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.

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 \(s\)