# Solving hotelling function code

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Tino on 21 Oct 2020
Hello
I am trying to use the following code to implement the function T2Hot2ihe
[filename, pathname] = uigetfile('*.csv');
Bix = table2array(ogi);
[e] = T2Hot2ihe(Bix, 0.05);
The data in excel is
x y z
0.1 0.3 0.4
0.2 0.3 0.3
0.2 0.3 0.5
0.2 0.3 0.5
0.2 0.3 0.5
0.2 0.3 0.5
0.2 0.3 0.5
0.2 0.3 0.5
0.2 0.6 0.6
0.4 0.7 0.9
I am getting the error
Index exceeds the number of array elements (0).
Error in T2Hot2ihe (line 116)
r1=n(1);
Error in happier (line 6)
[e] = T2Hot2ihe(Bix, 0.05);
I will be grateful if anyone help me to overcome this error so that I can run the code.
The function is shown below:
..........................................................................................................................................................................
function [T2Hot2ihe] = T2Hot2ihe(X,alpha)
%Hotelling's T-Squared test for two multivariate independent samples
%with unequal covariance matrices.
%
% Syntax: function [T2Hot2ihe] = T2Hot2ihe(X,alpha)
%
% Inputs:
% X - multivariate data matrix.
% alpha - significance level (default = 0.05).
%
% Output:
% n1 - sample-size one.
% n2 - sample-size two.
% p - variables.
% T2 - Hotelling's T-Squared statistic.
% Chi-sqr. or F - the approximation statistic test.
% df's - degrees' of freedom of the approximation statistic test.
% P - Probability that null Ho: is true.
%
% For this test it is highly recommended both sample-sizes must be greater than 50.
% The Hotelling's T-Squared takes a Chi-square approximation.
%
% Example: For a two groups (g = 2) with three independent variables (p = 3) and
% considering unequal covariance matrices (tested by the MBoxtest function),
% we are interested to test any difference between its mean vectors with
% a significance level = 0.05.
% The two groups have the same sample-size, n1 = n2 = 5.
% Group
% ---------------------------------------
% 1 2
% ---------------------------------------
% x1 x2 x3 x1 x2 x3
% ---------------------------------------
% 23 45 15 277 230 63
% 40 85 18 153 80 29
% 215 307 60 306 440 105
% 110 110 50 252 350 175
% 65 105 24 143 205 42
% ---------------------------------------
%
% Total data matrix must be:
% X=[1 23 45 15;1 40 85 18;1 215 307 60;1 110 110 50;1 65 105 24;
% 2 277 230 63;2 153 80 29;2 306 440 105;2 252 350 175;2 143 205 42];
%
% Calling on Matlab the function:
% T2Hot2ihe(X)
% -Do you have an expected mean vector? (y/n):
% That for this example we must to put:
% n (meaning 'no')
% Otherwise (y; meaning 'yes') you must to give the expected mean vector.
% If both sample-sizes are less or equal to 50, the program gives the next:
% WARNING: For this test it is highly recommended both sample-sizes
% must be greater than 50.
%
% WARNING: For this test it is highly recommended both sample-sizes must be greater than 50.
%
% -----------------------------------------------------------------------------
% n1 n2 Variables T2 Chi-sqr. df P
% -----------------------------------------------------------------------------
% 5 5 3 11.1037 11.1037 3 0.0112
% -----------------------------------------------------------------------------
% Mean vectors result significant.
%
%
% Created by A. Trujillo-Ortiz and R. Hernandez-Walls
% Universidad Autonoma de Baja California
% Apdo. Postal 453
% Mexico.
% atrujo@uabc.mx
% And the special collaboration of the post-graduate students of the 2002:2
% Multivariate Statistics Course: Karel Castro-Morales, Alejandro Espinoza-Tenorio,
% Andrea Guia-Ramirez.
%
%
% References:
%
% Johnson, R. A. and Wichern, D. W. (1992), Applied Multivariate Statistical Analysis.
% 3rd. ed. New-Jersey:Prentice Hall. pp. 238-241.
%
if nargin < 1,
error('Requires at least one input arguments.');
end;
if nargin < 2,
alpha = 0.05; %(default)
end;
if (alpha <= 0 | alpha >= 1)
fprintf('Warning: significance level must be between 0 and 1\n');
return;
end;
g = max(X(:,1)); %Number of groups.
n = []; %Vector of groups-size.
indice = X(:,1);
for i = 1:g
Xe = find(indice==i);
eval(['X' num2str(i) '= X(Xe,2:end);']);
eval(['n' num2str(i) '= length(X' num2str(i) ') ;'])
eval(['xn= n' num2str(i) ';'])
n = [n,xn];
end;
[f,c] = size(X);
X = X(:,2:c);
[N,p]=size(X);
r=1;
r1=n(1);
bandera=2;
for k=1:g
if n(k)>=20;
bandera=1;
end;
end;
if (n(1) <= p)|(n(2) <= p),
error('Requires that one of the sample-sizes must be greater than the number of variables (p).');
end;
ask=input('Do you have an expected means vector? (y/n): ','s');
mu=input('Give me the expected means vector: ');
else
mu=zeros([1,p]);
end;
r=1;
r1=n(1);
for k=1:g
eval(['S' num2str(k) '=cov(X(r:r1,:));';]); %Partition of the sample covariance matrices.
eval(['M' num2str(k) '= mean(X(r:r1,:));']); %Partition of the sample mean vectors.
if k < g
r=r+n(k);
r1=r1+n(k+1);
end;
end;
dM=(M1-M2)-mu;
T2=dM*inv((S1/n(1))+(S2/n(2)))*dM'; %Hotelling's T-Squared statistic.
if (n(1) < 50) | (n(2) < 50);
disp(' ')
disp('WARNING: For this test it is highly recommended both sample-sizes must be greater than 50.');
end
X2=T2;
v=p;
P=1-chi2cdf(X2,v); %probability that null Ho: is true.
disp(' ')
fprintf('--------------------------------------------------------------------------------\n');
disp(' n1 n2 Variables T2 Chi-sqr. df P')
fprintf('--------------------------------------------------------------------------------\n');
fprintf('%5.i%8.i%12.i%14.4f%15.4f%12.i%13.4f\n',n(1),n(2),p,T2,X2,v,P);
fprintf('--------------------------------------------------------------------------------\n');
if P >= alpha
disp('Mean vectors result not significant.');
else
disp('Mean vectors result significant.');
end
return;
..................................................................................................................................................................................................

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