Published

May 4, 2019

## A General Symbol Guide

There are a lot of symbols (often greek letters or ligatures on English letters) used in statistics and econometrics. Luckliy, most of them follow some standard patterns, and are consistent across textbooks and research (note there are exceptions!).

Style Examples Meaning
Greek letters $$\beta_0, \beta_1, \sigma, u$$ True parameters of population
Hats $$\hat{\beta_0}, \hat{\beta_1}, \hat{\sigma}, \hat{u}$$ Our statistical estimates of population parameters, from sample data
English capital letters $$X_1, X_2, Y$$ (Random) variables in our sample data
English lowercase letters $$x_{1i}, x_{2i}, y_i$$ Individual observations of variables in our sample data
Modified capital letters $$\bar{X}, \bar{Y}$$ Statistics calculated from our sample data (e.g. sample mean)
Bold capital letters $$X= \begin{bmatrix} x_1, x_2, \cdots , x_n \\ \end{bmatrix}$$ $$\mathbf{\beta} = \begin{bmatrix} \beta_1, \beta_2, \cdots , \beta_k \\ \end{bmatrix}$$ Vector or matrix

## Sample Statistics vs Population Parameters Formulae

Sample Population
Population $$n$$ $$N$$
Mean $$\bar{x} = \frac{1}{n} \displaystyle\sum^n_{i=1} x_i$$ $$\mu = \frac{1}{N} \displaystyle\sum^N_{i=1} x_i$$
Variance $$s^2=\frac{1}{n-1} \displaystyle\sum^n_{i=1} (x_i-\bar{x})^2$$ $$\sigma^2=\frac{1}{N} \displaystyle\sum^N_{i=1} (x_i-\mu)^2$$
Standard Deviation $$s = \sqrt{s^2}$$ $$\sigma = \sqrt{\sigma^2}$$