Sampling error
Sampling error is the gap between a sample statistic and the true population parameter that arises solely because a sample, not the full population, was measured. It shrinks as sample size grows and vanishes in a census.
See it move
A retailer's full transaction records show a true population average order value of €85.00. A random sample of 50 orders gives a sample mean of €88.50. The sampling error is €88.50 − €85.00 = €3.50: the sample overstated the true average purely because of which 50 orders happened to be drawn.
The formula
Variables
- Sampling error
- Sample statistic (e.g. sample mean or sample proportion)
- True population parameter
Measures the gap between a sample-based estimate and the true population value, caused purely by observing a sample rather than the whole population.
Check yourself
A factory's full production log (the population) shows that exactly 4.0% of all units made this month were defective. A quality inspector who has not seen the full log draws a random sample of 200 units and finds 10 defective, a sample proportion of 5.0%. What is the sampling error, expressed as a percentage-point difference?