({{, (RefLink[SignificanceLevel, paclet:ref/SignificanceLevel]) 
is an option to (RefLink[VarianceTest, paclet:ref/VarianceTest]) and similar functions that controls cutoffs for diagnostic tests as well as test conclusions. }})

OpenersNotesSection(Spacer1)Details

The setting (RefLink[SignificanceLevel, paclet:ref/SignificanceLevel])->α with 0<α<1 indicates a significance level of α.

The level α used for verifying assumptions such as normality is taken to be α/k where k is the number of datasets being tested.

OpenersPrimaryExamplesSection(Spacer1)Examples  (4)

OpenersExampleSection0(Spacer1)Basic Examples  (2)

Set test sizes for diagnostics used in (RefLink[LocationTest, paclet:ref/LocationTest]):

BlockRandom[SeedRandom[11];
data=RandomVariate[StudentTDistribution[5],100]];

LocationTest[data,0,"T",SignificanceLevel->0.05]

The p-value is equivalent but a warning is issued:

LocationTest[data,0,"T",SignificanceLevel->0.1]

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

BlockRandom[SeedRandom[1];
data=RandomVariate[StudentTDistribution[5],100]];

DistributionFitTest[data,NormalDistribution[μ,σ],"ShortTestConclusion",SignificanceLevel->0.1]

DistributionFitTest[data,NormalDistribution[μ,σ],"ShortTestConclusion",SignificanceLevel->0.05]

By default, 0.05 is used:

DistributionFitTest[data,NormalDistribution[μ,σ],"TestConclusion",SignificanceLevel->Automatic]//TraditionalForm

OpenersExampleSection2(Spacer1)Properties & Relations  (2)

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

BlockRandom[SeedRandom[9];data1=RandomVariate[NormalDistribution[0,1],25];
data2=RandomVariate[NormalDistribution[0,1.5],25]];

TTest[{data1,data2},0,"DegreesOfFreedom",SignificanceLevel->0.05]

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

TTest[{data1,data2},0,"DegreesOfFreedom",SignificanceLevel->0.25]

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

BlockRandom[SeedRandom[123];data=RandomVariate[NormalDistribution[],{50,100}]];

LocationEquivalenceTest[data,"KSampleT",SignificanceLevel->0.05]

Using (9/10) with 50 tests for normality results in each one being tested at the (9/500) level:

LocationEquivalenceTest[data,"KSampleT",SignificanceLevel->9/10]

({{DocumentationFooterIconsRelatedFunction.png, ({{See Also}, {(RefLink[DistributionFitTest, paclet:ref/DistributionFitTest])  ▪  (RefLink[LocationTest, paclet:ref/LocationTest])  ▪  (RefLink[LocationEquivalenceTest, paclet:ref/LocationEquivalenceTest])  ▪  (RefLink[VarianceTest, paclet:ref/VarianceTest])  ▪  (RefLink[VarianceEquivalenceTest, paclet:ref/VarianceEquivalenceTest])}})}})

({{DocumentationFooterIconsRelatedGuide.png, ({{Related Guides}, {▪(RefLinkPlain[Hypothesis Tests, paclet:guide/HypothesisTests])}})}})