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.

Want to know more?

Wiki of Science - Descriptive statistics: This page provides access to statistic technologies used for describing a group or even a whole population.