Bivariate, Multivariate, and Experimental Research Methods

Comprehensive practice vocabulary flashcards covering bivariate correlations, multivariate regression and longitudinal designs, and simple experimental methodologies.

Association Claim

A claim about at least two variables, in which the value or level of one variable is said to vary systematically with the value or level of another variable.

Bivariate Correlation

An association that involves exactly two measured variables, regardless of whether the variables are numeric or categorical.

Correlation Coefficient ($r$)

A numeric value ranging from $-1.0$ to $+1.0$ that describes both the direction and the magnitude of a linear relationship between two quantitative variables.

Scatterplot

A visual display used to plot bivariate data when both measured variables are quantitative and continuous.

Two-Sample $t$-Test

A statistical test used to evaluate the association between a categorical variable with exactly two levels and a continuous numeric variable by comparing group means.

Analysis of Variance (ANOVA)

A statistical test used to evaluate mean differences when examining an association between a categorical variable with more than two levels and a continuous numeric variable.

Chi-Square Test ($\chi^2$)

A statistical test used to evaluate the association between two categorical variables.

Bar Graph (in Bivariate Research)

A graph commonly used to display the association between one categorical variable and one continuous numeric variable, where the height of each bar represents a group mean.

Box Plot

A graphical display of data distributions where the lower whisker, lower half of the box, upper half of the box, and upper whisker each delineate $25\%$ of the data.

Violin Plot

A data visualization combining a box plot with a probability density plot to display the distribution shape, spread, and summary statistics across categorical groups.

Covariance

The first criterion for establishing causality, requiring that two variables are correlated and that variability in one variable is systematically linked to variability in the other.

Temporal Precedence

The second criterion for establishing causality, requiring that the causal variable reliably comes before the outcome variable in time.

Internal Validity

The third criterion for establishing causality, assessing the degree to which a study rules out plausible alternative explanations or confounding third variables for an association.

Directionality Problem

A temporal precedence problem in correlational research occurring because both variables are measured at roughly the same time, making it unclear which variable occurred first.

Third-Variable Problem

A threat to internal validity in correlational research where an unmeasured confounding variable is independently associated with both variables, creating a non-causal relationship between them.

Spurious Correlation

An apparent statistical relationship between two variables that seems real but is actually nonexistent or entirely explained by an extraneous third variable.

Construct Validity (in Association Claims)

An interrogation evaluating how well each of the measured variables in an association claim was operationalized, including evidence for reliability and measurement validity.

External Validity (in Association Claims)

An interrogation assessing the extent to which the observed association between variables generalizes to a larger population, other contexts, or other times.

Moderating Variable (Moderator)

A variable that, depending on its level, alters the strength or direction of the relationship between two other variables.

Effect Size

The magnitude or strength of a relationship between two or more variables, reflected quantitatively in bivariate numeric research by the correlation coefficient ($r$).

Confidence Interval (CI)

A range of plausible values indicating the precision of an estimate, which tends to narrow as sample size increases when all else is held equal.

Statistical Significance (via Confidence Intervals)

A statistical inference in which a correlation is considered statistically significant if its $95\%$ confidence interval does not contain the null hypothesized value ($0$).

Replication

The scientific process of conducting a study again with a new sample to test whether the original empirical findings are consistent.

Outlier

An extreme score that stands out as either much higher or much lower than most other scores in a sample, exerting disproportionate influence in smaller sample sizes.

Curvilinear Association

A nonlinear relationship between two variables, such as a pattern that is positive up to a certain point and then becomes negative, which Pearson's $r$ will under-estimate.

Multivariate Design

A correlational research design that measures more than two variables in the same study to help address temporal precedence or internal validity.

Longitudinal Design

A multivariate correlational study in which the same variables are measured in the exact same individuals at multiple points in time to help address temporal precedence.

Cross-Sectional Correlation

In a longitudinal design, a correlation between two distinct variables that are measured at the exact same point in time.

Autocorrelation

In a longitudinal design, the correlation of a single variable with itself across two different points in time, assessing whether the variable is stable over time.

Cross-Lag Correlation

In a longitudinal design, a correlation between an earlier measure of one variable and a later measure of a different variable, used to establish temporal precedence.

Simple Linear Regression

A statistical technique estimating the straight line that best fits a cloud of data points to predict the value of a criterion variable ($y$) from a single predictor variable ($x$).

Regression Line Equation

The mathematical equation $y = a + b \times x$ or $Y = \beta_0 + \beta_1 X + e$ that models the predicted linear relationship between variables.

$y$-Intercept ($\beta_0$ or $a$)

The expected value of the criterion variable ($y$) when the predictor variable ($x$) is equal to $0$.

Slope Estimate ($\beta_1$ or $b$)

The parameter in a linear regression model that indicates how much the criterion variable ($y$) is expected to change for every one-unit increase in the predictor variable ($x$).

Residuals ($e$)

The error terms representing the discrepancy between observed data points and values predicted by the regression line.

Multiple Regression

A statistical technique that computes the linear relationship between a criterion variable and multiple predictor variables while controlling for one or more other variables.

Criterion Variable

The primary outcome variable in a multiple regression analysis that researchers are most interested in predicting or explaining (the $y$ variable).

Predictor Variable

A variable in a multiple regression analysis used to explain variance in the criterion variable (the $x$ variable).

Controlling For

Statistically holding a potential third variable at a constant level while evaluating the unique association between two other variables (also called adjusting or accounting for).

Beta ($\beta$)

A standardized regression coefficient indicating the strength and direction of the linear relationship between a predictor and the criterion while holding all other predictors constant.

Unstandardized Slope ($b$)

A regression slope coefficient whose magnitude is expressed in the original measurement units of the predictor and criterion variables.

Omitted Variable Limitation in Regression

The principle that multiple regression cannot establish causality because it can only control for third variables that researchers intentionally measure, not unmeasured confounds.

Mediator (Mediating Variable)

An intermediate variable that serves as the explanatory mechanism through which an independent or predictor variable influences an outcome variable.

Temporal Sequence in Mediation

The causal ordering required by a mediation hypothesis in which Variable A leads to Mediating Variable C, which in turn leads to Outcome Variable B.

Mediator vs. Third Variable

A mediator is an internal causal mechanism explaining why two variables relate, whereas a third variable is an external confounding nuisance that creates a spurious relationship.

Moderator (in Multivariate Context)

A variable that identifies subgroups or boundary conditions under which an association between two other variables becomes stronger, weaker, or changes direction.

Moderator vs. Third-Variable Problem

A moderator changes the relationship between two variables across groups without invalidating it, whereas a third variable accounts for the entire association, showing it was not genuine.

Difference Between Mediators and Moderators

Mediators explain why or how two variables are related, whereas moderators specify for whom, when, or under what conditions the two variables are related.

Mehl et al. (2010) Study

A study demonstrating that deep talk correlates positively with subjective well-being, where quality of social ties was proposed as a mediating variable.

Barros et al. (2009) Study

A study examining whether recess minutes predicted fewer classroom behavior problems after statistically controlling for school socioeconomic status via free lunch eligibility.

Experiment

A research design where investigators manipulate at least one independent variable and measure at least one dependent variable to establish causal claims.

Independent Variable (IV)

In an experiment, the variable that is deliberately manipulated by the researcher, consisting of two or more levels or conditions.

Condition (Level)

One of the specific variations or treatment categories of an independent variable presented to participants in an experimental design.

Dependent Variable (DV)

In an experiment, the outcome variable that is measured to assess whether manipulation of the independent variable caused a change.

Control Variable

A potential confounding variable in an experiment that the researcher purposefully holds constant across all conditions to ensure internal validity.

Comparison Group

A group in an experiment whose level on the independent variable differs from that of the treatment group in an intended and meaningful way.

Control Group

A baseline level of an independent variable intended to represent no treatment or a neutral condition.

Treatment Group

The group of participants in an experiment exposed to the active level of an independent variable, such as a medication, therapy, or behavioral manipulation.

Placebo Group

A control group in an experiment exposed to an inert treatment, such as a sugar pill, to control for participant expectations.

Confounding Variable (Confound)

A variable that confuses the interpretation of results by serving as a potential alternative explanation for changes in the dependent variable.

Systematic Variability

A threat to internal validity where the levels of an extraneous variable coincide in a predictable manner with the experimental conditions.

Unsystematic Variability

Random or haphazard variation across experimental participants that does not coincide systematically with the experimental conditions.

Design Confound

An experimenter error in which a second variable accidentally varies systematically along with the independent variable, offering an alternative explanation for the results.

Selection Effect

A threat to internal validity in independent-groups designs where the participants assigned to one condition are systematically different from those assigned to another.

Random Assignment

The procedure of assigning participants to conditions by chance, converting potential individual differences into unsystematic variability and eliminating selection effects.

Matched Groups

An assignment method where participants are measured on a key variable, grouped into matched sets, and then randomly assigned across experimental conditions to prevent selection effects.

Independent-Groups Design

An experimental design in which different groups of participants are exposed to different levels of the independent variable, so that each participant experiences only one condition (between-subjects).

Within-Groups Design

An experimental design in which each participant is exposed to all levels of the independent variable (within-subjects).

Posttest-Only Design

An independent-groups design in which participants are randomly assigned to an independent variable condition and tested on the dependent variable only once, following exposure.

Pretest/Posttest Design

An independent-groups design in which participants are tested on the dependent variable twice: once before and once after exposure to the independent variable.

Repeated-Measures Design

A within-groups experimental design where participants respond to the dependent variable more than once, immediately after exposure to each level of the independent variable.

Concurrent-Measures Design

A within-groups experimental design where participants are exposed to all levels of an independent variable at roughly the same time and a single preference or behavior is measured.

Order Effects

An internal validity threat in within-groups designs where exposure to earlier experimental conditions alters how participants perform or respond in subsequent conditions.

Counterbalancing

The technique of presenting the levels of an independent variable to participants in varying sequential orders to eliminate order effects in within-groups designs.

Latin Square

A formal partial counterbalancing technique ensuring that every experimental condition appears in each ordinal position in the sequence at least once.

Demand Characteristics

Cues in an experimental setting that lead participants to guess the research hypothesis and consciously or unconsciously modify their behavior accordingly.

Manipulation Check

An extra dependent variable inserted into an experiment to empirically confirm whether the independent variable manipulation had its intended psychological or physical effect.

Pilot Study

A simple trial study conducted prior to the main experiment using a separate group of participants to confirm the effectiveness and operationalization of manipulations.

Cohen's $d$

A standardized effect size index expressing the distance between two condition means in standard deviation units and indicating the extent of distribution overlap.