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One sample t-test

Regular test

# HypothesisTests.OneSampleTTest — Type.

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OneSampleTTest(d::AbstractUncertainValue, n::Int = 1000;
    μ0::Real = 0) -> OneSampleTTest

Perform a one sample t-test of the null hypothesis that the uncertain value has a distribution with mean μ0 against the alternative hypothesis that its distribution does not have mean μ0. n indicates the number of draws during resampling.

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Example:

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# Normally distributed uncertain observation with mean = 2.1
uv = UncertainValue(Normal, 2.1, 0.2)

# Perform a one-sample t-test to test the null hypothesis that
# the sample comes from a distribution with mean μ0
OneSampleTTest(uv, 1000, μ0 = 2.1)

Which gives the following output:

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# Which results in
One sample t-test
-----------------
Population details:
    parameter of interest:   Mean
    value under h_0:         2.1
    point estimate:          2.1031909275381566
    95% confidence interval: (2.091, 2.1154)

Test summary:
    outcome with 95% confidence: fail to reject h_0
    two-sided p-value:           0.6089

Details:
    number of observations:   1000
    t-statistic:              0.5117722099885472
    degrees of freedom:       999
    empirical standard error: 0.00623505433839

Thus, we cannot reject the null-hypothesis that the sample comes from a distribution with mean = 2.1. Therefore, we accept the alternative hypothesis that our sample does in fact come from such a distribution. This is of course true, because we defined the uncertain value as a normal distribution with mean 2.1.

Pooled test

# UncertainData.UncertainStatistics.OneSampleTTestPooled — Function.

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

First, sample n draws of each uncertain value in each dataset, pooling the draws from the elements of d1 and the draws from the elements of d2 separately. Then, perform a paired sample t-test of the null hypothesis that the differences between pairs of uncertain values in d1 and d2 come from a distribution with mean μ0 against the alternative hypothesis that the distribution does not have mean μ0.

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Element-wise test

# UncertainData.UncertainStatistics.OneSampleTTestElementWise — Function.

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

Perform a one sample t-test of the null hypothesis that the uncertain value has a distribution with mean μ0 against the alternative hypothesis that its distribution does not have mean μ0 for uncertain value in d.

n indicates the number of draws during resampling.

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