Formal procedures for analyzing experimental data and assessing the uncertainty of the analysis results. Hypothesis testing and parameter estimation are two important statistical inference topics.

the generalization of findings from a sample to the broader population from which the sample has been randomly drawn. A variety of statistical tests, such as the chi-square, help in estimating the level of probability that such inferences about the population are true, given the sample size. This is expressed as the statistical significance of the finding.

The process of making conclusions about a population using data collected from a sample.

an estimate, prediction, or other generalization about a population based on information contained in a sample

Statistical inference makes use of information from a sample to draw conclusions (inferences) about the population from which the sample was taken ie it is the act of drawing conclusions about a population from a sample.

The extension of sample results to a larger population. Descriptive statistics (such as the mean or a histogram) provide concise methods for summarizing a lot of information. However, it is inferential statistics that allows one to make statements about the population from a sample. For example, it is often virtually impossible to measure an entire population, but by statistical inference one can use the measured sample statistics to make statements about the unmeasured population (see estimation). However, in order to use the power of statistical inference, certain assumptions about the statistic must first be met. For example, making correct inferences about a population from a sample can often require that random sampling be employed.

Inferential statistics or statistical induction comprises the use of statistics to make inferences concerning some unknown aspect of a population. It is distinguished from descriptive statistics.