# Calculations For Sample Size

The equations behind the MitchellScience Sample Size Calculators are listed below. If you are interested in the theory behind these equations, and other background information, you may find additional information in a good statistics textbook.

## Definition of Terms

We define the following terms:

confidence level (%) | |

finite population correction | |

margin of error (converted from a percentage by dividing by 100) | |

population percentage (converted from a percentage by dividing by 100) | |

population size | |

sample size | |

z score (1.96 if C is 95%, or 2.576 if C is 99%) |

These terms are defined more completely on the survey calculator definitions page.

## Sample Size

In the MitchellScience calculators, the sample size is computed from the other parameters using the following unrestricted equation:

(for large and small populations) |

The unrestricted equation for sample size may be derived by isolating the sample size in the unrestricted margin of error equation. That equation contains a term called the "finite population correction", which is needed when the population size is small, but has negligible effect when the population size is large. The finite population correction term is:

As the population size increases, the finite population correction tends towards one, and the sample size reduces to:

(for large populations only) |

In the
Simple Sample Size Calculator,
we use a "worst case" value of P_{p}=50% to produce a conservative value for S. In the
Advanced Sample Size Calculator,
an estimate of the P_{p} is used to get a more accurate value for S.