myBinomTest(s,n,p,S​ided)

1 or 2 sided binomial test with arbitrary binomial probabilities

%function pout=myBinomTest(s,n,p,Sided)
%
% Performs a binomial test of the number of successes given a total number
% of outcomes and a probability of success. Can be one or two-sided.
%
% Inputs:
% s- (Scalar or Array) The observed numebr of successful outcomes
% n- (Scalar or Array) The total number of outcomes (successful or not)
% p- (Scalar or Array) The proposed probability of a successful outcome
% Sided- (String) can be 'one', 'two' (the default), or 'two, equal
% counts'. A value of 'one' will perform a one-sided test to
% determine if the observed number of successes are either
% significantly greater than or less than the expected number
% of successes, depending on whether s is greater than or less
% than the observed number of successes. 'Two' will use the
% method of small p-values (see reference below) to perform a
% two-tailed test to calculate the probability of observing
% any equally unlikely or more unlikely value greater than or
% less than the expected number of successes (ie with the
% same cdf value of the distribution. 'Two, equal counts'
% will perform a two-sided test that the that the actual
% number of success is different from the expected number of
% successes in any direction.
%
% Outputs:
% pout- The probability of observing the resulting value of s or
% another value more extreme (the precise meaning of which
% depends on the value of Sided) given n total outcomes with
% a probability of success of p.
%
% s, n and p can be scalars or arrays of the same size. The
% dimensions and size of pout will match that of these inputs.
%
% For example, the signtest is a special case of this where the value of p
% is equal to 0.5 (and a 'success' is dfeined by whether or not a given
% sample is of a particular sign.), but the binomial test and this code is
% more general allowing the value of p to be any value between 0 and 1.
%
% The results when Sided='two' and when Sided='two, equal counts' are
% identical only when p=0.5, but are different otherwise. For more
% description, see the second reference below.
%
% References:
% http://en.wikipedia.org/wiki/Binomial_test
% http://www.graphpad.com/guides/prism/6/statistics/index.htm?stat_binomial.htm
%
% by Matthew Nelson July 21st, 2009
%
% Last Updated by Matthew Nelson May 23, 2015
% [e-mail]