A two-sided test for the null hypothesis that the mean of list1 is different to the mean of list2.

The variance of the lists should be equal but the sample size of each last can be different.

Returns the t statistic, and the p value.

Example

iex> Statistics.Tests.TTest.ind_samples([1,2,3,2,1], [3,2,4,3,5])
%{p: 0.022802155958137702, t: -2.82842712474619}

iex> Statistics.Tests.TTest.ind_samples([1,2,3,2,1], [3,2,4,3,5,4,5,6])
%{p: 0.0044530673387188, t: -3.5858542135407596}

A two-sided test for the null hypothesis that the expected value (mean) of a sample of independent observations a is equal to the given population mean, popmean.

Returns the t statistic, and the p value.

Example

iex> Statistics.Tests.TTest.one_sample([1,2,3,2,1], 3)
%{p: 0.023206570788795993, t: -3.585685828003181}