How to Use Yamane’s Formula Calculator
Have you just decided to use Yamane’s formula, but don’t want to compute it manually? Our calculator does the math for you and teaches you how to compute it manually. Here’s how the calculator works:
- Enter the population size (N)
- Choose the margin of error (e). You should enter this as a decimal (e.g, 0.05 for a 5% margin of error)
- Click the “Calculate” button
The calculator applies Taro Yamane’s formula and shows you the minimum sample size you need for your study.
Yamane’s Sample Size Formula
Yamane’s formula is one of the most common sample size determination formulas. It helps researchers and scholars estimate the minimum sample size needed for their study, especially when the population size is known and finite. In other words, the formula can help you select a representative sample while keeping the margin of error within acceptable limits.
The Yamane’s formula was developed in 1967 by a statistician named Taro Yamane. Since then, the formula has been popular in research due to its simplicity and ability to estimate sample size without complex statistical assumptions.
The Yamane’s formula is n = N / (1 + Ne^2)
Where:
- N is the size of the finite population
- n is the minimum sample size
- e is the margin of error
When Should You Use Yamane’s Formula?
The Yamane’s sample size formula works best when:
- The population size is known
- The population is finite (not extremely large or infinite)
- You are using simple random sampling
- You do not have a prior estimate of population variance
In simple terms, use Yamane’s sample size formula if you know the number of people or items in your target population. It will give you a reasonable sample size without complex computations.
However, if the population is very large and infinite, or you have an estimate of the population variability, then you should use Cochran’s formula.
Yamane Formula vs Slovin Formula
Many students and researchers wonder whether the Yamane formula and Slovin’s formula are the same. Although they are closely related, they have small differences. The table below summarizes the two formulas to help you identify the similarities and differences.
| Feature | Yamane Formula | Slovin’s Formula |
|---|---|---|
| Purpose | Estimate the minimum sample size from a finite population | Estimate the minimum sample size from a finite population |
| Formula | ||
| Origin | Developed by Taro Yamane (1967) | Popularized by Slovin (1960s) |
| Usage | Widely used in theses, dissertations, surveys, and research projects | Common in surveys and academic research, especially for student projects |
| Key Difference | Often preferred in academic research due to clear citation and origin | Sometimes considered a simplified or alternative naming of Yamane’s formula |
Still unsure which formula to use between Slovin’s and Yamane’s formula? My advice is to use Taro Yamane for academic work, such as dissertations, and Slovin’s for Surveys. They’ll always give you the same answer. The only difference is the naming and citation.
