randtest1

 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/

Demonstration 1

 % 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)

pval = 0.29688

Demonstration 2

 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)

pval = 0.015625

Package: statistics-resampling