Equal variance t-test

Regular test

HypothesisTests.EqualVarianceTTest — Type

EqualVarianceTTest(d1::AbstractUncertainValue, d2::AbstractUncertainValue,
    n::Int = 1000; μ0::Real = 0) -> EqualVarianceTTest

Consider two samples s1 and s2, each consisting of n random draws from the distributions furnishing d1 and d2, respectively.

This function performs a two-sample t-test of the null hypothesis that s1 and s2 come from distributions with equal means and variances against the alternative hypothesis that the distributions have different means but equal variances.

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Example

Let's create two uncertain values furnished by distributions of different types. We'll perform the equal variance t-test to check if there is support for the null-hypothesis that the distributions furnishing the uncertain values come from distributions with equal means and variances.

We expect the test to reject this null-hypothesis, because we've created two very different distributions.

uv1 = UncertainValue(Normal, 1.2, 0.3)
uv2 = UncertainValue(Gamma, 2, 3)

# EqualVarianceTTest on 1000 draws for each variable
EqualVarianceTTest(uv1, uv2, 1000)

The output is:

Two sample t-test (equal variance)
----------------------------------
Population details:
    parameter of interest:   Mean difference
    value under h_0:         0
    point estimate:          -4.782470406651697
    95% confidence interval: (-5.0428, -4.5222)

Test summary:
    outcome with 95% confidence: reject h_0
    two-sided p-value:           <1e-99

Details:
    number of observations:   [1000,1000]
    t-statistic:              -36.03293014520585
    degrees of freedom:       1998
    empirical standard error: 0.1327249931487462

The test rejects the null-hypothesis, so we accept the alternative hypothesis that the samples come from distributions with different means and variances.

Pooled test

UncertainData.UncertainStatistics.EqualVarianceTTestPooled — Function

EqualVarianceTTestPooled(d1::UncertainDataset, d2::UncertainDataset,
    n::Int = 1000; μ0::Real = 0) -> EqualVarianceTTest

Consider two samples s1[i] and s2[i], each consisting of n random draws from the distributions furnishing the uncertain values d1[i] and d2[i], respectively. Gather all s1[i] in a pooled sample S1, and all s2[i] in a pooled sample S2.

Perform a two-sample t-test of the null hypothesis that S1 and S2 come from distributions with equal means and variances against the alternative hypothesis that the distributions have different means but equal variances.

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Element-wise test

UncertainData.UncertainStatistics.EqualVarianceTTestElementWise — Function

EqualVarianceTTestElementWise(d1::UncertainDataset, d2::UncertainDataset,
    n::Int = 1000; μ0::Real = 0) -> Vector{EqualVarianceTTest}

Consider two samples s1[i] and s2[i], each consisting of n random draws from the distributions furnishing the uncertain values d1[i] and d2[i], respectively. This function performs an elementwise EqualVarianceTTest on the pairs (s1[i], s2[i]). Specifically:

Performs an pairwise two-sample t-test of the null hypothesis that s1[i] and s2[i] come from distributions with equal means and variances against the alternative hypothesis that the distributions have different means but equal variances.

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