GL-1

A

analysis of variance (ANOVA) A hypothesis test typically used with one or more nominal (and sometimes ordinal) independent variables (with at least three groups overall) and a scale-dependent variable.

assumption A characteristic that we ideally require the population from which we are sampling to have so that we can make accurate inferences.

B

bar graph A visual depiction of data in which the independent variable is nominal or ordinal and the dependent variable is scale. The height of each bar typically represents the average value of the dependent variable for each category.

between-groups ANOVA A hypothesis test in which there are more than two samples, and each sample is composed of different participants.

between-groups research design An experimental design in which participants experience one and only one level of the independent variable.

between-groups variance An estimate of the population variance, based on the differences among the means.

bimodal A distribution that has two modes, or most common scores.

C

ceiling effect A situation in which a constraint prevents a variable from taking on values above a given number.

cell A box that depicts one unique combination of levels of the independent variables in a factorial design.

central limit theorem The idea that a distribution of sample means is a more normal distribution than a distribution of scores, even when the population distribution is not normal.

central tendency A descriptive statistic that best represents the center of a data set, the particular value that all the other data seem to be gathering around.

chartjunk Any unnecessary information or feature in a graph that detracts from a viewer’s ability to understand the data.

chi-square test for goodness of fit A nonparametric hypothesis test that is used when there is one nominal variable.

chi-square test for independence A nonparametric hypothesis test that is used when there are two nominal variables.

coefficient alpha A commonly used estimate of a test or measure’s reliability, symbolized as α, and is calculated by taking the average of all possible split-half correlations; sometimes called Cronbach’s alpha.

Cohen’s d A measure of effect size that assesses the difference between two means in terms of standard deviation, not standard error.

confidence interval An interval estimate based on a sample statistic; it includes the population mean a certain percentage of the time if the same population is sampled from repeatedly.

confirmation bias Our usually unintentional tendency to pay attention to evidence that confirms what we already believe and to ignore evidence that would disconfirm our beliefs. Confirmation biases closely follow illusory correlations.

confounding variable Any variable that systematically varies with the independent variable so that we cannot logically determine which variable is at work; also called a confound.

continuous observation Observed data point that can take on a full range of values (e.g., numbers out to several decimal places); an infinite number of potential values exists.

control group A level of the independent variable that does not receive the treatment of interest in a study. It is designed to match an experimental group in all ways but the experimental manipulation itself.

convenience sample A subset of a population that uses participants who are readily available.

correlation An association between two or more variables.

correlation coefficient A statistic that quantifies a relation between two variables.

Cramér’s V The standard effect size used with the chi-square test for independence; also called Cramér’s phi, symbolized as ϕ.

critical region The area in the tails of the comparison distribution in which the null hypothesis can be rejected.

critical value A test statistic value beyond which we reject the null hypothesis; often called a cutoff.

D

defaults The options that the software designer has preselected; these are the built-in decisions that the software will implement if you do not instruct it otherwise.

degrees of freedom The number of scores that are free to vary when we estimate a population parameter from a sample.

dependent variable The outcome variable that we hypothesize to be related to or caused by changes in the independent variable.

descriptive statistic Statistical technique that organizes, summarizes, and communicates a group of numerical observations.

deviation from the mean The amount that a score in a sample differs from the mean of the sample; also called a deviation.

discrete observation Observed data point that can take on only specific values (e.g., whole numbers); no other values can exist between these numbers.

distribution of means A distribution composed of many means that are calculated from all possible samples of a given size, all taken from the same population.

duck A form of chartjunk in which a feature of the data has been dressed up to be something other than merely data.

GL-2

E

effect size A standardized value that indicates the size of a difference and is unaffected by sample size.

expected relative-frequency probability The likelihood of an event occurring based on the actual outcome of many, many trials.

experiment A study in which participants are randomly assigned to a condition or level of one or more independent variables.

experimental group A level of the independent variable that receives the treatment or intervention of interest in an experiment.

F

F statistic A ratio of two measures of variance: (1) between-groups variance, which indicates differences among sample means, and (2) within-groups variance, which is essentially an average of the sample variances.

factor A term used to describe an independent variable in a study with more than one independent variable.

factorial ANOVA A statistical analysis used with one scale dependent variable and at least two nominal independent variables (also called factors); also called a multifactorial ANOVA.

floor effect A situation in which a constraint prevents a variable from taking values below a certain point.

frequency distribution A distribution that describes the pattern of a set of numbers by displaying a count or proportion for each possible value of a variable.

frequency polygon A line graph, with the x-axis representing values (or midpoints of intervals) and the y-axis representing frequencies; a dot is placed at the frequency for each value (or midpoint), and the dots are connected.

frequency table A visual depiction of data that shows how often each value occurred, that is, how many scores were at each value. Values are listed in one column, and the numbers of individuals with scores at that value are listed in the second column.

G

generalizability Researchers’ ability to apply findings from one sample or in one context to other samples or contexts; also called external validity.

grand mean The mean of every score in a study, regardless of which sample the score came from.

grids Chartjunk that take the form of a background pattern, almost like graph paper, on which the data representations, such as bars, are superimposed.

grouped frequency table A visual depiction of data that reports frequencies within a given interval rather than the frequencies for a specific value.

H

heteroscedastic A term given to populations that have different variances.

histogram A graph that looks like a bar graph but depicts just one variable, usually based on scale data, with the values of the variable on the x-axis and the frequencies on the y-axis.

homoscedastic A term given to populations that have the same variance; homoscedasticity is also called homogeneity of variance.

hypothesis testing The process of drawing conclusions about whether a particular relation between variables is supported by the evidence.

I

illusory correlation The phenomenon of believing one sees an association between variables when no such association exists.

independent variable A variable that has at least two levels that we either manipulate or observe to determine its effects on the dependent variable.

independent-samples t test A hypothesis test used to compare two means for a between-groups design, a situation in which each participant is assigned to only one condition.

inferential statistic Statistical technique that uses sample data to make general estimates about the larger population.

interaction A statistical interaction that occurs in a factorial design when two or more independent variables have an effect on the dependent variable in combination that neither independent variable has on its own.

intercept The predicted value for Y when X is equal to 0, which is the point at which the line crosses, or intercepts, the y-axis.

interval estimate An estimate based on a sample statistic that provides a range of plausible values for the population parameter.

interval variable A variable used for observations that have numbers as their values; the distance (or interval) between pairs of consecutive numbers is assumed to be equal.

L

level A discrete value or condition that a variable can take on.

line graph A graph used to illustrate the relation between two scale variables.

linear relation A relation between variables best described by a straight line.

M

main effect A result occurring in a factorial design when one of the independent variables has an influence on the dependent variable.

Mann–Whitney U test A nonparametric hypothesis test used when there are two groups, a between-groups design, and an ordinal dependent variable.

marginal mean The mean of a row or a column in a table that shows the cells of a study with a two-way ANOVA design.

mean The arithmetic average of a group of scores. It is calculated by summing all the scores in a data set and then dividing this sum by the total number of scores.

median The middle score of all the scores in a sample when the scores are arranged in ascending order. If there is no single middle score, the median is the mean of the two middle scores.

meta-analysis A study that involves the calculation of a mean effect size from the individual effect sizes of many studies.

mode The most common score of all the scores in a sample.

moiré vibrations Any visual patterns that create a distracting impression of vibration and movement.

multimodal A distribution that has more than two modes, or most common scores.

multiple regression A statistical technique that includes two or more predictor variables in a prediction equation.

GL-3

N

negative correlation An association between two variables in which participants with high scores on one variable tend to have low scores on the other variable.

negatively skewed Data that have a distribution with a tail that extends to the left, in a negative direction.

nominal variable A variable used for observations that have categories, or names, as their values.

nonlinear relation A relation between variables best described by a line that breaks or curves in some way.

nonparametric test An inferential statistical analysis that is not based on a set of assumptions about the population.

normal curve A specific bell-shaped curve that is unimodal, symmetric, and defined mathematically.

normal distribution A specific frequency distribution that is a bell-shaped, symmetric, unimodal curve.

null hypothesis A statement that postulates that there is no difference between populations or that the difference is in a direction opposite of that anticipated by the researcher.

O

one-tailed test A hypothesis test in which the research hypothesis is directional, positing either a mean decrease or a mean increase in the dependent variable, but not both, as a result of the independent variable.

one-way ANOVA A hypothesis test that includes both one nominal independent variable with more than two levels and a scale-dependent variable.

operational definition The operations or procedures used to measure or manipulate a variable.

ordinal variable A variable used for observations that have rankings (i.e., 1st, 2nd, 3rd. . .) as their values.

orthogonal variable An independent variable that makes a separate and distinct contribution in the prediction of a dependent variable, as compared with the contributions of another variable.

outcome In reference to probability, the result of a trial.

P

p level The probability used to determine the critical values, or cutoffs, in hypothesis testing (often called alpha).

paired-samples t test A test used to compare two means for a within-groups design, a situation in which every participant is in both samples; also called a dependent-samples t test.

parameter A number based on the whole population; parameters are usually symbolized by Greek letters.

parametric test An inferential statistical analysis based on a set of assumptions about the population.

Pareto chart A type of bar graph in which the categories along the x-axis are ordered from highest bar on the left to lowest bar on the right.

Pearson correlation coefficient A statistic that quantifies a linear relation between two scale variables.

personal probability A person’s own judgment about the likelihood that an event will occur; also called subjective probability.

pictorial graph A visual depiction of data typically used for an independent variable with very few levels (categories) and a scale dependent variable. Each level uses a picture or symbol to represent its value on the scale dependent variable.

pie chart A graph in the shape of a circle, with a slice for every level (category) of the independent variable. The size of each slice represents the proportion (or percentage) of each level.

point estimate A summary statistic from a sample that is just one number used as an estimate of the population parameter.

pooled variance A weighted average of the two estimates of variance—one from each sample—that are calculated when conducting an independent-samples t test.

population All possible observations about which we’d like to know something.

positive correlation An association between two variables such that participants with high scores on one variable tend to have high scores on the other variable as well, and those with low scores on one variable tend to have low scores on the other variable.

positively skewed Data for which the distribution’s tail extends to the right, in a positive direction.

post hoc test A statistical procedure frequently carried out after the null hypothesis has been rejected in an analysis of variance; it allows us to make multiple comparisons among several means; often referred to as a follow-up test.

probability The likelihood that a particular outcome—out of all possible outcomes—will occur.

proportionate reduction in error A statistic that quantifies how much more accurate predictions are when we use the regression line instead of the mean as a prediction tool; also called the coefficient of determination.

psychometricians The statisticians and psychologists who develop tests and measures.

psychometrics The branch of statistics used in the development of tests and measures.

Q

qualitative interaction A particular type of quantitative interaction of two (or more) independent variables in which one independent variable reverses its effect depending on the level of the other independent variable.

quantitative interaction An interaction in which the effect of one independent variable is strengthened or weakened at one or more levels of the other independent variable, but the direction of the initial effect does not change.

R

R² The proportion of variance in the dependent variable that is accounted for by the independent variable.

random assignment The protocol established for an experiment whereby every participant in a study has an equal chance of being assigned to any of the groups, or experimental conditions, in the study.

random sample A subset of a population in which every member of the population has an equal chance of being selected into the study.

GL-4

range A measure of variability calculated by subtracting the lowest score (the minimum) from the highest score (the maximum).

range-frame A scatterplot or related graph that indicates the range of the data on each axis; the lines extend only from the minimum to the maximum scores.

ratio variable A variable that meets the criterion for an interval variable but also has a meaningful zero point.

raw score A data point that has not yet been transformed or analyzed.

regression to the mean The tendency of scores that are particularly high or low to drift toward the mean over time.

relative risk A measure created by making a ratio of two conditional proportions; also called relative likelihood or relative chance.

reliability The consistency of a measure.

replication The duplication of scientific results, ideally in a different context or with a sample that has different characteristics.

research hypothesis A statement that postulates that there is a difference between populations or sometimes, more specifically, that there is a difference in a certain direction, positive or negative; also called an alternative hypothesis.

robust A term given to a hypothesis test that produces fairly accurate results even when the data suggest that the population might not meet some of the assumptions.

S

sample A set of observations drawn from the population of interest.

scale variable A variable that meets the criteria for an interval variable or a ratio variable.

scatterplot A graph that depicts the relation between two scale variables.

simple linear regression A statistical tool that lets us predict a person’s score on the dependent variable from his or her score on one independent variable.

single-sample t test A hypothesis test in which we compare a sample from which we collect data to a population for which we know the mean but not the standard deviation.

skewed distribution A distribution in which one of the tails of the distribution is pulled away from the center.

slope The amount that Y is predicted to increase for an increase of 1 in X.

source table A table that presents the important calculations and final results of an ANOVA in a consistent and easy-to-read format.

Spearman rank-order correlation coefficient A nonparametric statistic that quantifies the association between two ordinal variables.

standard deviation The square root of the average of the squared deviations from the mean; it is the typical amount that each score varies, or deviates, from the mean.

standard error The name for the standard deviation of a distribution of means.

standard error of the estimate A statistic that indicates the typical distance between a regression line and the actual data points.

standard normal distribution A normal distribution of z scores.

standardization A way to convert individual scores from different normal distributions to a shared normal distribution with a known mean, standard deviation, and percentiles.

standardized regression coefficient A standardized version of the slope in a regression equation, it is the predicted change in the dependent variable in terms of standard deviations for an increase of 1 standard deviation in the independent variable; symbolized by β and often called beta weight.

statistic A number based on a sample taken from a population; statistics are usually symbolized by Latin letters.

statistical power A measure of the likelihood that we will reject the null hypothesis, given that the null hypothesis is false.

statistically significant A name given to a finding in which the data differ from what we would expect by chance if there were, in fact, no actual difference.

success In reference to probability, the outcome for which we’re trying to determine the probability.

sum of squares The sum of each score’s squared deviation from the mean; symbolized as SS.

T

t statistic A statistic that indicates the distance of a sample mean from a population mean in terms of the estimated standard error.

test–retest reliability A method that determines whether the scale being used provides consistent information every time the test is taken.

time plot, or time series plot A graph that plots a scale variable on the y-axis as it changes over an increment of time (e.g., second, day, century) labeled on the x-axis.

trial In reference to probability, each occasion that a given procedure is carried out.

Tukey HSD test A widely used post hoc test that determines the differences between means in terms of standard error; the HSD is compared to a critical value; sometimes called the q test.

two-tailed test A hypothesis test in which the research hypothesis does not indicate a direction of the mean difference or change in the dependent variable, but merely indicates that there will be a mean difference.

two-way ANOVA A hypothesis test that includes two nominal independent variables, regardless of their numbers of levels, and a scale dependent variable.

Type I error The result when we reject the null hypothesis, but the null hypothesis is correct.

Type II error The result when we fail to reject the null hypothesis, but the null hypothesis is false.

U

unimodal A distribution that has one mode, or most common score.

V

validity The extent to which a test actually measures what it was intended to measure.

GL-5

variability A numerical way of describing how much spread there is in a distribution.

variable Any observation of a physical, attitudinal, or behavioral characteristic that can take on different values.

variance The average of the squared deviations from the mean.

volunteer sample A special kind of convenience sample in which participants actively choose to participate in a study; also called a self-selected sample.

W

within-groups ANOVA A hypothesis test in which there are more than two samples, and each sample is composed of the same participants; also called a repeated-measures ANOVA.

within-groups research design An experimental design in which all participants in the study experience the different levels of the independent variable; also called a repeated-measures design.

within-groups variance An estimate of the population variance, based on the differences within each of the three (or more) sample distributions.

Z

z distribution A normal distribution of standardized scores.

z score The number of standard deviations a particular score is from the mean.