Psychometrics, Regression, and Reliability Lecture Notes

Flashcards covering statistical concepts, regression analysis, classical test theory, and reliability estimation methods.

Variance

An index of the extent to which scores in a distribution deviate from central tendency, defined as the average squared deviation from the mean.

Standard Deviation

The square root of variance, which allows one to determine how deviant a score is within a distribution.

Z-score

A score expressing the distance of a score from the mean of its distribution, used to standardize data points from different distributions onto a common scale.

Correlation ($r_{xy}$)

A measure of association between two variables that indicates direction and magnitude, ranging from $-1$ to $+1$.

Covariance

An unstandardized measure reflecting the extent to which variability in one variable is associated with variability in another, expressed in raw units.

Coefficient of Determination ($r_{xy}^2$)

The proportion of variance in a test score that is shared between two variables, always expressed as a percentage.

Restriction of Range

A situation where the full range of test scores is not observed, which acts to reduce variability and attenuate correlation.

Simple Regression

A statistical method that allows the prediction of scores on one variable from scores on another variable.

Regression Line

A line used to predict scores on $Y$ ($Y'$) from scores on $X$ that minimizes the residual (the difference between observed and predicted scores).

Residual

The difference between an observed score and a predicted score in regression analysis.

Root Mean Squared Error (RMSE)

The average distance of observed scores from predicted scores ($Y'$), serving as an index of error or accuracy in prediction.

Coefficient of Determination ($R^2$)

The proportion of variance in the criterion accounted for by the predictors in regression.

Unstandardized Regression Coefficient ($b$)

A coefficient indicating the expected amount of change in the criterion per unit change in the predictor.

Standardized Regression Coefficient

A metric representing the relation between predictor and criterion in standard deviation units; it is equivalent to the zero-order correlation in simple regression and to the partial correlation in multiple regression.

Multiple Regression

A technique allowing the prediction of a criterion score ($Y$) from a group of predictor variables ($X$), assessing their combined variance explained and individual unique contributions.

Zero-Order Correlation

The correlation between two variables where no other variables are statistically controlled.

Semi-Partial Correlation

The correlation between a criterion and a predictor that remains after controlling for the variance that the predictor shares with other predictors.

Partial Unstandardized Regression Coefficient ($b_1$)

The expected change in $Y$ per unit change in $X_1$, controlling for other predictors, expressed in original raw units.

Partial Standardized Regression Coefficient ($\beta_1$)

A unit-free coefficient indicating the relation between $X_1$ and $Y$ in standard deviation units while controlling for other predictors, equivalent to a semi-partial correlation.

Reliability

The consistency of a test, defined theoretically as the proportion of total test variance attributable to true (systematic) variance.

Classical Reliability Theory

The framework stating that total test variance equals systematic variance (true score) plus random measurement error.

Systematic Variance

Variance that is predictably related to an independent variable or deliberate experimental manipulation rather than random chance.

Random Measurement Error

An unsystematic influence on test scores that is not formally measured, has a mean of zero, is normally distributed, and is uncorrelated with true scores or errors on different tests.

Test-Retest Method

A reliability estimation method involving the administration of the same test to examinees on two separate occasions.

Coefficient of Stability

The correlation between scores across two different test administrations, used as an index of test-retest reliability.

Alternate (Parallel) Forms Method

A reliability method administering two different forms of the same test that possess identical psychometric properties.

Coefficient of Equivalence

The correlation between scores on two alternate forms of a test, serving as an index of reliability.

Split-Half Method

An internal consistency reliability method where a single test is divided in half and the two halves are correlated.

Spearman-Brown Prophecy Formula

A formula used to correct split-half reliability estimates, determine the test length adjustment needed to reach a desired reliability, or evaluate the reliability of a short form.

Cronbach's Coefficient Alpha

An internal consistency measure treating each test item as an alternate form, which uses the average inter-item correlation to provide a single overall reliability estimate.

Item-Total Correlation

The correlation between an individual test item and the total test score, which should be positive and of relatively consistent magnitude across items.