Reduce the inputs for the chi2gof function (follow-up question of: Using chi2gof to test two distributions)

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Sim 2024-7-16，15:38

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https://ww2.mathworks.cn/matlabcentral/answers/2137763-reduce-the-inputs-for-the-chi2gof-function-follow-up-question-of-using-chi2gof-to-test-two-distrib

编辑： Sim 2024-7-16，15:40

This is a follow-up question of Using chi2gof to test two distributions.

@Allie had the following inputs, i.e. the binned observational data (x), the binned model data (y), and the bin edges (bins):

x= [41 22 11 10 9 5 2 3 2];
y= [38.052 24.2655 15.4665 9.8595 6.2895 4.011 2.562 1.6275 2.8665];
bins=[0:9:81];

and asked how to use "chi2gof to test if two distributions come from a common distribution (null hypothesis) or if they do not come from a common distribution (alternative hypothesis)".

The accepted answer comes from @Jeff Miller:

bins=[0:9:81];
xvals = bins(1:end-1)+4.5;   % Here are some fake data values that belong in each bin.
xcounts= [41 22 11 10 9 5 2 3 2];  % These are the counts of the data values in each bin.
y= [38.052 24.2655 15.4665 9.8595 6.2895 4.011 2.562 1.6275 2.8665];
[h,p,stat]=chi2gof(xvals,'Edges',bins,'Expected',y,'Frequency',xcounts,'EMin',1)
h = 0
p = 0.7905
stat = struct with fields:
    chi2stat: 4.6864
          df: 8
       edges: [0 9 18 27 36 45 54 63 72 81]
           O: [41 22 11 10 9 5 2 3 2]
           E: [38.0520 24.2655 15.4665 9.8595 6.2895 4.0110 2.5620 1.6275 2.8665]

However, by re-doing all the calculations, i.e.

% inputs
alpha = 0.05;
x= [41 22 11 10 9 5 2 3 2];                                           % <-- observed data
y= [38.052 24.2655 15.4665 9.8595 6.2895 4.011 2.562 1.6275 2.8665];  % <-- expected data
% Chi-square goodness-of-fit test
chi2 = sum(((x-y).^2)./y);       % <-- chi-square value
df = length(x)-1;                % <-- degrees of freedom
p = chi2cdf(chi2,df,'upper');    % <-- p-value calculated from the chi-square distribution with "df" degrees of freedom
if p>alpha                       % <-- accept or reject the null hypothesis, based on the p-value
    h = 0;                       % <-- disp('we fail to reject the null hypothesis')
else
    h = 1;                       % <-- disp('we reject the null hypothesis')
end
table([chi2; df; p; h],'RowNames',{'chi-square','df','p-value','h'},'VariableNames',{'Stats'})
ans = 4x1 table
                   Stats 
                  _______

    chi-square     4.6864
    df                  8
    p-value       0.79051
    h                   0