Introduction
This topic explains how conclusions about a whole population are drawn from a sample. It covers the difference between descriptive and inferential statistics, point and interval estimation of population parameters, the standard error, the confidence interval, and the principles of calculating the sample size needed for a study.
Descriptive and inferential statistics
Descriptive statistics summarise the data that have actually been collected, without going beyond them. Inferential statistics use a sample to draw conclusions about the larger population from which it came, and state how uncertain those conclusions are.
Population parameters and point estimation
Population parameters are fixed but usually unknown values, such as the mean \mu, the standard deviation \sigma and the proportion \pi. They are estimated from sample statistics: the sample mean \bar{x}, the sample standard deviation s and the sample proportion p. A single number of this kind is called a point estimate.
- A good estimator is unbiased (its expected value equals the parameter), consistent (it approaches the parameter as the sample grows) and efficient (it has the smallest variance among such estimators).
- The sample mean is an unbiased estimate of the population mean. The sample variance calculated with the denominator n minus 1 is an unbiased estimate of the population variance.
- A point estimate alone says nothing about its precision, which is why interval estimation is also needed.