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# Slovin's formula sampling techniques

Updated February 21, 2017

When it is not possible to study an entire population (such as the population of the United States), a smaller sample is taken using a random sampling technique. Slovin's formula allows a researcher to sample the population with a desired degree of accuracy. It gives the researcher an idea of how large his sample size needs to be to ensure a reasonable accuracy of results.

## When to Use Slovin's Formula

If a sample is taken from a population, a formula must be used to take into account confidence levels and margins of error. When taking statistical samples, sometimes a lot is known about a population, sometimes a little and sometimes nothing at all. For example, we may know that a population is normally distributed (e.g., for heights, weights or IQs), we may know that there is a bimodal distribution (as often happens with class grades in mathematics classes) or we may have no idea about how a population is going to behave (such as polling college students to get their opinions about quality of student life). Slovin's formula is used when nothing about the behaviour of a population is known at all.

## How to Use Slovin's Formula

Slovin's formula is written as:

n = N / (1 + Ne^2)

n = Number of samples N = Total population e = Error tolerance

To use the formula, first figure out what you want your error of tolerance to be. For example, you may be happy with a confidence level of 95 per cent (giving a margin error of 0.05), or you may require a tighter accuracy of a 98 per cent confidence level (a margin of error of 0.02). Plug your population size and required margin of error into the formula. The result will be the number of samples you need to take.

For example, suppose that you have a group of 1,000 city government employees and you want to survey them to find out which tools are best suited to their jobs. You decide that you are happy with a margin of error of 0.05. Using Slovin's formula, you would be required to survey n = N / (1 + Ne^2) people:

1,000 / (1 + 1000 * 0.05 * 0.05) = 286