Initial setup

rm(list=ls())
library(ggplot2)
library(MASS)
library(effects)
ts=25



Correlation

Example of scatter plot featuring a correlation of exactly r = 0.40.

It can be understood as a +1.00 SD increase in one variable corresponding to an estimated +0.40 SD increase in the other one.

Standardized regression coefficient in a linear model (continuous predictor) can be interpreted in a similar fashion.




Standardized Mean Difference

SMDs (e.g., Cohen’s d, possibly with Hedges’ correction for small samples) are reported to compare group average values on a standardized metric. Here is an example of Cohen's d = 1.50 between “population green” and “population purple”.

Height is commonly used for offering examples to understand SMDs, because it is an immediately visible, non-latent, more or less normally-distributed trait. For example, from Funder and Ozer (2019):