“How did you decide your sample size?” is one of the most common viva questions. Here are the three methods most students in Pakistan use, explained simply. You can also use our free sample size calculator.
1. Cochran’s formula (large or unknown population)
n₀ = Z² × p × (1 − p) / e²
- Z = 1.96 for 95% confidence
- p = estimated proportion (use 0.5 if unknown — it gives the safest, largest sample)
- e = margin of error (usually 0.05)
Example: 1.96² × 0.5 × 0.5 / 0.05² = 384.16 → 385.
Finite population correction (when you know the population N): n = n₀ / (1 + (n₀ − 1) / N). For N = 2,000: 384.16 / (1 + 383.16/2000) ≈ 323.
2. Yamane’s formula (known population)
n = N / (1 + N × e²)
Example: N = 2,000 and e = 0.05 → 2000 / (1 + 2000 × 0.0025) = 2000 / 6 = 333.3 → 334.
3. Krejcie & Morgan (1970) table
This table gives ready sample sizes for known populations at 95% confidence and 5% margin of error. For example, N = 1,000 → 278; N = 2,000 → 322; N = 10,000 → 370; very large populations → about 384. It is based on the same logic as Cochran’s formula, which is why the numbers are similar.
Which one should I use?
- Population known → Krejcie & Morgan or Yamane (state which one).
- Population unknown or very large → Cochran.
- Experiments or complex models (regression with many predictors, SEM) → a power analysis with G*Power is stronger.
Plan for non-response
If you expect only 80% of questionnaires back, divide by 0.8: 334 / 0.8 ≈ 418 questionnaires to distribute.
How to write it in Chapter 3
The population of the study comprised 2,000 nurses working in public hospitals of Bahawalpur. Using Yamane’s (1967) formula with a 5% margin of error, the required sample size was 334. To allow for non-response, 400 questionnaires were distributed.
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