How to Use Slovin’s Formula

Hypothesis Testing, Other Distributions, Sample Size 11 Comments

If you take a population sample, you must use a formula to figure

out what sample size you need to take. Sometimes you know

something about a population, which can help you determine a

sample size. For example, it’s well known that IQ scores follow a

normal distribution pattern. But what about if you know nothing

about your population at all? That’s when you can use Slovin’s

formula to figure out what sample size you need to take, which is

written as n = N / (1 + Ne2) where n = Number of samples, N =

Total population and e = Error tolerance

Sample question: Use Slovin’s formula to find out what sample of

a population of 1,000 people you need to take for a survey on their

soda preferences.

Step 1: Figure out what you want your confidence level to be. For

example, you might want a confidence level of 95 percent (which

will give you a margin error of 0.05), or you might need better

accuracy at the 98 percent confidence level (which produces a

margin of error of 0.02).

Step 2. Plug your data into the formula. In this example, we’ll

use a 95 percent confidence level with a population size of 1,000.

n = N / (1 + N e2) =

1,000 / (1 + 1000 * 0.05 2) = 285.714286

Step 3: Round your answer to a whole number (because you

can’t sample a fraction of a person or thing!)

285.714286 = 286