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# EPPP - Statistics &amp; Research Methods

## Terms

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AB Design
Single-subject research design involving one baseline phase (A) and one treatment phase (B).
Alpha Level
The probability of rejecting the null hypothesis when it is true; i.e., the probability of making a Type I error. Its value is set by the researcher prior to data collection or analysis.
ANCOVA
Analysis of Covariance; an analysis of variance which allows for the statistical control of one or more than one unstudied but related variables. For example, in studying various types of reading programs for different aged children, the effect of the chi
ANOVA
Analysis of variance. A statistical test for at least one independent variable and one dependent variable. Includes one-way ANOVA (for one independent variable) and factorial ANOVA (for two or more independent variables). The factorial ANOVA allows the ex
Case Study
The in-depth study of a single unit of investigation (e.g., individual, community, institution). From an experimental viewpoint, case studies are primarily useful to identify variables for future research.
Chi-Square Test
Statistical hypothesis test used with nominal (categorical) data. Assesses the probability that observed frequencies within categories significantly differ from what is expected under the null hypothesis.
Coefficient Of Determination
The square of the correlation coefficient; indicates the percentage of variability shared by two variables.
Cohort Effects
Differences between subjects of cross-sectional research that have to do with experience rather than with age. Cohort effects threaten the conclusion that observed differences between subjects are related to age.
Confounding Variable
An extraneous, uncontrolled variable, the effects of which can't be separated from those of the independent variable.
Control Group
In a research study, the comparison group that is not exposed to the "active" level of the independent variable; i.e., a "no-treatment" or placebo group.
Correlation Coefficient
A statistical index ranging from -1.00 and +1.00 which expresses how closely two variables are related to each other. The coefficient can be either positive or negative. The types of correlation coefficients include (among others) Pearson r, Spearman's rh
Correlational Research
The type of investigation in which variables are measured only, not manipulated, in order to determine the relationships among these variables.
Counterbalancing
Method used in repeated measures designs to control for order effects. Involves dividing the subjects into groups and then administering the treatments in a different order for each group.
Cross-Sectional Research
Research design in which a sample of individuals representative of several dimensions of the population is assessed at the same time. For instance, in studying the effects of age, the design might include young, middle-aged, and older subjects.
Cross-Sequential Research
Research in which individuals representing several different age groups are studied over a period of time. Cross-sequential research combines the methodologies of cross-sectional and longitudinal research and reduces the problems associated with both.
Cross-Validation
Process of re-establishing a test's criterion-related validity, by determining how valid its items are for a new sample of test takers. Usually, the validity coefficient "shrinks" upon cross-validation.
Degrees Of Freedom
A value used in the calculation of values yielded by statistical hypotheses tests; reflects the number of scores that, given a fixed value (e.g., a sample mean) are "free to vary."
Demand Characteristics
Cues in an experimental setting that allow subjects to guess the experimental hypothesis.
Dependent Variable
The variable which shows an effect or is the outcome of an experiment. The dependent variable is measured after the investigator manipulates the independent variable.
Double-Blind Design
An experimental design in which neither the subjects nor the experimenters are aware of the hypothesis being tested, or which subjects are in the control group or experimental group. This design is used to control for experimenter effects and demand chara
Experimental Research
Research characterized by random assignment of subjects to experimental groups, experimenter manipulation of the independent variable(s), and experimenter control over the research setting and conditions. In experimental research, as compared to other typ
External Validity
The degree to which the results of an experiment are generalizable to a population beyond the experimental group.
Factorial Experimental Design
n a study with multiple independent variables, the combination of every level of one independent variable with every level of the other independent variable(s). The design permits the assessment of interaction effects among the independent variables.
Hawthorne Effect
Confounding nonspecific effects on an experiment caused by the subjects' responding to being in an experiment, rather than to the actual conditions of the experiment.
History
A confounding external event, not relevant to the independent variable, that exerts an effect on the dependent variable and thereby threatens a research study's internal validity.
Independent Variable
he variable which is posited as the cause of a given effect. This causative variable is manipulated by the investigator in an experiment.
Inferential Statistics
Procedures which allow us to estimate population values (e.g., population means) using samples from that population.
Interaction Effect
Occurs when the effects of one independent variable are different at different levels of another independent variable. For instance, if a particular treatment worked for males but not females, there would be an interaction: the effects of treatment would
Internal Validity
In an experiment, the plausibility of the conclusion that the independent variable, and not extraneous factors, is responsible for observed scores or status on the dependent variable.
Interval Scale
Data in which all successive data points are equidistant from each other; does not contain an absolute zero point. Example: IQ scores.
Longitudinal Study
Research study conducted over an extended period of time using the same subjects, usually to assess change over time.
Mann-Whitney U Test
Nonparametric statistical test used when a research study involves two independent groups and the data are rank-ordered.
MANOVA
Multiple analysis of variance. A statistical test for studies that have one or more independent variables and two or more dependent variables.
Matching
A method of controlling for confounds in a research study. Involves creating sets of subjects who are similar in terms of their status on the confounding variable, and then assigning members of each set to different treatment group. Ensures that each grou
Maturation
Internal event (e.g., hunger, fatigue, development), that occurs within research subjects and is not the independent variable, that threatens the study's internal validity by accounting for observed results on a dependent variable.
Mean
The arithmetic average of a set of scores.
Median
The middle score in a distribution of scores when the scores have been ordered from lowest to highest.
Meta-Analysis
Method of analyzing a group of independent studies with a common conceptual basis, using results from each study as the data, resulting in an effect size indicating the average difference between the treatment groups and the control groups.
Mode
Most frequently occurring score in a set of scores.
Multiple Baseline Design
Single-subject research design in which an intervention is sequentially administered across different baselines (i.e., across behaviors, settings, or subjects).
Multiple Correlation Coefficient
Correlation coefficient that provides an index of the magnitude of the relationship between two or more predictor variables and one criterion variable.
Multiple Regression
The use of two or more predictor variables to predict scores on one criterion variable.
Negatively Skewed Distribution
An asymmetrical distribution of scores in which most scores fall at the high end of the scale and relatively few fall at the low end, moving the mean lower, away from the center and toward the negative end of the distribution.
Nominal Scale
Data that consists of unordered categories; examples include gender, DSM diagnosis, and ethnic group.
Nonparametric Tests
Inferential statistical tests used with non-continuous data (i.e., nominal categories or ordinally scaled data). Unlike parametric tests, nonparametric tests do not assume homogeneity of variance or that the data is normally distributed. Also referred to
Normal Distribution
A symmetrical distribution of scores in which half fall above the mean and half below it. When plotted on a graph depicting the scores on one axis and the frequency of occurrence of each score on the other, the result appears as a bell-shaped curve.
Null Hypothesis
A statistical hypothesis stating that there is no difference between or among treatment/control groups. It is the hypothesis the experimenter attempts to disprove. The opposite of the null hypothesis is the experimental, or the alternative, hypothesis.
Ordinal Scale
Data which consists of ordered categories, in which successive data points do not necessarily represent equal distances from each other (e.g., the difference between 1st and 2nd is not necessarily equivalent to the distance between 2nd and 3rd). Example:
Parametric Tests
Statistical hypothesis tests used with continuous (interval or ratio) data that assume a normal population distribution of data and homogeneity of variance; more powerful than nonparametric tests.
Path Analysis
A procedure which involves ordering of relationships among variables based on the correlations between them. Path analysis is used to model and test various hypotheses regarding causal relationships without actually manipulating any variable.
Pearson r
Correlation coefficient used to determine the direction and strength of the relationship between two variables when both variables are measured on a continuous (interval or ratio) scale.
Percentile Rank
A score which reflects the percentage of scores falling below a given score in a distribution. For example, if a person's score on a test is higher than 95% of the scores of others who have taken the test, the person is in the 95th percentile.
Placebo
Any inert treatment used as a control condition in psychotherapy and psychopharmacological research; e.g., pill without the active ingredient of a drug being studied.
Positively Skewed Distribution
An asymmetrical distribution of scores in which most scores fall at the low end of the scale and few fall at the high end, moving the mean higher, away from the center toward the positive end of the distribution.
Post-Hoc Test
Statistical test used after an ANOVA (or other omnibus statistical test) yields statistically significant results; used to pinpoint the specific results which account for significance in the omnibus test. Examples include Tukey and Scheffe.
Power
The ability of a research study to detect a treatment effect when one exists. Power is usually a function of sample size. The larger the sample size, the more power.
Quasi-Experimental Research
Research in which the experimenter does not have control over the assignment of subjects to groups; for example, studies in which intact groups are used. Has weaker internal validity than experimental research.
Random Assignment
Assigning subjects to treatment groups so that every subject has an equal chance of being assigned to each of the groups.
Random Selection (or Random Sampling)
Selecting subjects from a population in such a way that every member of the population has an equal chance of being selected.
Ratio Scale
A scale of measurement in which all successive data points are equidistant from each other and which has an absolute zero point.
Regression Equation
Mathematical equation used for the purposes of predicting a score on one measure on the basis of the score on another measure.
Reversal Design
Single-subject research design in which treatment is applied then removed in order to determine if behavior will revert back to baseline levels. Includes ABA and ABAB design.
Rosenthal Effect
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Sampling Error
Extent to which sample statistics vary from the true population values.
Single-Subject Design
Research involving a single unit of investigation at a time. Includes AB, reversal, and multiple baseline designs.
Standard Deviation
The square root of the variance of a set of scores. The standard deviation is a measure of a score distribution's variability; it indicates how spread out scores are around the mean.
Standard Error Of The Mean
An indication of how close a sample mean is to the corresponding population mean. The formula is the population standard deviation divided by the square root of the sample size.
Statistical Regression
A statistical artifact predicting that extreme scores will, on the average, be less extreme on retesting.
Stratified Random Sampling
Method of random sampling in which a population is divided into separate subgroups (or strata) and then individuals from each strata are randomly selected.
Theoretical Sampling Distribution
Distribution of a large number of sample statistics drawn from randomly selected samples (e.g., means) of the same size from the same population. Theoretical in that no one goes out and actually collects a sampling distribution; however, the presumed char
Trend Analysis
A statistical technique used to determine the trend or shape that best describes the relationship between two variables. The technique basically involves collecting data on two variables and running statistical analyses to determine what trend or trends (
T-Test
Statistical hypothesis test that is used to assess whether two means differ significantly from each other.
Type I Error
An error made when an experimenter erroneously rejects the null hypothesis, i.e., the hypothesis that there is no difference between or among populations studied. In other words, the experimenter concludes that a difference exists, when in reality no diff
Type II Error
An error made when an experimenter erroneously accepts the null hypothesis, i.e., the hypothesis that there is no difference between or among populations studied. In other words, the experimenter fails to find an effect that actually exists.
Variance
The average of the squared differences from the mean of each score. Variance is a measure of how widespread the score distribution is. The square root of the variance is the standard deviation.
Z-Score
Type of standard score that indicates how many standard deviations a raw score is from the mean of the distribution.

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