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. Slovin's formula gives the researcher an idea of how large the sample size needs to be to ensure a reasonable accuracy of results.

#### TL;DR (Too Long; Didn't Read)

Slovin's Formula provides the sample size (*n*) using the known population size (*N*) and the acceptable error value (*e*). Fill the *N* and *e* values into the formula *n* = *N* ÷(1 + *Ne*^{2}). The resulting value of *n* equals the sample size to be used.

## 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 may be known and sometimes nothing is known at all. For example, a population may be normally distributed (e.g., for heights, weights or IQs), there may be a bimodal distribution (as often happens with class grades in mathematics classes) or there may be no information about how a population will behave (such as polling college students to get their opinions about quality of student life). Use Slovin’s formula when nothing is known about the behavior of a population.

## How to Use Slovin's Formula

Slovin's formula is written as:

where *n* = Number of samples, *N* = Total population and *e* = Error tolerance.

To use the formula, first figure out the error of tolerance. For example, a confidence level of 95 percent (giving a margin error of 0.05) may be accurate enough, or a tighter accuracy of a 98 percent confidence level (a margin of error of 0.02) may be required. Plug the population size and required margin of error into the formula. The result equals the number of samples required to evaluate the population.

For example, suppose that a group of 1,000 city government employees needs to be surveyed to find out which tools are best suited to their jobs. For this survey a margin of error of 0.05 is considered sufficiently accurate. Using Slovin’s formula, the required sample survey size equals:

The survey therefore needs to include 286 employees.

## Limitations of Slovin's Formula

Slovin's formula calculates the number of samples required when the population is too large to directly sample every member. Slovin's formula works for simple random sampling. If the population to be sampled has obvious subgroups, Slovin's formula could be applied to each individual group instead of the whole group. Consider the example problem. If all 1,000 employees work in offices, the survey results would most likely reflect the needs of the entire group. If, instead, 700 of the employees work in offices while the other 300 do maintenance work, their needs will differ. In this case, a single survey might not provide the data required whereas sampling each group would provide more accurate results.

References

About the Author

Stephanie Ellen teaches mathematics and statistics at the university and college level. She coauthored a statistics textbook published by Houghton-Mifflin. She has been writing professionally since 2008. Ellen holds a Bachelor of Science in health science from State University New York, a master's degree in math education from Jacksonville University and a Master of Arts in creative writing from National University.