# Hypothesis Test [MATLAB]

Using Randomization to test the disprove the null hypothesis

Let’s pose the null hypothesis that the two sets of data come from the same probability distribution (not necessarily Gaussian). Under the null hypothesis, the two sets of data are interchangeable, so if we aggregate the data points and randomly divide the data points into two sets, then the results should be comparable to the results obtained with the original data.

## Statistical Analysis [MATLAB]

For more details on the hypothesis testing, please visit this page.

So, the strategy is to generate random datasets, with replacement (bootstrapping), compute difference in means (or difference in medians or any other reliable statistic), and then compare the resulting values to the statistic computed from the original data.

```
%% Hypothesis Testing
clear; close all; clc;
data1=randn(100,1);
data2=(randn(150,1).^2)*10 + 20;
all_data=[data1; data2];
```

- Null hypothesis is that the two distribution that we are sampling are from the same population.

```
%% First Sample
mu1=mean(data1);
%% Second Sample
mu2=mean(data2);
actualdiffmn=(mu1-mu2)
```

- Now, since our null hypothesis is that the two distribution comes from the same population, we can mix it to draw two samples again.

```
%% Using Randomization to test the hypothesis
numsim = 10000; % number of simulations to run
mn1=zeros(1,numsim);
mn2=zeros(1,numsim);
diffmn = zeros(1,numsim);
for num=1:numsim
% vector of indices (a random ordering of the integers between
% 1 and n where n is the number of data points)
indx = randperm(length(all_data));
data_sim=all_data(indx);
data_sim1=data_sim(1:length(data1));
data_sim2=data_sim(1:length(data2));
mn1(num)=mean(data_sim1);
mn2(num)=mean(data_sim2);
diffmn(num)=(mn1(num)-mn2(num));
end
% visualize
figure; hold on;
hist(diffmn,100);
ax = axis;
plot(repmat(actualdiffmn,[1 2]),ax(3:4),'r-');
pval = sum(abs(diffmn) > abs(actualdiffmn)) / length(diffmn);
title(sprintf('Actualdiffmean = %.4f; p-value (two-tailed) = %.6f',actualdiffmn,pval));
legend('Results of simulation','Actual difference in means')
xlabel('Difference in means'), ylabel('Frequency')
```

```
actualdiffmn =
-28.5153
```

- For details see: Lectures on Statistics and Data Analysis in MATLAB

#### Disclaimer of liability

The information provided by the Earth Inversion is made available for educational purposes only.

Whilst we endeavor to keep the information up-to-date and correct. Earth Inversion makes no representations or warranties of any kind, express or implied about the completeness, accuracy, reliability, suitability or availability with respect to the website or the information, products, services or related graphics content on the website for any purpose.

UNDER NO CIRCUMSTANCE SHALL WE HAVE ANY LIABILITY TO YOU FOR ANY LOSS OR DAMAGE OF ANY KIND INCURRED AS A RESULT OF THE USE OF THE SITE OR RELIANCE ON ANY INFORMATION PROVIDED ON THE SITE. ANY RELIANCE YOU PLACED ON SUCH MATERIAL IS THEREFORE STRICTLY AT YOUR OWN RISK.

## Leave a comment