Sample-size planning

Learning objectives

• Estimate sample size for a mean and for a proportion in a free spreadsheet.
• Choose margin of error, confidence and pilot variability defensibly.
• Adjust for finite populations and non-response only when material.

Core idea

Sample size depends on precision (E), variability (s or p), confidence (z), power and design. Predefine what effect matters; do not re-tune n after seeing significance.

Formula lab

• Mean: n = (z * s / E)² → =CEILING((NORM.S.INV(1-alpha/2)*s/E)^2, 1).
• Proportion: n = z² * p*(1−p) / E² → =CEILING(NORM.S.INV(1-alpha/2)^2 * p*(1-p)/E^2, 1).
• Use p = 0.5 when no prior information (most conservative).
• Finite-population correction: n_adj = n / (1 + (n−1)/N).

Garment-factory example

For chest width, pilot SD = 0.4 cm, desired margin ±0.1 cm, 95% confidence: n = (1.96 × 0.4 / 0.1)² ≈ 62. For first-pass yield with p = 0.5 and E = 0.05: n = 1.96² × 0.25 / 0.0025 ≈ 385.

Method

1. State the parameter and the effect worth detecting.
2. Take pilot variability from representative data.
3. Round up; document assumptions in the workbook.

Common mistakes

• Choosing n by habit rather than by required precision.
• Changing n after peeking at the results.