confidence_intervals.m

function [ Conf_intervals ] = confidence_intervals( samples, interval, islognorm )
% Find the confidence intervals for a set of data for use with the errorbar function in MATLAB
% 
% Syntax:	[Conf_intervals] = CONFIDENCE_INTERVALS( samples, interval )
% Pass the samples to the function with the desired confidence interval (95
% for 95%). Samples should be in each row of a column where the column is 
% the dataset to analyse
% 
% Inputs: 
% 	samples   - A 1D or 2D array of samples where each column is a dataset
%               for which the confidence intervals are calculated.
% 	interval  - The confidence interval as a percentage (e.g. 95 for 95%
%               confidence intervals).
%   islognorm - Finds the confidence intervals using the log-normal
%               variance if set to TRUE.
% 
% Outputs: 
% 	Conf_intervals - Confidence intervals for use with the errorbar
%                    function in MATLAB.
%
% Example Usage:
%       load count.dat;
%       samples = count';
%       X=1:size(samples,2);
%       ConfIntervals = confidence_intervals(samples,95);
%       errorbar(X,mean(samples),ConfIntervals(:,1),ConfIntervals(:,2),'rx');
%       axis([0 25 0 250]);
% 
% See also: errorbar.m

% Author: Jacob Donley
% University of Wollongong
% Email: jrd089@uowmail.edu.au
% Copyright: Jacob Donley 2017
% Date: 19 September 2016
% Revision: 0.2
% 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

if nargin < 3
    islognorm = false;
end
if nargin < 2
    interval = 95;	%  Confidence = 95%
end

L = size(samples,1);
a = 1 - interval/100;
ts = tinv([a/2,  1-a/2],L-1);	% T-Score

if islognorm
    v = var(samples);
    m = mean(samples);
    sigm = sqrt( log( 1 + v./m.^2 ) );
else
    sigm = std(samples);
end

Conf_intervals(:,1) = ts(1)*sigm/sqrt(L);	% Confidence Intervals
Conf_intervals(:,2) = ts(2)*sigm/sqrt(L);	% <-'


end