AlternativeHypothesis

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

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Basic 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:

Wolfram Research (2010), AlternativeHypothesis, Wolfram Language function, https://reference.wolfram.com/language/ref/AlternativeHypothesis.html.

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: 22-February-2025 ]}

BibLaTeX

@online{reference.wolfram_2025_alternativehypothesis, organization={Wolfram Research}, title={AlternativeHypothesis}, year={2010}, url={https://reference.wolfram.com/language/ref/AlternativeHypothesis.html}, note=[Accessed: 22-February-2025 ]}