Stat Trek

Teach yourself statistics

# Statistics Formulas Used on Stat Trek

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

## Statistics

Unless otherwise noted, these formulas assume simple random sampling.

## Random Variables

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

## 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.

## 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. ## Problem?

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