90-symbols.Rmd

# (APPENDIX) Appendix {-}

# Symbols

## 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.

## Table of symbols

```{r echo=FALSE}
tibble::tribble(~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 $s$"
                ) %>%
  knitr::kable()
```

# Bibliography