Taro Yamane (1967)
The workhorse of survey research with a known, finite population. Use it when you can state the exact size of your study population, such as staff strength, registered members, or listed firms.
n = N / (1 + N e²)
Required sample size
Cochran (1977)
Use Cochran's formula when the population is very large or unknown, or when you want the sample size driven by a chosen confidence level and expected proportion. Where the population is finite and known, apply the finite population correction below the first result.
n₀ = Z²pq / e² then n = n₀ / (1 + (n₀ − 1)/N)
Required sample size
Which formula should you use?
| Situation | Recommended approach |
|---|---|
| Known, finite population (e.g. 842 staff of selected banks) | Taro Yamane may provide a simple starting point where its assumptions and the selected precision level are justified. |
| Very large or unknown population (e.g. bank customers in Lagos) | Cochran with p = 0.5, which maximises variance and therefore gives the most conservative sample. |
| Census is feasible for a small population | Consider studying the complete accessible population. Explain coverage, non-response and data-quality limitations rather than assuming that census design removes every source of error. |
| Secondary panel data (e.g. 26 NGX-listed firms over 14 years) | Sample size formulas do not apply; justify the sample by selection criteria (purposive or filter-based) and data availability instead. |
Methodology chapter tip: whichever formula you use, show the substitution step, not just the answer. "n = 1250 / (1 + 1250(0.05)²) = 303.03 ≈ 303" reads as competence; a bare "the sample size was 303" invites a question you do not need.
Beyond the formula
Sample size is necessary, not sufficient. The methodology must also justify the sampling frame, selection technique, expected non-response and consistency between the stated population and the analysis actually performed.