# T-test¶

OneSampleTTest(v::AbstractVector{T<:Real}, mu0::Real=0)

Perform a one sample t-test of the null hypothesis that the data in vector v comes from a distribution with mean mu0 against the alternative hypothesis that the distribution does not have mean mu0.

Implements: pvalue, confint

OneSampleTTest(xbar::Real, stdev::Real, n::Int, mu0::Real=0)

Perform a one sample t-test of the null hypothesis that n values with mean xbar and sample standard deviation stdev come from a distribution with mu0 against the alternative hypothesis that the distribution does not have mean mu0.

Implements: pvalue, confint

OneSampleTTest(x::AbstractVector{T<:Real}, y::AbstractVector{T<:Real}, mu0::Real=0)

Perform a paired sample t-test of the null hypothesis that the differences between pairs of values in vectors x and y come from a distribution with mu0 against the alternative hypothesis that the distribution does not have mean mu0.

Implements: pvalue, confint

EqualVarianceTTest(x::AbstractVector{T<:Real}, y::AbstractVector{T<:Real})

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

Implements: pvalue, confint

UnequalVarianceTTest(x::AbstractVector{T<:Real}, y::AbstractVector{T<:Real})

Perform an unequal variance two-sample t-test of the null hypothesis that x and y come from a distributions with the same mean against the alternative hypothesis that the distributions have different means.

This test is also known as 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:

$\nu_{\chi'} \approx \frac{\left(\sum_{i=1}^n k_i s_i^2\right)^2} {\sum_{i=1}^n \frac{(k_i s_i^2)^2}{\nu_i}}$

Implements: pvalue, confint