Market Research: Foundations to Practice · Sampling and Panels
Sample Size and Margin of Error
Sample size decisions are often made by gut feel or arbitrary round numbers, when a straightforward formula can answer the question precisely once the required confidence and precision are specified. This chapter covers how that formula actually works.
Margin of error quantifies the uncertainty introduced by surveying a sample rather than the entire population; a survey reporting 40 percent approval with a margin of error of plus or minus 3 percent at 95 percent confidence means that if the same survey were run repeatedly, the true population figure would fall between 37 and 43 percent in 95 percent of those repeated survey runs [10].
Key Takeaways
- Margin of error quantifies sampling uncertainty; a ±3% margin at 95% confidence means the true figure would fall in that range 95% of the time if repeated.
- Cochran's formula (n0 = Z² × p × (1-p) / e²) calculates the sample size needed for a chosen confidence level and margin of error.
- Margin of error shrinks with the square root of sample size, producing strong diminishing returns as sample size grows further.
- Confidence level should match decision stakes: 90% for exploratory work, 95% as the standard, 99% for genuinely high-stakes decisions.