is an option for hypothesis testing functions like LocationTest that specifies the alternative hypothesis.
AlternativeHypothesis
is an option for hypothesis testing functions like LocationTest that specifies the alternative hypothesis.
Details
- For a hypothesis test with test statistic , AlternativeHypothesis can be used to test the null hypothesis against particular alternatives .
- Typical settings include:
-
"Unequal" and"Less" and"Greater" and
- For functions using AlternativeHypothesis , a two-sided test is performed by default.
Examples
open all close allBasic Examples (2)
Perform a two-sided test for location:
The setting "Unequal" is chosen by default:
Perform one of the two one-sided alternatives:
Properties & Relations (3)
The -value from a two-sided test is twice the smaller one-sided -value:
The interpretation of a two-sided test:
The -value can be interpreted as an area under the distribution of the test statistic:
Interpretation of both one-sided alternatives:
The areas are equivalent to the -values returned by the test:
See Also
Related Guides
History
Text
Wolfram Research (2010), AlternativeHypothesis, Wolfram Language function, https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.
CMS
Wolfram Language. 2010. "AlternativeHypothesis." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.
APA
Wolfram Language. (2010). AlternativeHypothesis. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/AlternativeHypothesis.html
BibTeX
@misc{reference.wolfram_2025_alternativehypothesis, author="Wolfram Research", title="{AlternativeHypothesis}", year="2010", howpublished="\url{https://reference.wolfram.com/language/ref/AlternativeHypothesis.html}", note=[Accessed: 10-January-2026]}
BibLaTeX
@online{reference.wolfram_2025_alternativehypothesis, organization={Wolfram Research}, title={AlternativeHypothesis}, year={2010}, url={https://reference.wolfram.com/language/ref/AlternativeHypothesis.html}, note=[Accessed: 10-January-2026]}