Unequal variance t-test

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

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

Perform an unequal variance two-sample t-test of the null hypothesis that s1 and s2 come from distributions with equal means against the alternative hypothesis that the distributions have different means.

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

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.

This function performs an unequal variance two-sample t-test of the null hypothesis that S1 and S2 come from distributions with equal means against the alternative hypothesis that the distributions have different means.

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

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 unequal variance two-sample t-test of the null hypothesis that s1[i] and s2[i] come from distributions with equal means against the alternative hypothesis that the distributions have different means.

This test is sometimes known as Welch's t-test. It differs from the equal variance t-test in that it computes the number of degrees of freedom of the test using the Welch-Satterthwaite equation:

\[ ν_{χ'} ≈ \frac{\left(\sum_{i=1}^n k_i s_i^2\right)^2}{\sum_{i=1}^n \frac{(k_i s_i^2)^2}{ν_i}}\]