A Symbols

A.1 General notes

• Greek letters represent population parameter values; roman letters represent sample values.

• A Greek letter with a "hat" represents and estimate of the population value from the sample; i.e., $\mu_x$ represents the true population mean of $X$, while $\hat{\mu}_x$ represents its estimate from the sample.

A.2 Table of symbols

symbol	pronunciation	definition
$\mu$	meeYU	generally, a population mean; sometimes, a model intercept. $\mu_x$ represents the mean of x
$\sigma$	sigma	lower case sigma is the standard deviation; $\sigma_x$ is the standard deviation of $X$
$\sigma^2$	sigma squared	variance
$\rho$	row	population correlation; $\rho_{xy}$ is the correlation in the population between $X$ and $Y$
$r$	row	sample correlation; r_{xy} is the correlation in the sample between $X$ and $Y$
$\mathbf{\Sigma}$	sigma	the capital letter sigma in boldface represents a variance-covariance matrix
$\sum$	sigma	upper case sigma is an instruction to add; e.g., $\sum X_i$ is the instruction to sum together all values of X.
$\beta$	beta	regression coefficient
$\sim$	is distributed as	e.g., $e \sim N\left(\mu, \sigma^2\right)$ means that $e$ is distributed as a Normal distribution with mean $\mu$ and variance $$\sigma^2$$
$\gamma$	gamma	fixed effects, correlation coefficients in a mixed-effects regression
$\tau$	tau	by-subject variance component (random effects parameter) in a mixed-effects regression
$\omega$	omega	by-stimulus variance component (random effects parameter) in a mixed-effects regression
$S_{0s}$	S sub zero S	by-subject random intercept effect for subject $s$
$S_{1s}$	S sub one S	by-subject random slope effect for subject $s$