is an option to VarianceTest and similar functions that controls cutoffs for diagnostic tests as well as test conclusions.


  • The setting SignificanceLevel->α with 0<α<1 indicates a significance level of α.
  • The level used for verifying assumptions such as normality is taken to be where is the number of datasets being tested.


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Basic Examples  (2)

Set test sizes for diagnostics used in LocationTest:

The -value is equivalent but a warning is issued:

Set the cutoff used in "TestConclusion" and "ShortTestConclusion" properties:

By default, 0.05 is used:

Properties & Relations  (2)

The significance level can affect the degrees of freedom for some tests:

An assumption of equal variances is rejected at the 25% level and a Satterthwaite approximation is used for the degrees of freedom:

The significance level is divided by the number of comparisons when assumptions are checked:

Using with 50 tests for normality results in each one being tested at the level:

Wolfram Research (2010), SignificanceLevel, Wolfram Language function,


Wolfram Research (2010), SignificanceLevel, Wolfram Language function,


@misc{reference.wolfram_2020_significancelevel, author="Wolfram Research", title="{SignificanceLevel}", year="2010", howpublished="\url{}", note=[Accessed: 16-April-2021 ]}


@online{reference.wolfram_2020_significancelevel, organization={Wolfram Research}, title={SignificanceLevel}, year={2010}, url={}, note=[Accessed: 16-April-2021 ]}


Wolfram Language. 2010. "SignificanceLevel." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2010). SignificanceLevel. Wolfram Language & System Documentation Center. Retrieved from