function STATS=testt(varargin)
%Student's t test for unpaired or paired samples.
% This file is applicable for equal or unequal sample sizes; for paired or
% unpaired samples. When the test is unpaired, the Fisher-Snedecor F-test is
% performed to assess the equality of variance. If variances are not equal,
% Satterthwaite's approximate t test is performed.
% Testt requires powerStudent by Trujillo-Ortiz, A. and R. Hernandez-Walls.
% URL http://www.mathworks.com/matlabcentral/fileexchange/2907
%
% Syntax: TESTT(X1,X2,TST,ALPHA,TAIL)
%
% Inputs:
% X1 and X2 - data vectors (default = example data).
% TST - unpaired (0) or paired (1) test (default = 0).
% ALPHA - significance level (default = 0.05).
% TAIL - 1-tailed test (1) or 2-tailed test (2). (default = 2).
% Outputs:
% - t value.
% - degrees of freedom.
% - Confidence interval of means difference (for paired test)
% - Critical value
% - p-value
%
% Example:
%
% X1=[77 79 79 80 80 81 81 81 81 82 82 82 82 83 83 84 84 84 84 85 ...
% 85 86 86 87 87];
%
% X2=[82 82 83 84 84 85 85 86 86 86 86 86 86 86 86 86 87 87 87 88 ...
% 88 88 89 90 90];
%
% Calling on Matlab the function: testt
%
% Answer is:
%
% FISHER-SNEDECOR F-TEST FOR EQUALITY OF VARIANCES
%
% ------------------------------------------------------------
% F DFn DFd p-value
% ------------------------------------------------------------
% 1.53788 24 24 0.29861
% ------------------------------------------------------------
% Variances are equal
% ------------------------------------------------------------
%
% STUDENT'S T-TEST FOR UNPAIRED SAMPLES
%
% ------------------------------------------------------------
% t DF tail p-value
% ------------------------------------------------------------
% 5.24110 48.0000 2 0.00000
% ------------------------------------------------------------
% It is a two-tailed hypothesis test.
% (The null hypothesis was statistically significative.)
%
% Power is: 0.9989
%
% STATS=TESTT(...) returns a structure with all test(s) statistics
%
% Created by Giuseppe Cardillo
% giuseppe.cardillo-edta@poste.it
%
% To cite this file, this would be an appropriate format:
% Cardillo G. (2006). Student t-Test for unpaired or paired samples.
% http://www.mathworks.com/matlabcentral/fileexchange/12699
global n v alpha
%Input Error handling
args=cell(varargin);
nu=numel(args);
if isempty(nu) || nu==1
error('Warning: Two data vectors are required')
elseif nu>5
error('Warning: Max three input data are required')
end
default.values = {[77 79 79 80 80 81 81 81 81 82 82 82 82 83 83 84 84 84 84 85 ...
85 86 86 87 87],[82 82 83 84 84 85 85 86 86 86 86 86 86 86 86 86 87 87 87 ...
88 88 88 89 90 90],0,0.05,2};
default.values(1:nu) = args;
[x1 x2 tst alpha tail] = deal(default.values{:});
if ~isvector(x1) || ~isvector(x2)
error('TESTT requires vector rather than matrix data.');
end
if ~all(isfinite(x1)) || ~all(isnumeric(x1)) || ~all(isfinite(x2)) || ~all(isnumeric(x2))
error('Warning: all X1 and X2 values must be numeric and finite')
end
if nu>2
if ~isscalar(tst) || ~isfinite(tst) || ~isnumeric(tst) || isempty(tst)
error('Warning: it is required a scalar, numeric and finite TST value.')
end
if tst ~= 0 && tst ~= 1 %check if tst is 0 or 1
error('Warning: TST must be 0 for unpaired test or 1 for paired test.')
end
if tst==1
if ((numel(x1) ~= numel(x2))),
error('Warning: for paired test TESTT requires the data vectors to have the same number of elements.');
end
end
end
if nu>3
if ~isscalar(alpha) || ~isnumeric(alpha) || ~isfinite(alpha) || isempty(alpha)
error('Warning: it is required a numeric, finite and scalar ALPHA value.');
end
if alpha <= 0 || alpha >= 1 %check if alpha is between 0 and 1
error('Warning: ALPHA must be comprised between 0 and 1.')
end
end
if nu>4
if ~isscalar(tail) || ~isfinite(tail) || ~isnumeric(tail) || isempty(tail)
error('Warning: it is required a scalar, numeric and finite TAIL value.')
end
if tail ~= 2 && tail ~= 1 %check if tail is 1 or 2
error('Warning: TAIL must be 1 or 2.')
end
end
clear args default nu
tr=repmat('-',1,60);
switch tst
case 0 %unpaired test
n=[length(x1) length(x2)]; %samples sizes
m=[mean(x1) mean(x2)]; %samples means
v=[var(x1) var(x2)]; %samples variances
%Fisher-Snedecor F-test
if v(2)>v(1)
v=fliplr(v);
m=fliplr(m);
n=fliplr(n);
end
F=v(1)/v(2); %variances ratio
DF=n-1;
p = fcdf(F,DF(1),DF(2)); %p-value
p = 2*min(p,1-p);
if nargout
STATS.Fvalue=F;
STATS.DFn=DF(1);
STATS.DFd=DF(2);
STATS.FPvalue=p;
end
%display results
disp('FISHER-SNEDECOR F-TEST FOR EQUALITY OF VARIANCES')
disp(' ')
disp(tr)
fprintf('F\t\t\t\tDFn\t\t\tDFd\t\t\tp-value\n')
disp(tr)
fprintf('%0.5f\t\t\t%d\t\t\t%d\t\t\t%0.5f\n',F,DF,p)
disp(tr)
if p<alpha %unequal variances (Behrens-Welch problem)
fprintf('Variances are different: Behrens-Welch problem\n')
disp(tr)
disp(' ')
%Satterthwaite's approximate t test
a=v./n; b=sum(a);
denom=sqrt(b);
gl=b^2/sum(a.^2./(n-1));
disp('SATTERTHWAITE''S APPROXIMATE T-TEST FOR UNPAIRED SAMPLES')
disp(' ')
disp(tr)
else %equal variances
fprintf('Variances are equal\n')
disp(tr)
disp(' ')
gl=sum(n)-2; %degrees of freedom
s=sum((n-1).*v)/(sum(n)-2); %combined variance
denom=sqrt(sum(s./n));
disp('STUDENT''S T-TEST FOR UNPAIRED SAMPLES')
disp(' ')
disp(tr)
end
dm=diff(m); %Difference of means
clear H n m v a b s %clear unnecessary variables
case 1 %paired test
disp('STUDENT''S T-TEST FOR PAIRED SAMPLES')
disp(' ')
disp(tr)
n=length(x1); %samples size
gl=n-1; %degrees of freedom
d=x1-x2; %samples difference
dm=mean(d); %mean of difference
vc=tinv(1-alpha/tail,gl); %critical value
ic=[abs(dm)-vc abs(dm)+vc]; %Confidence interval
denom=sqrt((sum((d-dm).^2))/(n*(n-1))); %standard error of difference
clear n d %clear unnecessary variables
fprintf('Mean of difference\t\t\t\t')
str=[num2str((1-alpha)*100) '%% C.I.\n'];
fprintf(str)
disp(tr)
fprintf('%0.4f\t\t\t\t\t%0.4f\t\t\t%0.4f\n',abs(dm),ic)
disp(tr)
end
t=abs(dm)/denom; %t value
p=(1-tcdf(t,gl))*tail; %t-value associated p-value
%display results
fprintf('t\t\t\t\tDF\t\t\t tail\t\t\tp-value\n')
disp(tr)
fprintf('%0.5f\t\t\t%0.4f\t\t\t%d\t\t\t%0.5f\n',t,gl,tail,p)
disp(tr)
if nargout
STATS.tvalue=t;
STATS.tdf=gl;
STATS.ttail=tail;
STATS.tpvalue=p;
end
try
powerStudent(t,gl,tail,alpha)
catch ME
disp(ME)
disp('I am trying to download the powerStudent function by Antonio Trujillo Ortiz from FEX')
[F,Status]=urlwrite('http://www.mathworks.com/matlabcentral/fileexchange/2907-powerstudent?controller=file_infos&download=true','powerStudent.zip')
if Status
unzip(F)
powerStudent(t,gl,tail,alpha)
end
clear F Status
end
