# 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 \(s\) |