Inferential statistics

Inferential statistics are a set of technologies (ie, formulas and procedures) used for inferring mathematical properties of an unmeasured population based on the mathematical properties of a sample. The adequacy and appropriateness of using inferential statistics is dependent, at least in part, on the mathematical characteristics of the sample, in part on the quality of the methods used. The mathematical characteristics of the sample can be ascertained with descriptive statistics2.

It is necessary to emphasise that inferential statistics is a step removed from the reality of the data, and that bad data and bad methods, as well as inferences beyond the limitations of the original sample and dataset, is a recipe for pseudoscience.

Illustration 1 offers a snapshot of typical inferential statistics.

Illustration 1. Inferential statistics
Key concepts
Type of analysis nominal ordinal interval
Uncertainty --- --- standard error
Theoretical distribution --- ranked distribution z-distribution
~ --- --- t-distribution
~ --- --- F-distribution
Statistics for describing the population
Type of analysis nominal ordinal interval
Central tendency --- confidence interval of the median confidence interval of the mean
Dispersion --- --- confidence interval of the standard deviation
Graphs histogram with normal curve
Tests of significance
Type of analysis nominal ordinal interval
Group difference chi-square U test t-test
~ --- W test oneway, anova
Time difference --- t-test
References
1. full reference in the following format AUTHOR (date work).Title. Reference location, date publication. ISBN/ISSN.
+++ Notes +++
2. Inferential statistics are unnecessary when a whole population, rather than a sample, is the object of study, as there is no need to infer mathematical properties of a population whose mathematical properties are known with the use of descriptive statistics.

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