized as S(X - )

sum of the squared Xs A result calculated by squaring each score in a sample and adding the squared scores

sum of X The sum of the scores in a sample; symbolized by SX

sum of X The sum of the scores in a sample

s_X The symbol used to estimate the variability in the population

s1-2 The symbol for the standard error of the difference

s²error The symbol for the error variance

s²treat The symbol for treatment variance

s²x The symbol used when describing the true population variability

s The symbol for the standard error of the mean when used in the z-test






tail The far-left or far-right portion of a frequency polygon, containing the relatively low-frequency, extreme scores

test of independence A name for the two-way chi square, because it tests whether the frequencies in the categories of one variable are independent of the categories of the other variable

tied rank The situation that occurs when two subjects in a sample receive the same rank-order score on a variable

transformation A systematic mathematical procedure for converting a set of scores into a different but equivalent set of scores

treatment The condition of the independent variable; also called level

treatment The condition of the independent variable; also called level

treatment effect The result of changing the conditions of an independent variable so that different populations of scores having different µs are produced

treatment variance In ANOVA, the variability between scores from different populations that would be created by the different levels of a factor

Tukey's HSD multiple comparisons test The post hoc procedure performed with ANOVA to compare means from a factor in which all levels have equal n

two-tailed test The test used to evaluate a statistical hypothesis that predicts a relationship but not whether scores will increase or decrease

two-way , between-subjects ANOVA The parametric inferential procedure performed when both factors are between-subjects factors

two-way ANOVA The parametric inferential procedure performed when an experiment contains two independent variables

two-way chi square The chi square procedure for testing whether, in the population, frequency of category membership on one variable is independent of frequency of category membership on the other variable

two-way interaction effect In a two-way ANOVA, the combination of the levels of one factor with the levels of the other factor

two-way, mixed-design ANOVA The parametric inferential procedure performed wwehn the design involves one within-subjects factor and one between-subjects factor

two-way, within-subjects ANOVA The parametric inferential procedure performed when both factors are within-subjects factors

Type I error A statistical decision-making error in which a large amount of sampling error causes rejection of the null hypothesis when the null hypothesis is true (that is, when the predicted relationship does not exist)

Type II error A statistical decision-making error in which the closeness of the sample statistic to the population parameter described by the null hypothesis causes the null hypothesis to be retained when it is false (that is, when the predicted relationship does exist

type of relationship The form of the correlation between the X scores and the Y scores in a set of data, determined by the overall direction in which the Y scores change as the X scores change






unbiased estimator A formula for a sample's variability that involves dividing by N - 1 that equally often under- and over-estimate the corresponding population variability

unconfounded comparison In a two-way ANOVA, a comparison between two cells that differ along only one factor

ungrouped distribution A distribution that shows information about each score individually

unimodal distribution A distribution whose frequency polygon has only one hump and thus has only one score qualifying as the mode

univariate statistics Procedures applied to a study that measures only one dependent variable






variable Anything that, when measured, can produce two or more different scores

variance of the Y scores around Y' In regression, the average squared deviation between the actual Y scores and corresponding predicted Y' scores






Wilcoxon T text The nonparametric version of the related-samples t-test for ranked scores

within-subjects ANOVA The type of ANOVA performed when a study involves within-subjects factors

within-subjects factor The type of factor created when an independent variable is studied using related samples in all conditions because subjects are either matched or repeatedly measured






X²-distribution The sampling distribution of all possible vaules of X2 that occur when the samples represent the distribution of frequencies described by the null hypothesis