# 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 $$s$$