12. Video: Notation for Parameters vs. Statistics
Notation Parameters vs. Statistics
There should be a 'hat' on the \sigma^2 in the statistics side at 0:47 (i.e. \hat{\sigma}^2).
As you saw in this video, we commonly use Greek symbols as parameters and lowercase letters as the corresponding statistics. Sometimes in the literature, you might also see the same Greek symbols with a "hat" to represent that this is an estimate of the corresponding parameter.
Below is a table that provides some of the most common parameters and corresponding statistics, as shown in the video.
Remember that all parameters pertain to a population, while all statistics pertain to a sample.
| Parameter | Statistic | Description |
|---|---|---|
| \mu | \bar{x} | "The mean of a dataset" |
| \pi | p | "The mean of a dataset with only 0 and 1 values - a proportion" |
| \mu_1 - \mu_2 | \bar{x}_1-\bar{x}_2 | "The difference in means" |
| \pi_1 - \pi_2 | p_1-p_2 | "The difference in proportions" |
| \beta | b | "A regression coefficient - frequently used with subscripts" |
| \sigma | s | "The standard deviation" |
| \sigma^2 | s^2 | "The variance" |
| \rho | r | "The correlation coefficient" |