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 behavior 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 percent (giving a margin error of 0.05), or you may require a tighter accuracy of a 98 percent 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
- Principles and Methods of Research; Ariola et al. (eds.); 2006
How to Calculate Margin of Error
The margin of error is a number that represents the accuracy of a poll. One can determine this amount by using an...
How to Calculate Sample Size Formula
While it is often impossible to sample an entire population of organisms, you can make valid scientific arguments about a population by...
How to Compute the Margin of Error (3 Easy Methods)
The margin of error is a statistical calculation that pollsters report along with the results of their surveys. It represents the approximate...
How to Create Statistical Formulas for Excel
Microsoft Excel is a versatile program for handling a variety of data formats. Numerical and financial data is commonly entered into Excel,...
How to Calculate Sampling Distribution
The sampling distribution can be described by calculating its mean and standard error. The central limit theorem states that if the sample...
How to Calculate Animal Population Density
The calculations involved in estimating animal population density are relatively straightforward. However, reasonable estimates require accurate raw data. A random sample must...
The Advantages of Proportional Allocation
To get input about a certain population, such as the students at a particular university, it is convenient to use a representative...
Types of Random Sampling Techniques
In 1936, Literary Digest polled its readers and concluded that Kansas governor Alfred Landon would beat Franklin Roosevelt in the presidential election...