Usage of chi2gof

(A very silly question) From the chi2gof documentation I see that chi2gof takes 1 argument

h = chi2gof(x)

Since the chi-square test is just a comparison between observed (O) and expected (E) values, throught the formula (\sum_i (O_i - E_i)^2 / E_i), I guess that the argument "x" would refer to the observed data (O), but.... where should I insert/add the expected (E) values there?

Can you show any example of comparison among observed (O) and expected (E) data, like when I would need to compare two distributions?

(for example the expected (E) values might refer to any theoretical distribution that I want /need to compare to my observed (O) data)

Answer 1

[Aman]

Hi Sim,

You can add expected value as a parameter as given in chi2gof documentation.

Here is an example for the same,

observed_data = exprnd(2, 100, 1);

num_bins = 10;
bin_edges = linspace(min(observed_data), max(observed_data), num_bins+1);
expected_counts = numel(observed_data) * diff(chi2cdf(bin_edges, 1));

[h, p] = chi2gof(observed_data, 'Expected', expected_counts)

You can add other parameter according to your needs. For further help, check the documentation.

Hope this helps!

[Sim]

Thanks a lot@Aman! Just a question.... what if my data come from a fitting distribution?? How to derive the "expected_counts" from the fitting distribution?

observed_data = exprnd(2, 100, 1);
xgrid = linspace(0,100,1000)';
pd = fitdist(observed_data,'Exponential'); % <-- fitting distribution
hold on
line(xgrid,pdf(pd,xgrid),'Linewidth',2,'color','b')
histogram(observed_data,100,'Normalization','pdf','facecolor','blue')
hold off

% how to get the "expected_counts" from "pd =
% fitdist(observed_data,'Exponential')"??
% [h, p] = chi2gof(observed_data, 'Expected', expected_counts)

[Aman]

We can use cdf, like this:

expected_counts = numel(observed_data) * diff(cdf(pd,bin_edges));

[Sim]

thanks a lot @Aman!!