hypothesis testing in matlab

There are various statistical hypothesis tests available in MATLAB. Here is one example of how to perform the hypothesis test for difference of means using the t-test:

Suppose we have two sets of data, x and y, and we want to test whether they have the same mean or not. We can perform a two-sample t-test as follows:

main.m
% Generate two sets of random data
x = randn(100,1); % sample size = 100
y = randn(100,1);

% Set significance level
alpha = 0.05; % 5% significance level

% Perform two-sample t-test assuming unequal variances
[h,p,ci,stats] = ttest2(x,y,'Vartype','unequal','Alpha',alpha);

% Display results
fprintf('t-statistic = %0.4f\n',stats.tstat);
fprintf('p-value = %0.4f\n',p);
if h == 1
    fprintf('Reject null hypothesis: Means are different\n');
else
    fprintf('Fail to reject null hypothesis: Means are the same\n');
end
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The function ttest2() performs a two-sample t-test assuming unequal variances by default. The 'Vartype' option can be set to 'equal' if we assume equal variances. The 'Alpha' option sets the significance level for the test. The function returns the test result h (1 if we reject the null hypothesis), the p-value p, the confidence interval ci for the difference of means, and the test statistics stats.

We can also plot the histograms of the two sets of data and the confidence interval as follows:

main.m
% Plot histograms of the two sets of data
histogram(x,'Normalization','pdf');
hold on
histogram(y,'Normalization','pdf');
hold off
legend('x','y')
xlabel('Data')
ylabel('PDF')
title('Histograms of Two Sets of Data')

% Plot confidence interval around difference of means
hold on
plot(ci,[0,0],'r','LineWidth',2)
hold off
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This will plot the histograms of the two sets of data and the confidence interval around the difference of means. If the confidence interval does not include zero, we can reject the null hypothesis at the specified significance level.

Note that the choice of hypothesis test depends on the type of data and the research question of interest. There are other hypothesis tests available in MATLAB, such as one-sample t-tests, paired t-tests, ANOVA, etc.