Lec 10

Pearson’s correlation coefficient

A statistic that quantifies the linear relationship between two variables measured on an interval or ratio scale.

Spearman’s correlation coefficient

A non-parametric statistic that quantifies the relationship between two variables using rank order.

Bivariate normality

An assumption that the joint distribution of two variables is normal.

Effect size (r²)

The proportion of variance in the outcome variable that can be accounted for by the predictor variable.

Standard error of estimate

A statistic that indicates the average distance between the observed values and the values predicted by the regression line.

Slope in regression

Indicates the amount of change in the predicted value of Y for each one-unit increase in X.

Intercept in regression

The predicted value of Y when the predictor variable X is equal to zero.

Null hypothesis

A statement that there is no effect or no relationship, often denoted as H0.

Alternative hypothesis

A statement that indicates the presence of an effect or relationship, often denoted as H1.

Cohen’s benchmarks for effect size

Cohen's benchmarks categorize effect sizes as small (±.10), medium (±.30), and large (±.50).

Monotonic relationship

A relationship between two variables that is either entirely non-increasing or non-decreasing.

Point-biserial correlation

A special case of Pearson’s correlation that measures the relationship between one dichotomous nominal variable and one continuous variable.

Phi coefficient

A correlation coefficient used when both variables are dichotomous.

Confidence interval

A range of values that is likely to contain the population parameter with a specified level of confidence.

Simple linear regression

A statistical method to model the relationship between one predictor variable and one outcome variable.

Residual error

The difference between the observed value and the predicted value from the regression model.

Standardized slope

A slope that has been standardized to enable comparison across variables measured on different scales.

Correlation coefficient interpretation benchmarks

Cohen (1988) proposes benchmarks to determine small, medium, and large correlation coefficients.

Scatterplot

A graphical representation used to visualize the relationship between two quantitative variables.

Assumptions of Pearson's correlation

The data should be at least interval scale, have a linear relationship, and exhibit bivariate normality.

Statistically significant correlation

A correlation that is unlikely to have occurred by chance, typically with p < .05.

Variance explained

The proportion of total variance in the dependent variable that can be attributed to the explanatory variable.