%
% Written by:
% -- 
% John L. Weatherwax                2008-02-20
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
%-----

clear all; 
close all; 
clc; 

addpath('../../Code/CSTool');
load lawpop;      % <- the total population 

% get a random sample from the total population of 15:
rand('seed',0); 
ns   = 15; 
%ns   = 25; 
%ns   = 50; 
inds = unidrnd(size(lawpop,1),1,ns);
law  = lawpop(inds,:); 

% get the population correlation coefficient: 
p=cross_corr_fn(lawpop); 

% estimate the correlation coefficient using our sample
t=cross_corr_fn(law);

% perform boostrap hypothesis testing to test the hypothesis that H_0: t>0
B = 1000; 
bootstat = bootstrp( B, @cross_corr_fn, law );  
% get the empricial quantiles for the distribution of our statistics: 
alpha = 0.01; % <- the probability of a type I error
ci = quantile( bootstat, [ 0.5*alpha, 1-0.5*alpha ] ); 

fprintf('for the correlation coefficient (CC)\n'); 
fprintf('the population CC and sample CC are = (%10.5f,%10.5f)\n',p,t);
fprintf('the bootstraped estimate 90%% quantiles of the CC coefficient are = (%10.5f,%10.5f)\n',ci(1),ci(2));