statistical inference

The process by which results from a sample may be applied more generally to a population. More precisely, how inferences may be drawn about a population, based on results from a sample of that population.

Inferential statistics are generally distinguished as a branch of statistical analysis from descriptive statistics, which describe variables and the strength and nature of relationships between them, but do not allow generalization. The ability to draw inferences about a population from a sample of observations from that population depends upon the sampling technique employed. The importance of a scientific sample is that it permits statistical generalization or inference. For example, if we survey a simple random sample of university students in Britain and establish their average (mean) height, we will be able to infer the likely range within which the mean height of all university students in Britain is likely to fall. Other types of sample, such as quota samples , do not allow such inferences to be drawn. The accuracy with which we are able to estimate the population mean from the sample will depend on two things (assuming that the sample has been drawn correctly): the size of the sample and the variability of heights within the population. Both these factors are reflected in the calculation of the standard error. The bigger the standard error, the less accurate the sample mean will be as an estimate of the population mean.

Strictly speaking, therefore, inferential statistics is a form of inductive inference in which the characteristics of a population are estimated from data obtained by sampling that population. In practice, however, the methods are called upon for the more ambitious purpose of prediction, explanation, and hypothesis testing.