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Unequal variance t-test - using R

Functions for multinomial and
two sample independent binomial

Note that because the X2 statistic is being compared to an estimate of the exact distribution, rather than to an approximate continuous model, the 'x2' function (below) does not use a continuity correction.
These instructions have to be entered before using the second set of code below.

Testing 4 frequencies (a,b,c,d) using the
multinomial model and mid-P inference


Gives something like this:

[1] 0.06270875

Testing 4 frequencies (a,b,c,d) using the two sample
independent binomial model and conventional inference


Gives something like this:

[1] 0.06894862

Remember, since these results are obtained by taking a finite number of random samples, they are only estimates of the statistic's 'exact' distribution, so will differ slightly upon repetition.