# Glossary

**a priori contrasts** – See planned comparisons.

**alternative hypothesis** – Generally, the antithesis of the null hypothesis. The alternative hypothesis is assumed to reflect the true status of the relationship between variables when the null hypothesis is rejected. Typically, the alternative hypothesis is the research hypothesis.

**animal research** – Research conducted with animal models.

**ANOVA** – Analysis of variance. An inferential statistical procedure involving the examination of mean differences when the independent variable has three or more levels to be compared.

**applied research** – Seeks to determine an immediate solution to be applied to a present problem; generally conducted to answer a precisely stated question.

**asymptotic** – Describes a curve that approaches but never touches the X-axis.

**basic research** – Seeks to increase the depth of understanding of a process by exploring fundamental principles; generally theoretical in nature.

**between-groups design** – Research design in which each subject appears in one group only.

**biased statistic** – A statistic is biased if the mean of its sampling distribution is *not* equal to the population parameter.

**Bonferroni adjustment** – A procedure to reduce the probability of a Type I error when performing multiple tests of significance.

**canonical model** – The general model of relating any number of predictor *(X)* variables with any number of predicted variables *(Y)*.

**central limit theorem** – A theory stating that with repeated samples, the sampling distribution of a statistic will become normally distributed regardless of the shape of the original population’s distribution.

**cluster sampling** – Method of deriving a sample from a population when natural groups of subjects are used as the sampling unit.

**coefficient of determination (r2)** – Statistic representing the percentage of variation in the predicted variable *(Y)* that can be accounted for by the value of the predictor variable *(X)*; the square of the correlation coefficient.

**complex comparison** – A multiple comparison procedure involving more than two means.

**conceptual replication** – A method of increasing external validity by modifying the independent variables or by measuring the dependent variable differently.

**concurrent validity** – A measurement procedure has concurrent validity when a correlation exists between the measure and a criterion measure obtained at the same point in time.

**confidence level** – A researcher-selected percentage (typically, 95% or 99%) indicating the relative confidence of a decision.

**consistency** – An estimate is consistent if it is more accurate as the sample size increases.

**construct validity** – A measurement procedure has construct validity when there is sufficient evidence suggesting that an unobservable construct exists.

**content validity** – A measurement procedure has content validity when it adequately assesses the content of the attribute being measured.

**continuous measurement** – Interval and ratio measurement scales are said to be continuous *(*see* interval *and* ratio)*.

**contrast-based error rate** – A multiple comparison procedure where the alpha level is applied to each contrast conducted.

**convenience sampling** – Selecting subjects who are conveniently available. Sometimes called *accidental sampling*.

**convergent validity** – A measurement has convergent validity when there is correlational evidence suggesting that two measures are assessing the same construct.

**correlation coefficient** – A statistic indicating the magnitude and direction of the relationship between two or more variables.

**correlational statistics** – Measurements obtained from a sample that seek to describe the relationship between two or more variables.

**Cronbach’s alpha** – An intraclass reliability coefficient.

**cross-sectional research** – A procedure in which different groups of subjects are measured at the same point in time and then group differences are extrapolated through comparison of the results. It provides a snapshot in time.

**deductive reasoning** – Reasoning that moves from observations of general information to the explanation of specific events; opposite of inductive reasoning.

**degrees of freedom** – The number of values in the calculation of a statistic that are free to vary when restrictions are placed on the data.

**dependent t -test** – A statistical procedure used to test mean differences between two matched, paired, or correlated groups of subjects. Also used for repeated-measures analysis.

**dependent variable** – The variable that is expected to change and is measured (the outcome). The symbol for the dependent variable is usually *Y*.

**descriptive research** – Describes the current status of behavior and events.

**descriptive statistics** – Measurements obtained from a sample that seek to describe the data set; they tell how alike or different the measures are.

**differential selection of subjects** – A threat to internal validity when the characteristics of the subjects are initially different in the treatment conditions because of improper or unavoidable selection and/or assignment procedures.

**discriminant validity** – A measurement has discriminant validity when there is correlational evidence suggesting that two measures do not assess the same construct.

**effect size (ES)** – A statistic that reflects the amount of difference between measures in terms of standard deviation units.

**efficiency** – The relative precision with which an estimator estimates a parameter.

**estimate** – See *statistic*.

**evidence-based** – Grounded on sound theory and data obtained from research conducted according to the scientific method.

**expectancy** – A threat to external validity where the researcher’s bias or prior beliefs about the study outcome cause unintentional effects on the study; also referred to as “the self-fulfilling prophecy.”

**expected mean square** – The mathematical expected value of the variance resulting from repeated sampling from a distribution.

**expected value** – The mean of a statistic’s sampling distribution.

**experimental mortality** – A threat to internal validity where uneven loss of subjects occurs from the various treatment conditions during the course of the study.

**experimental research** – Seeks to determine cause-and-effect relationships.

**external validity** – Evidence that the findings of a study can be generalized to other situations, subjects, or environments.

**face validity** – A measurement procedure has face validity when it appears to measure what it is supposed to measure.

**family-based error rate** – A multiple comparison procedure where the alpha level is applied to the entire set of contrasts conducted.

**fixed independent variables** – Independent variable levels that are selected by the researcher and thus are not selected at random.

**generalizability** – The certainty with which the findings of a study can be applied to other situations, subjects, or environments.

**Hawthorne effect** – A threat to external validity where subjects may change their behaviors or outcome because they are aware they are subjects in a study.

**histogram** – A graphical representation of the frequency of scores in a distribution; sometimes called a bar graph.

**homogeneity of variance** – A parametric statistic assumption for the* t* -test and ANOVA requiring that the variances of all groups are equivalent.

**human research** – Research conducted with human subjects.

**independent t -test** – A statistical procedure used to test mean differences between two independent groups of subjects.

**independent variable** – The variable that is manipulated by the researcher. In some situations, this is called the treatment, exposure, or predictor variable. The symbol for the independent variable is usually X.

**inductive reasoning** – Reasoning that moves from observations of specific events to predictions about general principles; opposite of deductive reasoning.

**inferential statistics** – Process of obtaining data on a sample and generalizing (i.e., inferring) its characteristics to the population from which the sample was drawn.

**instrumentation** – A threat to internal validity where measurement errors due to faulty equipment or a change in the definition of the measured variable result in incorrect data.

**interaction** – The combined effects of two or more independent variables on a dependent variable.

**interclass correlation** – A measure of the relationship between two variables. Often used to estimate reliability with the Pearson product-moment correlation coefficient.

**internal validity** – Evidence that the results of an experiment can be attributed to the effect of the independent variable rather than some confounding variable(s).

**interval estimate** – A range of values around a sample statistic developed with a selected level of confidence.

**interval measurement** – A measurement made by using a scale to quantify the amount of some characteristic possessed by the subjects. The zero value on the scale is arbitrarily chosen.

**intraclass correlation** – A measure of the relationship between two or more repeatedly measured variables. Often used to estimate reliability. (See Cronbach’s alpha.)

**kurtosis** – A shape characteristic related to the variability and peakedness of a distribution; types of kurtosis are mesokurtic, leptokurtic, and platykurtic.

**leptokurtic** – The shape of a distribution that is peaked, with scores being more homogeneous (less scattered) than in a normal curve.

**level of confidence** – The researcher-chosen degree of certainty regarding the decision to reject or accept the null hypothesis.

**local history** – A threat to internal validity in which unanticipated events occurring during a study may alter the subjects’ behaviors in an uncontrolled and unaccountable way.

**longitudinal research** – A procedure in which changes are measured repeatedly over a period of time (e.g., weeks, months, even years) on the same subjects.

**MANOVA** – Multivariate ANOVA; an extension of ANOVA that permits the testing of multiple dependent variables.

**maturation of subjects** – A threat to internal validity when change affects the subjects’ characteristics due to growth or development.

**mean square** – An estimate of the population variance calculated by dividing the sum of squares by the associated degrees of freedom.

**mean** – The arithmetic average of a set of scores in a distribution.

**measures of central tendency** – Statistics that serve to quantify the center of a distribution.

**measures of variability** – Statistics that serve to quantify the dispersion or spread in a distribution of scores.

**median** – The point below and above which 50 percent of the scores in a distribution fall. The median is the 50th percentile and most typical score.

**mesokurtic** – The shape of a distribution resembling the normal distribution.

**mode** – The most frequently occurring score in a distribution.

**multiple comparisons (MC)** – Statistical methods used to investigate where mean differences are (typically following a significant omnibus test) after ANOVA or ANCOVA.

**multiple correlation** – A statistic representing the correlation between a predicted variable *(Y)* and more than one predictor variable *(X)*. The multiple correlation ranges from 0.00 to 1.00.

**multiple regression** – See *multiple correlation*.

**nominal measurement** – A measurement made by assessment of equality or difference; often uses descriptors to classify subjects into categories.

**nonparametric statistics** – A branch of statistics in which the data do not have to meet certain assumptions required for parametric statistics (e.g., continuous measurement, normality).

**null hypothesis** – A statement that the independent variable and the dependent variable are not related. It is the null hypothesis that researchers actually test and make decisions about, based on probability.

**objectivity** – The reliability of raters to record the same value for the same observation. Objectivity ranges from 0.00 to 1.00.

**omega squared (ω2)** – An estimate of the percentage of variability in the system that can be attributed to the influence of the independent variable.

**one-tailed test** – A statistical test where the probability of making a Type I error is all located in one end of the distribution.

**ordinal measurement** – A measurement made by ranking subjects based on whether one has more or less of some characteristic than another.

**overgeneralizing** – A threat to external validity resulting from a tendency to generalize beyond the levels of the independent and/or dependent variables in the study.

**parameter** – A fact about a population, typically represented by a Greek symbol.

**parametric statistics** – A branch of statistics whose accuracy is predicated on the validity of certain assumptions about the population from which the samples have been drawn and about the samples themselves.

**Pearson product-moment (PPM) correlation coefficient** – Correlation coefficient widely used in all sciences to quantify the magnitude and direction of the linear relationship between any two variables; also referred to as Pearson’s r. Ranges from –1.00 (perfect negative correlation) to +1.00 (perfect positive correlation). Zero indicates no correlation.

**percent improvement** – Reflects the percentage of change that occurred between measures from one occasion to another or the percentage of difference from baseline or control to subsequent measurements.

**percentile** – The percentage of scores falling at or below a given value.

**planned comparisons** – A multiple comparison procedure where the contrasts to be tested are identified before the study is conducted. Also referred to as *a priori* contrasts.

**platykurtic** – The shape of a distribution that is flatter than the normal curve, with more values in the tails of the distribution than in the normal curve.

**point estimate** – The value of a sample statistic used to estimate a parameter.

**population** – Any set of subjects that have at least one attribute in common.

**post hoc test** – Multiple comparison procedure designed to test the significance of group differences following the finding of a significant *F* -ratio.

**power** – The probability of rejecting the null hypothesis when it is false.

**predictive validity** – A measurement procedure has predictive validity when a correlation exists between the measure and a criterion measure to be obtained at some future point in time.

**pretest sensitization** – A threat to external validity that occurs when subjects’ subsequent behavior is influenced by having completed a pretest.

**pretesting** – A threat to internal validity where subjects’ characteristics may change due to administration of a pretest. Also a threat to external validity because subjects who have been pretested may no longer represent the population.

**qualitative research** – Seeks to describe and to qualify what occurs; relies on subjective and observational information.

**random independent variable** – Independent variable in which levels are selected by the researcher with random procedures.

**random sampling** – Method of deriving a sample from a population where every subject in the population has an equally likely chance of being selected to be in the sample and every subject in the population has an independent chance of being selected.

**range** – The difference between the high score and the low score. The exclusive range is the difference between the high and low score; the inclusive range is the exclusive range plus one.

**ratio measurement** – A measurement scale containing an absolute zero. Ratio measurements permit statements of comparison, such as “twice as much.”

**reliable (reliability)** – A characteristic indicating the consistency of measurement. Reliability ranges from 0.00 to 1.00.

**repeated-measures design** – An experimental design used to discover mean differences between a set of subjects measured on more than one occasion. Also called a within-subjects design.

**research hypothesis** – A prediction derived from theory or a researcher’s speculation regarding the likely outcome of an experiment.

**robust** – The ability of a statistical procedure to be valid even when the assumptions required for that procedure are not met.

**sample** – A subset of subjects selected from a population.

**sampling distribution** – A frequency distribution of a statistic developed from repeated samples of the same size taken from a defined population.

**sampling error** – The difference between a statistic and a parameter.

**scattergram** – Graph representing the relationship between two variables (*X* and *Y*). Also called *scatterplot*.

**scatterplot** – See *scattergram*.

**scientific method** – A method of knowing based on hypothesis development, data collection, and decision making. It is verifiable and reproducible.

**semi-interquartile range** – A measure of variability calculated as half the distance between the 75th and the 25th percentiles.

**significant** – A statistical result concluding that the observed differences are not attributable to chance. When the null hypothesis is rejected, the results are said to be statistically significant.

**simple comparison** – A multiple comparison procedure involving only two means.

**skewness** – A shape characteristic related to the degree to which a distribution departs from symmetry around its mean.

**sphericity** – An assumption for repeated-measures (within groups) designs that relates to the variances, the correlations, and score differences from all of the levels of the independent variable.

**standard deviation** – A linear measure of variability. The standard deviation is equal to the square root of the variance.

**standard error (SE)** – See *standard error of estimate*.

**standard error of estimate (SEE)** – A statistic indicating the amount of error present when predicting Y from one or more predictor variables (X) . Also called the standard error (SE) or standard error of prediction (SEP). The SEE is a standard deviation.

**standard error of measurement (SEM)** – A value reflecting the amount of variation in an observed score that is attributable to errors of measurement.

**standard error of prediction (SEP)** – See standard error of estimate.

**standard error of the mean** – A statistic reflecting the variability around a sample estimate. It is the standard deviation of a sampling distribution.

**standard scores** – Scores derived from an original distribution that results in a given mean and standard deviation. See *z-score* and *T-score*.

**statistic** – A fact about a sample, typically represented by a Roman letter.

**statistical regression** – A threat to internal validity resulting from the tendency for extreme scores to move toward the group mean when measured a second time; also referred to as regression to the mean.

**stratified sampling** – Method of deriving a sample from a population that ensures the sample is representative of the population for selected characteristics.

**sums of squares** – The sum of the squared deviations of each score from the mean. The numerator in a variance estimate.[/learn_more]

**systematic sample** – Method of deriving a sample from a population by selecting every *n* th subject from a list of every subject in the population.

**T -score** – A standardized score with a mean of 50 and standard deviation of 10.

**theory** – An educated supposition about the relationship among some natural phenomena, generally derived through observation, experimentation, and reflective thinking.

**transferability** – How well the results of a study can describe, explain, or predict the behaviors of individuals different from those in the study or in dissimilar situations and environments.

**two-tailed test** – A statistical test where the probability of making a Type I error is shared equally on both ends of the distribution.

**Type I error** – Rejecting the null hypothesis when it is actually true. An alpha (α) error.

**Type II error** – Failing to reject the null hypothesis when it is actually false. A beta error (β).

**valid** – A measurement that assesses what it is intended to assess (i.e., it is truthful).

**variable** – A measured characteristic that can take on different values (e.g., height, weight, BMI).

**variance** – *General definition:* The fact that that not all values are the same for measured characteristics; there is variability in things, persons, and observations. *Statistical definition:* A statistic quantifying the amount of variability in a set of scores. It is the average of the squared deviation from the mean.

**within-groups design** – Research design in which subjects appear in more than one group and are measured more than once. See also *repeated-measures design*.

**within-subjects design** – See *repeated-measures design*.

**z -score** – A standardized score with a mean of 0 and standard deviation of 1. *z* -score values are the same as standard deviation units.