Jump to navigation Jump to search Not to be confused with Statistical interference. Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistics can be contrasted with descriptive statistics. Descriptive statistics is inferential statistics definition investopedia forex concerned with properties of the observed data, and it does not rest on the assumption that the data come from a larger population.

Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling. Kitagawa state, “The majority of the problems in statistical inference can be considered to be problems related to statistical modeling”. Relatedly, Sir David Cox has said, “How translation from subject-matter problem to statistical model is done is often the most critical part of an analysis”. The conclusion of a statistical inference is a statistical proposition. Any statistical inference requires some assumptions. A statistical model is a set of assumptions concerning the generation of the observed data and similar data. Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference.

Fully parametric: The probability distributions describing the data-generation process are assumed to be fully described by a family of probability distributions involving only a finite number of unknown parameters. Non-parametric: The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal. Semi-parametric: This term typically implies assumptions ‘in between’ fully and non-parametric approaches. For example, one may assume that a population distribution has a finite mean. Incorrect assumptions of ‘simple’ random sampling can invalidate statistical inference. More complex semi- and fully parametric assumptions are also cause for concern.