Calculate the required sample size for surveys, polls, clinical trials, and research studies. Based on confidence level, margin of error, and population size.
| Parameter | Value |
|---|
Required sample sizes at 95% confidence, p=50%:
| Population | ±3% | ±5% | ±10% |
|---|
Determining an appropriate sample size is critical in survey research, clinical trials, and population studies. Australian researchers follow guidelines from the National Health and Medical Research Council (NHMRC) and the Australian Bureau of Statistics (ABS).
Infinite population: n = z² × p(1−p) / e²
Finite population correction: n_adj = n / (1 + (n−1)/N)
Where: z = z-score for confidence level, p = expected proportion, e = margin of error, N = population size.
The ABS conducts major surveys including the Census, Labour Force Survey, and National Health Survey. The Census (every 5 years) surveys the entire Australian population (~26 million). Other surveys use carefully designed probability samples, typically thousands of households.
There is a trade-off: higher confidence requires a larger sample. A 99% confidence level requires ~75% more respondents than 95% for the same margin of error. In most social research, 95% confidence with ±5% margin of error (n≈384 for infinite population) is the standard.