List of statistical tests

Statistical tests are used to test the fit between a hypothesis and the data.{{cite journal |last1=Parab |first1=Shraddha |last2=Bhalerao |first2=Supriya |title=Choosing statistical test |journal=International Journal of Ayurveda Research |date=2010 |volume=1 |issue=3 |pages=187–191 |doi=10.4103/0974-7788.72494 |doi-access=free |pmid=21170214 |pmc=2996580 |issn=0974-7788}}{{cite web |title=Entscheidbaum |url=https://www.empirical-methods.hslu.ch/entscheidbaum/ |access-date=8 February 2024 |language=de-DE}} Choosing the right statistical test is not a trivial task. The choice of the test depends on many properties of the research question. The vast majority of studies can be addressed by 30 of the 100 or so statistical tests in use.{{cite journal |last1=Nayak |first1=Barun K |last2=Hazra |first2=Avijit |title=How to choose the right statistical test? |journal=Indian Journal of Ophthalmology |date=2011 |volume=59 |issue=2 |pages=85–86 |doi=10.4103/0301-4738.77005 |doi-access=free |pmid=21350275 |pmc=3116565 |issn=0301-4738}}{{cite book |last1=Lewis |first1=Nancy D. |last2=Lewis |first2=Nigel Da Costa |last3=Lewis |first3=N. D. |title=100 Statistical Tests in R: What to Choose, how to Easily Calculate, with Over 300 Illustrations and Examples |date=2013 |publisher=Heather Hills Press |isbn=978-1-4840-5299-0 |url=https://books.google.com/books?id=wIs7mwEACAAJ |language=en}}{{cite book |last1=Kanji |first1=Gopal K. |title=100 Statistical Tests |date=18 July 2006 |publisher=SAGE |isbn=978-1-4462-2250-8 |url=https://books.google.com/books?id=c16MhjA4pHgC |language=en}}

Explanation of properties

Scaling of data: One of the properties of the tests is the scale of the data, which can be interval-based, ordinal or nominal. Nominal scale is also known as categorical.{{cite web |title=What is the difference between categorical, ordinal and interval variables? |url=https://stats.oarc.ucla.edu/other/mult-pkg/whatstat/what-is-the-difference-between-categorical-ordinal-and-interval-variables/ |website=stats.oarc.ucla.edu |access-date=10 February 2024}} Interval scale is also known as numerical. When categorical data has only two possibilities, it is called binary or dichotomous.

Assumptions, parametric and non-parametric: There are two groups of statistical tests, parametric and non-parametric. The choice between these two groups needs to be justified. Parametric tests assume that the data follow a particular distribution, typically a normal distribution, while non-parametric tests make no assumptions about the distribution.{{cite journal |last1=Huth |first1=R. |last2=Pokorná |first2=L. |title=Parametric versus non-parametric estimates of climatic trends |journal=Theoretical and Applied Climatology |date=1 March 2004 |volume=77 |issue=1 |pages=107–112 |doi=10.1007/s00704-003-0026-3 |bibcode=2004ThApC..77..107H |s2cid=121539673 |url=https://link.springer.com/article/10.1007/s00704-003-0026-3 |language=en |issn=1434-4483}} Non-parametric tests have the advantage of being more resistant to misbehaviour of the data, such as outliers. They also have the disadvantage of being less certain in the statistical estimate.

Type of data: Statistical tests use different types of data. Some tests perform univariate analysis on a single sample with a single variable. Others compare two or more paired or unpaired samples. Unpaired samples are also called independent samples. Paired samples are also called dependent. Finally, there are some statistical tests that perform analysis of relationship between multiple variables like regression.

Number of samples: The number of samples of data.

Exactness: A test can be exact or be asymptotic delivering approximate results.