This sample size calculator computes the minimum sample size for your study using Taro Yamane’s formula. To determine the required sample size for your study, enter the population size (N), the margin of error (e), and click the “Calculate” button.

The calculator will instantly give the minimum sample size, along with a step-by-step explanation of how to apply Yamane’s formula manually. This way, it not only gives you an answer but also helps you learn how to compute sample size using Taro Yamane’s formula by hand.

What is Yamane’s Sample Size Formula?

Yamane’s sample size formula was introduced by Taro Yamane, a Japanese statistician and economist, in his 1967 book Statistics: An Introductory Analysis. The formula is used to determine an appropriate sample size from a known and finite population using a chosen margin of error.

The formula has been so popular in studies assuming simple random sampling. Many students, researchers, and scholars use Yamane’s formula due to its simplicity. It helps them compute the minimum sample size for their studies without complex statistical computations.

Taro Yamane’s sample size formula is n = N / (1 + N·e²)

Where:

• n is the minimum sample size you want to calculate
• N is the size of the target population
• e is the margin of error

When Should You Use Yamane’s Formula?

You should use Yamane’s formula when:

• The population size is known and finite
• You are using simple random sampling
• Your study is in social sciences, education, or business research

However, if your target population is infinite or very large but known, you should use Cochran’s sample size formula.

Difference Between Slovin’s and Yamane’s Formula

In most cases, researchers treat Slovin’s and Yamane’s formulas as two different methods. However, they are mathematically the same. This means using either of these formulas will yield the same results.

The main difference between Slovin’s and Yamane’s sample size formula is the naming and citation. While Yamane’s formula is attributed to Taro Yamane (1967), Slovin’s formula was developed by Robert Slovin in 1960.

In fact, some studies argue that Slovin’s formula was first published in 1960 by Robert Slovin and later popularised by Taro Yamane in 1967.

Limitations of Yamane’s Formula

While Yamane’s formula is simple and widely used in many studies, it is associated with the following limitations:

• Does not account for stratified or complex sampling designs
• Does not include power analysis, which is required for hypothesis testing
• Does not consider effect size, making it less suitable for inferential studies

Therefore, for studies that required greater statistical rigor, you should consider advanced sample size determination formulas such as Cochran’s formula, power analysis, and software-based sample size estimation.