Important Statistics Formulas

This web page presents statistics formulas described in the Stat Trek tutorials. Each formula links to a web page that explains how to use the formula.

Parameters

Statistics

Unless otherwise noted, these formulas assume simple random sampling.

Correlation

Simple Linear Regression

Counting

Probability

Random Variables

In the following formulas, X and Y are random variables, and a and b are constants.

Sampling Distributions

Standard Error

Discrete Probability Distributions

Linear Transformations

For the following formulas, assume that Y is a linear transformation of the random variable X, defined by the equation: Y = aX + b.

Estimation

Hypothesis Testing

Degrees of Freedom

The correct formula for degrees of freedom (DF) depends on the situation (the nature of the test statistic, the number of samples, underlying assumptions, etc.).

Sample Size

Below, the first two formulas find the smallest sample sizes required to achieve a fixed margin of error, using simple random sampling. The third formula assigns sample to strata, based on a proportionate design. The fourth formula, Neyman allocation, uses stratified sampling to minimize variance, given a fixed sample size. And the last formula, optimum allocation, uses stratified sampling to minimize variance, given a fixed budget.