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 \(s\)