% dice simulation and Chi Squared test
% DiceSimulation.m
% L Braile 1/31/05
n = 120 % number of rolls
nd = zeros(1,6);
edges = [0:1:6];
for i = 1:n
    x = rand(1,1)*6; % simulate one roll of a die
                     % note that we used rand for a uniform distribution
                     % sample
    nd1 = histc(x,edges); % make the number 1, 2, 3... 6
    nd = nd + nd1(1:6);  % Accumulate number of 1's, 2's, etc.
end
sumrolls = sum(nd)  % check to be sure that all rolls are accounted for in nd
bar(nd) % plot histogram
xlabel('Die result')
ylabel('Number of occurrences in 120 rolls')
o = nd; % Observed number of 1's, etc.
e = ones(1,6)*(n/6); % Expected number in each bin
ChiSq = sum(((o - e).^2)./e)  % Calculate Chi-squared statistic for data
ChiTest = chi2inv(0.95,5)  % Obtain Chi-squared test statistic for 95% confidence 
% and 5 degrees of freedom.  For example, for many trials, the calculated
% value should exceed the test value only ~5% of the time by chance.