Inferential Statistics

Inferential Methods

Technically, inferential statistics refer to numerical indices used for inference, yet the term often is used to apply to a collection of methods for calculating inferential statistics. These methods include t procedures, analysis of variance, chi-square procedures, the Wilcoxon method, the Kruskal–Wallis method, and many others. A particular method is appropriate for specific configurations of the study, such as the number of explanatory and response variables, and whether the data for each variable are obtained at a categorical or quantitative level of measurement. The method leads to the calculation of statistics that can be used for inference, which is why both the methods and the statistics themselves often fall under the general heading of inferential statistics.

Types of Inferential Statistics

An inferential method applied to a set of data will result in an index that is an inferential statistic. For example, applying analysis of variance techniques to a set of data will result in an F statistic. Although this is an important inferential statistic, it is an intermediate step in the inferential process. In order to make inferences, the researcher must compare this observed statistic to the larger collection of all possible values that could have been obtained for the statistic. If researchers hypothesize characteristics of a population or multiple populations in a study (e.g., it might be hypothesized that the characteristics of multiple populations are all equal), they can calculate not only the possible values of an inferential statistic but also how likely it is to obtain a value of the inferential statistic that is within some specified range. For example, researchers might calculate that there is only a 5% chance that they will observe an F statistic that is greater than 4.0. This ability to make such calculations allows them to calculate inferential statistics that are linked to probability statements.

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