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.