Sample size is simply how many people you need to study so your results mean something — big enough to be trustworthy, small enough to be doable. You do not survey everyone; you survey a calculated portion. In Nigerian projects the most common way to work this out is the Taro Yamane formula, because it only needs two things: your population size and how much error you will accept.
The Taro Yamane Formula
The formula is: n = N / (1 + N(e)²), where n is your sample size, N is your population size, and e is the margin of error (usually 0.05, meaning 5%).
When to Use Taro Yamane
- You know (or can reasonably estimate) your population size.
- Your population is finite — a specific, countable group.
- You are doing a survey or descriptive study at undergraduate level.
- Your supervisor accepts it (it is widely used in Nigeria).
When Not to Use It
- You do not know the population size — Taro Yamane needs N. Consider Cochran’s formula, which works without a known population.
- Your population is extremely large or undefined.
- You are doing a qualitative study, where sample size is about saturation, not a formula.
Nigerian Project Example
Your study covers all 450 staff of [Organisation]. Using Taro Yamane with e = 0.05: n = 450 / (1 + 450 × 0.0025) = 450 / 2.125 ≈ 212. You would distribute your questionnaire to about 212 staff, often adding a few extra to allow for non-returns.
Undergraduate vs Postgraduate
Undergraduates almost always use Taro Yamane — it is simple and accepted. Postgraduates may need more rigorous approaches: Cochran's formula for unknown populations, power analysis for experiments, or saturation-based reasoning for qualitative work. The principle is the same; the justification expected is deeper.
Common Mistakes
- Stating a sample size with no formula or working shown.
- Using the wrong margin of error or applying the formula incorrectly.
- Forgetting to allow for questionnaires that are not returned.
- Using Taro Yamane when the population size is genuinely unknown.
Your sample size sits in the sampling section of your methodology — see how to write Chapter Three and the full research methodology guide. Then pick a technique: simple random, stratified or systematic sampling. Project Lab can check your calculation.
Frequently Asked Questions
What margin of error should I use?
0.05 (5%) is the standard in Nigerian undergraduate projects. A smaller error (0.03) needs a larger sample; a larger error (0.10) needs fewer respondents but gives less precise results.
What if I do not know my population size?
Taro Yamane needs a known population. If yours is unknown or very large, Cochran's formula is designed for that situation. Confirm with your supervisor which is appropriate.