Performs a permutation or randomization test to assess if a sample comes from
a population with a value given for the mean or some other location parameter
-- Function File: PVAL = randtest1 (A, M)
-- Function File: PVAL = randtest1 (A, M, NREPS)
-- Function File: PVAL = randtest1 (A, M, NREPS)
-- Function File: PVAL = randtest1 (A, M, NREPS, FUNC)
-- Function File: PVAL = randtest1 (A, M, NREPS, FUNC, SEED)
-- Function File: PVAL = randtest1 ([A, GA], ...)
-- Function File: [PVAL, STAT] = randtest1 (...)
-- Function File: [PVAL, STAT, FPR] = randtest1 (...)
-- Function File: [PVAL, STAT, FPR, PERMSTAT] = randtest1 (...)
'PVAL = randtest1 (A, M)' performs a randomization (or permutation) test
to ascertain whether data sample in the column vector A comes from a
population with mean equal to the value M. The value returned is a 2-
tailed p-value against the null hypothesis computed using the absolute
values of the mean. This function generates resamples by independently
and randomly flipping the signs of values in (A - M).
'PVAL = randtest1 (A, M, NREPS)' specifies the number of resamples to
take in the randomization test. By default, NREPS is 5000. If the number
of possible permutations is smaller than NREPS, the test becomes exact.
For example, if the number of sampling units (i.e. rows) in the sample
is 12, then the number of possible permutations is 2^12 = 4096, so NREPS
will be truncated at 4096 and sampling will systematically evaluate all
possible permutations.
'PVAL = randtest1 (A, M, NREPS, FUNC)' specifies a custom function
calculated on the original samples, and the permuted or randomized
resamples. Note that FUNC must compute a location parameter and
should either be a:
o function handle or anonymous function,
o string of function name, or
o a cell array where the first cell is one of the above function
definitions and the remaining cells are (additional) input arguments
to that function (other than the data arguments).
See the built-in demos for example usage using the mean.
'PVAL = randtest1 (A, M, NREPS, FUNC, SEED)' initialises the Mersenne
Twister random number generator using an integer SEED value so that
the results of 'randtest1' are reproducible when the test is approximate
(i.e. when using randomization if not all permutations can be
evaluated systematically).
'PVAL = randtest1 ([A, GA], M, ...)' also specifies the sampling
units (i.e. clusters) using consecutive positive integers in GA for A.
Defining the sampling units has applications for clustered resampling,
for example in the cases of nested experimental designs. Note that when
sampling units contain different numbers of values, function evaluations
after sampling cannot be vectorized. If the parallel computing toolbox
(Matlab) or parallel package (Octave) is installed and loaded, then the
function evaluations will be automatically accelerated by parallel
processing on platforms with multiple processors.
'[PVAL, STAT] = randtest1 (...)' also returns the test statistic.
'[PVAL, STAT, FPR] = randtest1 (...)' also returns the minimum false
positive risk (FPR) calculated for the p-value, computed using the
Sellke-Berger approach.
'[PVAL, STAT, FPR, PERMSTAT] = randtest1 (...)' also returns the
statistics of the permutation distribution.
randtest1 (version 2024.04.21)
Author: Andrew Charles Penn
https://www.researchgate.net/profile/Andrew_Penn/
Copyright 2019 Andrew Charles Penn
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
GNU General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see http://www.gnu.org/licenses/
The following code
% Mouse data from Table 2 (page 11) of Efron and Tibshirani (1993) treatment = [94 197 16 38 99 141 23]'; % Randomization test to test whether the treatment sample comes from a % population with mean of 56.2. control = 56.2; pval = randtest1 (treatment, control) % The above is equivalent to: % pval = randtest1 (treatment, control, 5000, @mean)
Produces the following output
pval = 0.29688
The following code
A = [21,26,33,22,18,25,26,24,21,25,35,28,32,36,38]'; GA = [1,1,2,2,3,3,4,4,5,5,6,6,7,7,8]'; % Randomization test to test whether the sample A comes from a population % population with mean of 30. Clusters of potentially correlated observations % are defined in GA M = 37; pval = randtest1 ([A GA], M) % The above is equivalent to: % pval = randtest1 ([A GA], M, 5000, @mean)
Produces the following output
pval = 0.015625
Package: statistics-resampling