Correlational Research Methods

Lecture 3 Overview

Simple Linear Regression

Model predicting Y from X using linear equation.

Standardised Regression Coefficient (𝛽)

Coefficient reflecting effect size in standardised units.

Total Variance Decomposition

Breakdown of variance in dependent variable Y.

R-squared (𝑅²)

Proportion of variance in Y explained by X.

Psychopathy

Personality disorder characterized by antisocial behavior.

Sadism

Pleasure derived from inflicting pain on others.

Linear Model

Mathematical representation of relationship between X and Y.

Regression Coefficient (𝑏₁)

Change in Y for a one-unit change in X.

Descriptive Statistics

Summary statistics describing characteristics of data.

Predicted Y (𝑌')

Estimated value of Y based on X's score.

Mean of X

Average value of independent variable X.

Mean of Y

Average value of dependent variable Y.

Z-scores

Standardized scores indicating distance from mean.

Hours Studied

Independent variable affecting exam grades in regression.

Exam Grade

Dependent variable predicted by hours studied.

Bitter Taste Preference

Associated with higher antisocial personality traits.

Prediction Error

Difference between observed and predicted values.

Graphic Representation

Visual depiction of regression analysis results.

Population Generalization

Applying sample results to the larger population.

Mean

Average value of a dataset.

Variance

Measure of data spread around the mean.

Z-score

Standardized score indicating relative position.

Unstandardized Coefficient (b)

Coefficient representing change in Y per unit change in X.

Standardized Coefficient (β)

Coefficient representing change in Y per standard deviation change in X.

Linear Regression Model

Predicts Y based on X using coefficients.

Intercept (b₀)

Value of Y when X is zero.

Regression Equation

Mathematical representation of the relationship between variables.

SPSS Output

Statistical software output for regression analysis.

R-squared (R²)

Proportion of variance explained by the model.

Adjusted R-squared

R-squared adjusted for number of predictors.

Numeric Example

Illustrative data used for calculations.

Correlation

Statistical measure of relationship between two variables.

Coefficient of Determination

R-squared value indicating model fit.

Effect Size

Magnitude of the relationship between variables.

Predictor Variable

Independent variable used to predict outcomes.

Standardized Model

Model without intercept, averages are zero.

Research Methods

Techniques for collecting and analyzing data.

Data Spread

Distribution of values in a dataset.

Statistical Significance

Likelihood that a result is not due to chance.

Independent Variable

Variable influencing the dependent variable, denoted as X.

Sum of Squares

Total variance in the dependent variable.

Regression

Statistical method for predicting Y from X.

Residual Variance

Variance not explained by the independent variable.

Mean Square

Average of squared deviations from the mean.

Significance Level (Sig.)

Probability of observing results by chance.

Regression Coefficient (B)

Change in Y for a one-unit change in X.

Standard Error

Estimate of the standard deviation of coefficients.

Standardized Coefficient (Beta)

Coefficient adjusted for variable scale differences.

Total Variance (S²)

Overall variance of the dependent variable.

Variance Explained (S² regression)

Variance in Y explained by X.

Variance Unexplained (S² residual)

Variance in Y not explained by X.

t-value

Ratio of the difference between group means.

Predicted Value (Y′)

Estimated value of Y based on regression.

Error (e)

Difference between observed and predicted values.

ANOVA Table

Summary of variance analysis results.

Correlational Research

Study of relationships between variables without manipulation.

Regression Analysis

Statistical method to predict dependent variable from independent.

Residuals

Differences between observed and predicted values.

Sum of Squares (SS)

Total variation in data, used in ANOVA.

SS Regression

Variation explained by the regression model.

SS Residual

Variation not explained by the regression model.

Standard Deviation (SD)

Square root of variance, indicates data spread.

ANOVA

Analysis of variance, compares means across groups.

F-test

Statistical test to compare variances of populations.

R Square

Proportion of variance explained by the model.

Adjusted R Square

R Square adjusted for number of predictors.

Degrees of Freedom (df)

Number of independent values in a calculation.

Predictors

Independent variables used in regression analysis.

Dependent Variable

Outcome variable predicted by independent variables.

Hypothesis Testing

Procedure to determine if a hypothesis is true.

Null Hypothesis (H0)

Assumes no effect or relationship exists.

Alternative Hypothesis (H1)

Assumes there is an effect or relationship.

Bitter Preference Scale

Scale measuring preference for bitter foods (1-6).

Psychopathy Scale

Measure of psychopathic traits in individuals.

Coefficients

Values that represent the relationship strength in regression.

Model Summary

Overview of regression model statistics and performance.