how to calculate the studentized range distribution in matlab

To calculate the Studentized Range Distribution in MATLAB, we can use the trnd function to generate random numbers from a t-distribution, and then follow the steps below:

1. Calculate the maximum range of the data set
2. Calculate the standard deviation of the range of the samples
3. Calculate the studentized range statistic using the formula:

main.m
sr = (max_range - mean_range) / std_range
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4. Calculate the critical value of the studentized range using the tinv function and the desired significance level and degrees of freedom
5. Determine whether the calculated studentized range statistic is greater than the critical value.

Here's an example code block that demonstrates this process for a sample dataset with n samples:

main.m
% Set up sample data
n = 10;
mu = 5;
sigma = 2;
data = mu + sigma * randn(n,1);

% Calculate maximum range
ranges = zeros(n-1,n);
for i = 2:n
    combs = nchoosek(1:n,i);
    for j = 1:size(combs,1)
        ranges(i-1,j) = max(data(combs(j,:))) - min(data(combs(j,:)));
    end
end
max_range = max(max(ranges));

% Calculate standard deviation of range
std_range = std(ranges(:));

% Calculate studentized range statistic
mean_range = mean(ranges(:));
sr = (max_range - mean_range) / std_range

% Set up hypothesis
alpha = 0.05;
df = n*(n-1)/2;
t_crit = tinv(1-alpha/2,df)

% Test hypothesis
if abs(sr) > t_crit
    disp('Reject null hypothesis')
else
    disp('Accept null hypothesis')
end
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This code generates a random dataset and then calculates the maximum range and standard deviation of the ranges for all possible combinations of samples. It then calculates the studentized range statistic and uses the tinv function to obtain the critical value for the given significance level and degrees of freedom. Finally, it tests the hypothesis and returns whether to accept or reject the null hypothesis.