From c22960f4841e1862471ac0d6ec22e2cf3bfa003d Mon Sep 17 00:00:00 2001 From: acp29 Date: Mon, 8 Jan 2024 23:24:38 +0000 Subject: [PATCH] updated package manual and toolbox installer --- docs/description.json | 2 +- docs/function/boot.html | 3 +- docs/function/boot1way.html | 39 +- docs/function/bootbayes.html | 22 +- docs/function/bootci.html | 375 ++++++++-------- docs/function/bootclust.html | 76 ++-- docs/function/bootknife.html | 619 +++++++++++++------------- docs/function/bootlm.html | 382 ++++++++-------- docs/function/bootmode.html | 14 +- docs/function/bootstrp.html | 6 +- docs/function/bootwild.html | 20 +- docs/function/images/boot1way_601.png | Bin 24409 -> 24266 bytes docs/function/images/boot1way_701.png | Bin 24882 -> 24156 bytes docs/function/randtest2.html | 8 +- docs/function/sampszcalc.html | 24 +- docs/index.html | 2 +- docs/readme.html | 6 + matlab/statistics-resampling.mltbx | Bin 302689 -> 302678 bytes matlab/statistics-resampling.prj | 10 +- 19 files changed, 815 insertions(+), 793 deletions(-) diff --git a/docs/description.json b/docs/description.json index 7af99553..085f84ca 100644 --- a/docs/description.json +++ b/docs/description.json @@ -8,7 +8,7 @@ "version": "5.5.4", "description": "The statistics-resampling package is an Octave package and Matlab toolbox that can be used to overcome a wide variety of statistics problems using non-parametric resampling methods. In particular, the functions included can be used to estimate bias, uncertainty (standard errors and confidence intervals), prediction error, and test hypotheses (p-values). Variations of the resampling methods are included that improve the accuracy of the statistics for small samples and samples with complex dependence structures.", "shortdescription": "The statistics-resampling package is an Octave package and Matlab toolbox that can be used to overcome a wide variety of statistics problems using non-parametric resampling methods", - "date": "2024-01-04", + "date": "2024-01-08", "title": "A statistics package with a variety of resampling tools", "author": "Andrew Penn ", "maintainer": "Andrew Penn ", diff --git a/docs/function/boot.html b/docs/function/boot.html index 0c6c37c1..18488900 100644 --- a/docs/function/boot.html +++ b/docs/function/boot.html @@ -205,6 +205,7 @@

Demonstration 4

The following code

+
  % Vector (X) as input; balanced resampling with replacement; setting weights
  x = [23; 44; 36];
  boot(x, 10, false, 1)            % equal weighting
@@ -226,7 +227,7 @@ 
Demonstration 5

 

 
The following code

 
- 
+
  % N as input; resampling without replacement; 3 trials
  boot(6, 1, false, 1) % Sample 1; Set random seed for first sample only
  boot(6, 1, false)    % Sample 2
diff --git a/docs/function/boot1way.html b/docs/function/boot1way.html
index 77facf77..f949bf3e 100644
--- a/docs/function/boot1way.html
+++ b/docs/function/boot1way.html
@@ -166,8 +166,7 @@ 
Demonstration 1

 
The following code

 
 
- ## EXAMPLE 1A: 
- ## ONE-WAY ANOVA WITH EQUAL SAMPLE SIZES: Treatment vs. Control (1)
+ % ONE-WAY ANOVA WITH EQUAL SAMPLE SIZES: Treatment vs. Control (1)
 
  y = [111.39 110.21  89.21  76.64  95.35  90.97  62.78;
       112.93  60.36  92.29  59.54  98.93  97.03  79.65;
@@ -180,7 +179,7 @@ 
Demonstration 1

 
  boot1way (y(:),g(:),'ref',1,'nboot',4999);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of bootstrap multiple comparison tests in a one-way layout
 *****************************************************************************
@@ -226,8 +225,7 @@ 
Demonstration 2

 
The following code

 
 
- ## EXAMPLE 1B: 
- ## ROBUST ONE-WAY ANOVA WITH EQUAL SAMPLE SIZES: Treatment vs. Control (1)
+ % ROBUST ONE-WAY ANOVA WITH EQUAL SAMPLE SIZES: Treatment vs. Control (1)
 
  y = [111.39 110.21  89.21  76.64  95.35  90.97  62.78;
       112.93  60.36  92.29  59.54  98.93  97.03  79.65;
@@ -240,7 +238,7 @@ 
Demonstration 2

 
  boot1way (y(:), g(:), 'ref', 1, 'nboot', 4999, 'bootfun', 'robust');
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of bootstrap multiple comparison tests in a one-way layout
 *****************************************************************************
@@ -286,9 +284,8 @@ 
Demonstration 3

 
The following code

 
 
- ## EXAMPLE 2A:
- ## COMPARISON OF TWO INDEPENDENT GROUPS WITH UNEQUAL SAMPLE SIZES 
- ## (analagous to Student's t-test)
+ % COMPARISON OF TWO INDEPENDENT GROUPS WITH UNEQUAL SAMPLE SIZES 
+ % (analagous to Student's t-test)
 
  y =    [54       43
          23       34
@@ -305,7 +302,7 @@ 
Demonstration 3

 
  boot1way (y(:), g(:), 'ref', 'male', 'nboot', 4999);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of bootstrap multiple comparison tests in a one-way layout
 *****************************************************************************
@@ -341,8 +338,7 @@ 
Demonstration 4

 
The following code

 
 
- ## EXAMPLE 2B:
- ## ONE-WAY ANOVA WITH UNEQUAL SAMPLE SIZES: pairwise comparisons
+ % ONE-WAY ANOVA WITH UNEQUAL SAMPLE SIZES: pairwise comparisons
 
  y = [54  87  45
       23  98  39
@@ -359,7 +355,7 @@ 
Demonstration 4

 
  boot1way (y(:), g(:), 'nboot', 4999);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of bootstrap multiple comparison tests in a one-way layout
 *****************************************************************************
@@ -397,8 +393,7 @@ 
Demonstration 5

 
The following code

 
 
- ## EXAMPLE 2C:
- ## COMPARE STANDARD DEVIATIONS BETWEEN 3 GROUPS: pairwise comparisons
+ % COMPARE STANDARD DEVIATIONS BETWEEN 3 GROUPS: pairwise comparisons
 
  y = [54  87  45
       23  98  39
@@ -451,14 +446,13 @@ 
Demonstration 6

 
The following code

 
 
- ## EXAMPLE 3:
- ## COMPARE CORRELATION COEFFICIENTS BETWEEN 2 DATA SETS
+ % COMPARE CORRELATION COEFFICIENTS BETWEEN 2 DATA SETS
  Y = randn (20, 2); g = [zeros(10, 1); ones(10, 1)];
  func = @(M) cor (M(:,1), M(:,2));
 
  boot1way (Y, g, 'bootfun', func);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of bootstrap multiple comparison tests in a one-way layout
 *****************************************************************************
@@ -473,7 +467,7 @@ 
Demonstration 6

 -----------------------------------------------------------------------------
 | Comparison |     Test # |      Ref # | Difference |          t |        p |
 |------------|------------|------------|------------|------------|----------|
-|          1 |          2 |          1 |    +0.3923 |      +0.77 |     .456 |
+|          1 |          2 |          1 |    +0.5212 |      +1.41 |     .135 |
 
 -----------------------------------------------------------------------------
 |    GROUP # |                                       GROUP label |        N |
@@ -494,8 +488,7 @@ 
Demonstration 7

 
The following code

 
 
- ## EXAMPLE 4:
- ## COMPARE SLOPES FROM LINEAR REGRESSION ON 2 DATA SETS
+ % COMPARE SLOPES FROM LINEAR REGRESSION ON 2 DATA SETS
  y = randn (20, 1); x = randn (20, 1); X = [ones(20, 1), x];
  g = [zeros(10, 1); ones(10, 1)];
  func = @(M) subsref (M(:,2:end) \ M(:,1), ...
@@ -503,7 +496,7 @@ 
Demonstration 7

 
  boot1way ([y, X], g, 'bootfun', func);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of bootstrap multiple comparison tests in a one-way layout
 *****************************************************************************
@@ -518,7 +511,7 @@ 
Demonstration 7

 -----------------------------------------------------------------------------
 | Comparison |     Test # |      Ref # | Difference |          t |        p |
 |------------|------------|------------|------------|------------|----------|
-|          1 |          2 |          1 |    +0.8151 |      +0.83 |     .376 |
+|          1 |          2 |          1 |    -0.1399 |      -0.26 |     .640 |
 
 -----------------------------------------------------------------------------
 |    GROUP # |                                       GROUP label |        N |
diff --git a/docs/function/bootbayes.html b/docs/function/bootbayes.html
index 3ead5349..dc7e2920 100644
--- a/docs/function/bootbayes.html
+++ b/docs/function/bootbayes.html
@@ -165,13 +165,13 @@ 
Demonstration 1

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  heights = [183, 192, 182, 183, 177, 185, 188, 188, 182, 185].';
 
- ## 95% credible interval for the mean 
- bootbayes(heights);
+ % 95% credible interval for the mean 
+ bootbayes (heights);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of Bayesian bootstrap estimates of bias and precision for linear models
 *******************************************************************************
@@ -186,14 +186,14 @@ 
Demonstration 1

 
 Posterior Statistics: 
  original     bias         median       stdev       CI_lower      CI_upper
- +184.5       +0.005727    +184.5       1.273       +182.2        +187.2

+ +184.5       +0.03166     +184.5       1.296       +182.0        +187.0

 

 
Demonstration 2

 

 
The following code

 
 
- ## Input bivariate dataset
+ % Input bivariate dataset
  X = [ones(43,1),...
      [01,02,03,04,05,06,07,08,09,10,11,...
       12,13,14,15,16,17,18,19,20,21,22,...
@@ -204,10 +204,10 @@ 
Demonstration 2

      168.0,170.0,178.0,182.0,180.0,183.0,178.0,182.0,188.0,175.0,179.0,...
      183.0,192.0,182.0,183.0,177.0,185.0,188.0,188.0,182.0,185.0]';
 
- ## 95% credible interval for the regression coefficents
- bootbayes(y,X);
+ % 95% credible interval for the regression coefficents
+ bootbayes (y, X);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

Produces the following output

Summary of Bayesian bootstrap estimates of bias and precision for linear models
 *******************************************************************************
@@ -222,8 +222,8 @@ 
Demonstration 2

 
 Posterior Statistics: 
  original     bias         median       stdev       CI_lower      CI_upper
- +175.5       -0.09008     +175.4       2.407       +170.8        +180.3    
- +0.1904      +0.002195    +0.1946      0.07956     +0.02477      +0.3431
+ +175.5 -0.07101 +175.4 2.403 +170.6 +179.7 + +0.1904 +0.001505 +0.1921 0.07932 +0.04185 +0.3468

Package: statistics-resampling

diff --git a/docs/function/bootci.html b/docs/function/bootci.html index 32811620..5348edfa 100644 --- a/docs/function/bootci.html +++ b/docs/function/bootci.html @@ -174,11 +174,11 @@

Demonstration 1

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 95% BCa bootstrap confidence intervals for the mean
+ % 95% BCa bootstrap confidence intervals for the mean
  ci = bootci (1999, @mean, data)

Produces the following output

ci =
@@ -191,14 +191,14 @@ 
Demonstration 2

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 95% calibrated percentile bootstrap confidence intervals for the mean
+ % 95% calibrated percentile bootstrap confidence intervals for the mean
  ci = bootci (1999, {@mean, data}, 'type', 'cal','nbootcal',199)
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

Produces the following output

ci =
 
@@ -210,15 +210,15 @@ 
Demonstration 3

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 95% calibrated percentile bootstrap confidence intervals for the median
- ## with smoothing
+ % 95% calibrated percentile bootstrap confidence intervals for the median
+ % with smoothing
  ci = bootci (1999, {@smoothmedian, data}, 'type', 'cal', 'nbootcal', 199)
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

Produces the following output

ci =
 
@@ -230,11 +230,11 @@ 
Demonstration 4

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% percentile bootstrap confidence intervals for the variance
+ % 90% percentile bootstrap confidence intervals for the variance
  ci = bootci (1999, {{@var,1}, data}, 'type', 'per', 'alpha', 0.1)

 
Produces the following output

 
ci =
@@ -247,11 +247,11 @@ 
Demonstration 5

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% BCa bootstrap confidence intervals for the variance
+ % 90% BCa bootstrap confidence intervals for the variance
  ci = bootci (1999, {{@var,1}, data}, 'type', 'bca', 'alpha', 0.1)

 
Produces the following output

 
ci =
@@ -264,15 +264,15 @@ 
Demonstration 6

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41]';
 
- ## 90% Studentized bootstrap confidence intervals for the variance
+ % 90% Studentized bootstrap confidence intervals for the variance
  ci = bootci (1999, {{@var,1}, data}, 'type', 'stud', ...
                                               'nbootstd', 50, 'alpha', 0.1)
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
ci =
 
@@ -284,15 +284,15 @@ 
Demonstration 7

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% calibrated percentile bootstrap confidence intervals for the variance
+ % 90% calibrated percentile bootstrap confidence intervals for the variance
  ci = bootci (1999, {{@var,1}, data}, 'type', 'cal', 'nbootcal', ...
               199, 'alpha', 0.1)
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
ci =
 
@@ -304,16 +304,16 @@ 
Demonstration 8

 
The following code

 
 
- ## Input bivariate dataset
+ % Input bivariate dataset
  x = [2.12,4.35,3.39,2.51,4.04,5.1,3.77,3.35,4.1,3.35, ...
       4.15,3.56, 3.39,1.88,2.56,2.96,2.49,3.03,2.66,3].';
  y  = [2.47,4.61,5.26,3.02,6.36,5.93,3.93,4.09,4.88,3.81, ...
        4.74,3.29,5.55,2.82,4.23,3.23,2.56,4.31,4.37,2.4].';
 
- ## 95% BCa bootstrap confidence intervals for the correlation coefficient
+ % 95% BCa bootstrap confidence intervals for the correlation coefficient
  ci = bootci (1999, @cor, x, y)
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
ci =
 
@@ -325,24 +325,29 @@ 
Demonstration 9

 
The following code

 
  
- ## Calculating confidence intervals for the coefficients from logistic 
- ## regression using an example with an ordinal response from:
- ## https://uk.mathworks.com/help/stats/mnrfit.html
+ % Calculating confidence intervals for the coefficients from logistic 
+ % regression using an example with an ordinal response from:
+ % https://uk.mathworks.com/help/stats/mnrfit.html
  
- ##>>>>>>>>> This code block must be run first in Octave only >>>>>>>>>>>>
+ %>>>>>>>>> This code block must be run first in Octave only >>>>>>>>>>>>
+
  try
    pkg load statistics
    load carbig
+   info = ver;
+   if ( str2num ({info.Version}{strcmp({info.Name},'statistics')}(1:3)) < 1.5)
+     error ('statistics package version must be > 1.5')
+   end
    if (~ exist ('mnrfit', 'file'))
-     ## Octave Statistics package does not currently have the mnrfit function,
-     ## so we will use it's logistic_regression function for fitting ordinal
-     ## models instead. 
+     % Octave Statistics package does not currently have the mnrfit function,
+     % so we will use it's logistic_regression function for fitting ordinal
+     % models instead. 
      function [B, DEV] = mnrfit (X, Y, varargin)
-       ## Note that the if the outcome has more than two levels, the
-       ## logistic_regression function is only suitable when the outcome 
-       ## is ordinal, so we would need to use append 'model', 'ordinal'
-       ## as a name-value pair in MATLAB when executing it's mnrfit
-       ## function (see below)
+       % Note that the if the outcome has more than two levels, the
+       % logistic_regression function is only suitable when the outcome 
+       % is ordinal, so we would need to use append 'model', 'ordinal'
+       % as a name-value pair in MATLAB when executing it's mnrfit
+       % function (see below)
        [INTERCEPT, SLOPE, DEV] = logistic_regression (Y - 1, X, false);
        B = cat (1, INTERCEPT, SLOPE);
      end
@@ -353,24 +358,25 @@ 
Demonstration 9

    fprintf ('\nSkipping this demo...')
    fprintf ('\nRequired features of the statistics package not found.\n\n');
  end
- ##<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
+
+ %<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
 
  if (stats_pkg)
 
-   ##>>>>>>>>>>>>>>>>>>> This code block is the demo >>>>>>>>>>>>>>>>>>>>>>
+   %>>>>>>>>>>>>>>>>>>> This code block is the demo >>>>>>>>>>>>>>>>>>>>>>
 
-   ## This demo requires the statistics package in Octave (equivalent to
-   ## the Statistics and Machine Learning Toolbox in Matlab)
+   % This demo requires the statistics package in Octave (equivalent to
+   % the Statistics and Machine Learning Toolbox in Matlab)
 
-   ## Create the dataset
+   % Create the dataset
    load carbig
    X = [Acceleration Displacement Horsepower Weight];
 
-   ## The responses 1 - 4 correspond to the following classification:
-   ## 1:  9 - 19 miles per gallon
-   ## 2: 19 - 29 miles per gallon
-   ## 3: 29 - 39 miles per gallon
-   ## 4: 39 - 49 miles per gallon
+   % The responses 1 - 4 correspond to the following classification:
+   % 1:  9 - 19 miles per gallon
+   % 2: 19 - 29 miles per gallon
+   % 3: 29 - 39 miles per gallon
+   % 4: 39 - 49 miles per gallon
    miles = [1,1,1,1,1,1,1,1,1,1,NaN,NaN,NaN,NaN,NaN,1,1,NaN,1,1,2,2,1,2, ...
             2,2,2,2,2,2,2,1,1,1,1,2,2,2,2,NaN,2,1,1,2,1,1,1,1,1,1,1,1,1, ...
             2,2,1,2,2,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1, ...
@@ -386,30 +392,31 @@ 
Demonstration 9

             3,3,3,3,3,3,3,3,3,3,3,3,3,2,NaN,3,2,2,2,2,2,1,2,2,3,3,3,2,2, ...
             2,3,3,3,3,3,3,3,3,3,3,3,2,3,2,2,3,3,2,2,4,3,2,3]';
 
-   ## Model coefficients from logistic regression
+   % Model coefficients from logistic regression
    B = mnrfit (X, miles, 'model', 'ordinal');
 
-   ## Bootsrap confidence intervals for each logistic regression coefficient
+   % Bootsrap confidence intervals for each logistic regression coefficient
    ci = bootci (1999, @(X, miles) mnrfit (X, miles, 'model', 'ordinal'), ...
                 X, miles);
    [B, ci']
 
-   ## Where the first 3 rows are the intercept terms, and the last 4 rows
-   ## are the slope coefficients. For each predictor, the slope coefficient
-   ## corresponds to how a unit change in the predictor impacts on the odds,
-   ## which are proportional across the (ordered) catagories, where each
-   ## log-odds in each case is:
-   ##
-   ##       ln ( ( P[below] ) / ( P[above] ) )
-   ##
-   ## Therefore, a positive slope value indicates that a unit increase in the
-   ## predictor increases the odds of running at fewer miles per gallon.
-
-   ## Note that ordinal and multinomial logistic regression (appropriate
-   ## for ordinal and nominal responses respectively) would be equivalent
-   ## for any binary outcome
-
-   ##<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
+   % Where the first 3 rows are the intercept terms, and the last 4 rows
+   % are the slope coefficients. For each predictor, the slope coefficient
+   % corresponds to how a unit change in the predictor impacts on the odds,
+   % which are proportional across the (ordered) catagories, where each
+   % log-odds in each case is:
+   %
+   %       ln ( ( P[below] ) / ( P[above] ) )
+   %
+   % i.e. in mnrfit, the reference class is the higher of the two classes.
+   % Therefore, a positive slope value indicates that a unit increase in the
+   % predictor increases the odds of running at fewer miles per gallon.
+
+   % Note that ordinal and multinomial logistic regression (appropriate
+   % for ordinal and nominal responses respectively) would be equivalent
+   % for any binary outcome
+
+   %<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
  
  end

 
Produces the following output

@@ -428,129 +435,129 @@ 
Demonstration 10

 
The following code

 
 
- ## Spatial Test Data from Table 14.1 of Efron and Tibshirani (1993)
- ## An Introduction to the Bootstrap in Monographs on Statistics and Applied 
- ## Probability 57 (Springer)
-
- ## AIM:
- ## To construct 90% nonparametric bootstrap confidence intervals for var(A,1)
- ## var(A,1) = 171.5
- ## Exact intervals based on Normal theory are [118.4, 305.2].
-
- ## Calculations using Matlab's 'Statistics and Machine Learning toolbox'
- ## (R2020b)
- ##
- ## A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
- ##      0 33 28 34 4 32 24 47 41 24 26 30 41].';
- ## varfun = @(A) var(A, 1);
- ## rng('default'); % For reproducibility
- ## rng('default'); ci1 = bootci (19999,{varfun,A},'alpha',0.1,'type','norm');
- ## rng('default'); ci2 = bootci (19999,{varfun,A},'alpha',0.1,'type','per');
- ## rng('default'); ci4 = bootci (19999,{varfun,A},'alpha',0.1,'type','bca');
- ## rng('default'); ci5 = bootci (19999,{varfun,A},'alpha',0.1,'type','stud');
- ##
- ## Summary of results from Matlab's 'Statistics and Machine Learning toolbox'
- ## (R2020b)
- ##
- ## method             |   0.05 |   0.95 | length | shape |  
- ## -------------------|--------|--------|--------|-------|
- ## ci1 - normal       |  108.9 |  247.4 |  138.5 |  1.21 |
- ## ci2 - percentile   |   97.6 |  235.8 |  138.2 |  0.87 |
- ## ci4 - BCa          |  114.9 |  260.5 |  145.6 |  1.57 |*
- ## ci5 - bootstrap-t  |   46.7 |  232.5 |  185.8 |  0.49 |** 
- ## -------------------|--------|--------|--------|-------|
- ## parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
- ##
- ## * Bug in the fx0 subfunction of MathWorks MATLAB bootci function
- ## ** Bug in the bootstud subfunction of MathWorks MATLAB bootci
-
- ## Calculations using the 'boot' and 'bootstrap' packages in R
- ## 
- ## library (boot)       # Functions from Davison and Hinkley (1997)
- ## A <- c(48,36,20,29,42,42,20,42,22,41,45,14,6, ...
- ##         0,33,28,34,4,32,24,47,41,24,26,30,41);
- ## n <- length(A)
- ##  var.fun <- function (d, i) { 
- ##        # Function to compute the population variance
- ##        n <- length (d); 
- ##        return (var (d[i]) * (n - 1) / n) };
- ##  boot.fun <- function (d, i) {
- ##        # Compute the estimate
- ##        t <- var.fun (d, i);
- ##        # Compute sampling variance of the estimate using Tukey's jackknife
- ##        n <- length (d);
- ##        U <- empinf (data=d[i], statistic=var.fun, type="jack", stype="i");
- ##        var.t <- sum (U^2 / (n * (n - 1)));
- ##        return ( c(t, var.t) ) };
- ## set.seed(1)
- ## var.boot <- boot (data=A, statistic=boot.fun, R=19999, sim='balanced')
- ## ci1 <- boot.ci (var.boot, conf=0.90, type="norm")
- ## ci2 <- boot.ci (var.boot, conf=0.90, type="perc")
- ## ci3 <- boot.ci (var.boot, conf=0.90, type="basic")
- ## ci4 <- boot.ci (var.boot, conf=0.90, type="bca")
- ## ci5 <- boot.ci (var.boot, conf=0.90, type="stud")
- ##
- ## library (bootstrap)  # Functions from Efron and Tibshirani (1993)
- ## set.seed(1); 
- ## ci4a <- bcanon (A, 19999, var.fun, alpha=c(0.05,0.95))
- ## set.seed(1); 
- ## ci5a <- boott (A, var.fun, nboott=19999, nbootsd=499, perc=c(.05,.95))
- ##
- ## Summary of results from 'boot' and 'bootstrap' packages in R
- ##
- ## method             |   0.05 |   0.95 | length | shape |  
- ## -------------------|--------|--------|--------|-------|
- ## ci1  - normal      |  109.6 |  246.7 |  137.1 |  1.22 |
- ## ci2  - percentile  |   97.9 |  234.8 |  136.9 |  0.86 |
- ## ci3  - basic       |  108.3 |  245.1 |  136.8 |  1.16 |
- ## ci4  - BCa         |  116.0 |  260.7 |  144.7 |  1.60 |
- ## ci4a - BCa         |  115.8 |  260.6 |  144.8 |  1.60 |
- ## ci5  - bootstrap-t |  112.0 |  291.8 |  179.8 |  2.02 |
- ## ci5a - bootstrap-t |  116.1 |  290.9 |  174.8 |  2.16 |
- ## -------------------|--------|--------|--------|-------|
- ## parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
+ % Spatial Test Data from Table 14.1 of Efron and Tibshirani (1993)
+ % An Introduction to the Bootstrap in Monographs on Statistics and Applied 
+ % Probability 57 (Springer)
+
+ % AIM:
+ % To construct 90% nonparametric bootstrap confidence intervals for var(A,1)
+ % var(A,1) = 171.5
+ % Exact intervals based on Normal theory are [118.4, 305.2].
+
+ % Calculations using Matlab's 'Statistics and Machine Learning toolbox'
+ % (R2020b)
+ %
+ % A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+ %      0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ % varfun = @(A) var(A, 1);
+ % rng('default'); % For reproducibility
+ % rng('default'); ci1 = bootci (19999,{varfun,A},'alpha',0.1,'type','norm');
+ % rng('default'); ci2 = bootci (19999,{varfun,A},'alpha',0.1,'type','per');
+ % rng('default'); ci4 = bootci (19999,{varfun,A},'alpha',0.1,'type','bca');
+ % rng('default'); ci5 = bootci (19999,{varfun,A},'alpha',0.1,'type','stud');
+ %
+ % Summary of results from Matlab's 'Statistics and Machine Learning toolbox'
+ % (R2020b)
+ %
+ % method             |   0.05 |   0.95 | length | shape |  
+ % -------------------|--------|--------|--------|-------|
+ % ci1 - normal       |  108.9 |  247.4 |  138.5 |  1.21 |
+ % ci2 - percentile   |   97.6 |  235.8 |  138.2 |  0.87 |
+ % ci4 - BCa          |  114.9 |  260.5 |  145.6 |  1.57 |*
+ % ci5 - bootstrap-t  |   46.7 |  232.5 |  185.8 |  0.49 |** 
+ % -------------------|--------|--------|--------|-------|
+ % parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
+ %
+ % * Bug in the fx0 subfunction of MathWorks MATLAB bootci function
+ % ** Bug in the bootstud subfunction of MathWorks MATLAB bootci
+
+ % Calculations using the 'boot' and 'bootstrap' packages in R
+ % 
+ % library (boot)       % Functions from Davison and Hinkley (1997)
+ % A <- c(48,36,20,29,42,42,20,42,22,41,45,14,6, ...
+ %         0,33,28,34,4,32,24,47,41,24,26,30,41);
+ % n <- length(A)
+ %  var.fun <- function (d, i) { 
+ %        % Function to compute the population variance
+ %        n <- length (d); 
+ %        return (var (d[i]) * (n - 1) / n) };
+ %  boot.fun <- function (d, i) {
+ %        % Compute the estimate
+ %        t <- var.fun (d, i);
+ %        % Compute sampling variance of the estimate using Tukey's jackknife
+ %        n <- length (d);
+ %        U <- empinf (data=d[i], statistic=var.fun, type="jack", stype="i");
+ %        var.t <- sum (U^2 / (n * (n - 1)));
+ %        return ( c(t, var.t) ) };
+ % set.seed(1)
+ % var.boot <- boot (data=A, statistic=boot.fun, R=19999, sim='balanced')
+ % ci1 <- boot.ci (var.boot, conf=0.90, type="norm")
+ % ci2 <- boot.ci (var.boot, conf=0.90, type="perc")
+ % ci3 <- boot.ci (var.boot, conf=0.90, type="basic")
+ % ci4 <- boot.ci (var.boot, conf=0.90, type="bca")
+ % ci5 <- boot.ci (var.boot, conf=0.90, type="stud")
+ %
+ % library (bootstrap)  % Functions from Efron and Tibshirani (1993)
+ % set.seed(1); 
+ % ci4a <- bcanon (A, 19999, var.fun, alpha=c(0.05,0.95))
+ % set.seed(1); 
+ % ci5a <- boott (A, var.fun, nboott=19999, nbootsd=499, perc=c(.05,.95))
+ %
+ % Summary of results from 'boot' and 'bootstrap' packages in R
+ %
+ % method             |   0.05 |   0.95 | length | shape |  
+ % -------------------|--------|--------|--------|-------|
+ % ci1  - normal      |  109.6 |  246.7 |  137.1 |  1.22 |
+ % ci2  - percentile  |   97.9 |  234.8 |  136.9 |  0.86 |
+ % ci3  - basic       |  108.3 |  245.1 |  136.8 |  1.16 |
+ % ci4  - BCa         |  116.0 |  260.7 |  144.7 |  1.60 |
+ % ci4a - BCa         |  115.8 |  260.6 |  144.8 |  1.60 |
+ % ci5  - bootstrap-t |  112.0 |  291.8 |  179.8 |  2.02 |
+ % ci5a - bootstrap-t |  116.1 |  290.9 |  174.8 |  2.16 |
+ % -------------------|--------|--------|--------|-------|
+ % parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
  
- ## Calculations using the 'statistics-resampling' package for Octave/Matlab
- ##
- ## A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
- ##      0 33 28 34 4 32 24 47 41 24 26 30 41].';
- ## ci1 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','norm','seed',1);
- ## ci2 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','per','seed',1);
- ## ci3 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','basic','seed',1);
- ## ci4 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','bca','seed',1);
- ## ci5 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','stud',...
- ##                                              'nbootstd',100,'seed',1);
- ## ci6 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','cal', ...
- ##                                              'nbootcal',499,'seed',1);
- ##
- ## Summary of results from 'statistics-resampling' package for Octave/Matlab
- ##
- ## method             |   0.05 |   0.95 | length | shape |  
- ## -------------------|--------|--------|--------|-------|
- ## ci1 - normal       |  110.1 |  246.2 |  136.1 |  1.22 |
- ## ci2 - percentile   |   98.1 |  234.7 |  136.6 |  0.86 |
- ## ci3 - basic        |  108.4 |  245.0 |  136.1 |  1.17 |
- ## ci4 - BCa          |  116.1 |  259.3 |  143.2 |  1.59 |
- ## ci5 - bootstrap-t  |  114.0 |  290.3 |  176.3 |  2.07 |
- ## ci6 - calibrated   |  115.3 |  276.4 |  161.1 |  1.87 |
- ## -------------------|--------|--------|--------|-------|
- ## parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
- ##
- ## Simulation results for constructing 90% confidence intervals for the
- ## variance of a population N(0,1) from 1000 random samples of size 26
- ## (analagous to the situation above). Simulation performed using the
- ## bootsim script with nboot of 1999.
- ##
- ## method               | coverage |  lower |  upper | length | shape |
- ## ---------------------|----------|--------|--------|--------|-------|
- ## normal               |    81.5% |   3.0% |  15.5% |   0.77 |  1.21 |
- ## percentile           |    81.5% |   0.9% |  17.6% |   0.76 |  0.91 |
- ## basic                |    81.1% |   2.5% |  16.4% |   0.78 |  1.09 |
- ## BCa                  |    84.2% |   5.4% |  10.4% |   0.86 |  1.82 |
- ## bootstrap-t          |    89.2% |   4.3% |   6.5% |   0.99 |  2.15 |
- ## calibrated           |    87.4% |   4.2% |   8.4% |   0.91 |  2.03 |
- ## ---------------------|----------|--------|--------|--------|-------|
- ## parametric - exact   |    90.8% |   3.7% |   5.5% |   0.99 |  2.52 |

+ % Calculations using the 'statistics-resampling' package for Octave/Matlab
+ %
+ % A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
+ %      0 33 28 34 4 32 24 47 41 24 26 30 41].';
+ % ci1 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','norm','seed',1);
+ % ci2 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','per','seed',1);
+ % ci3 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','basic','seed',1);
+ % ci4 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','bca','seed',1);
+ % ci5 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','stud',...
+ %                                              'nbootstd',100,'seed',1);
+ % ci6 = bootci (19999,{{@var,1},A},'alpha',0.1,'type','cal', ...
+ %                                              'nbootcal',499,'seed',1);
+ %
+ % Summary of results from 'statistics-resampling' package for Octave/Matlab
+ %
+ % method             |   0.05 |   0.95 | length | shape |  
+ % -------------------|--------|--------|--------|-------|
+ % ci1 - normal       |  110.1 |  246.2 |  136.1 |  1.22 |
+ % ci2 - percentile   |   98.1 |  234.7 |  136.6 |  0.86 |
+ % ci3 - basic        |  108.4 |  245.0 |  136.1 |  1.17 |
+ % ci4 - BCa          |  116.1 |  259.3 |  143.2 |  1.59 |
+ % ci5 - bootstrap-t  |  114.0 |  290.3 |  176.3 |  2.07 |
+ % ci6 - calibrated   |  115.3 |  276.4 |  161.1 |  1.87 |
+ % -------------------|--------|--------|--------|-------|
+ % parametric - exact |  118.4 |  305.2 |  186.8 |  2.52 |
+ %
+ % Simulation results for constructing 90% confidence intervals for the
+ % variance of a population N(0,1) from 1000 random samples of size 26
+ % (analagous to the situation above). Simulation performed using the
+ % bootsim script with nboot of 1999.
+ %
+ % method               | coverage |  lower |  upper | length | shape |
+ % ---------------------|----------|--------|--------|--------|-------|
+ % normal               |    81.5% |   3.0% |  15.5% |   0.77 |  1.21 |
+ % percentile           |    81.5% |   0.9% |  17.6% |   0.76 |  0.91 |
+ % basic                |    81.1% |   2.5% |  16.4% |   0.78 |  1.09 |
+ % BCa                  |    84.2% |   5.4% |  10.4% |   0.86 |  1.82 |
+ % bootstrap-t          |    89.2% |   4.3% |   6.5% |   0.99 |  2.15 |
+ % calibrated           |    87.4% |   4.2% |   8.4% |   0.91 |  2.03 |
+ % ---------------------|----------|--------|--------|--------|-------|
+ % parametric - exact   |    90.8% |   3.7% |   5.5% |   0.99 |  2.52 |

 
gives an example of how 'bootci' is used.

 
 
diff --git a/docs/function/bootclust.html b/docs/function/bootclust.html
index 3f15b5fc..456c9b6b 100644
--- a/docs/function/bootclust.html
+++ b/docs/function/bootclust.html
@@ -154,11 +154,11 @@ 
Demonstration 1

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 95% expanded BCa bootstrap confidence intervals for the mean
+ % 95% expanded BCa bootstrap confidence intervals for the mean
  bootclust (data, 1999, @mean);

 
Produces the following output

 
Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -169,25 +169,25 @@ 
Demonstration 1

  Resampling method: Balanced, bootstrap cluster resampling 
  Number of resamples: 1999 
  Confidence interval (CI) type: Expanded bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 95% (1.4%, 97.7%)
+ Nominal coverage (and the percentiles used): 95% (1.1%, 97.3%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +29.65       -3.197e-14   +2.514       +23.91       +34.42

+ +29.65       +3.553e-15   +2.514       +23.66       +34.35

 
 
Demonstration 2

 

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
  clustid = {'a';'a';'b';'b';'a';'c';'c';'d';'e';'e';'e';'f';'f'; ...
             'g';'g';'g';'h';'h';'i';'i';'j';'j';'k';'l';'m';'m'};
 
- ## 95% expanded BCa bootstrap confidence intervals for the mean with
- ## cluster resampling
+ % 95% expanded BCa bootstrap confidence intervals for the mean with
+ % cluster resampling
  bootclust (data, 1999, @mean, [0.025,0.975], clustid);

 
Produces the following output

 
Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -198,23 +198,23 @@ 
Demonstration 2

  Resampling method: Balanced, bootstrap cluster resampling 
  Number of resamples: 1999 
  Confidence interval (CI) type: Expanded bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 95% (1.3%, 99.0%)
+ Nominal coverage (and the percentiles used): 95% (1.1%, 98.8%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +29.65       -0.03397     +2.855       +23.10       +36.14

+ +29.65       -0.05243     +2.947       +22.59       +35.90

Demonstration 3

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% equal-tailed percentile bootstrap confidence intervals for
- ## the variance
+ % 90% equal-tailed percentile bootstrap confidence intervals for
+ % the variance
  bootclust (data, 1999, {@var, 1}, 0.1);

Produces the following output

Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -229,21 +229,21 @@ 
Demonstration 3

 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -6.778       +41.32       +96.51       +234.0
+ +171.5 -6.453 +42.73 +96.47 +237.0

Demonstration 4

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
  clustid = {'a';'a';'b';'b';'a';'c';'c';'d';'e';'e';'e';'f';'f'; ...
             'g';'g';'g';'h';'h';'i';'i';'j';'j';'k';'l';'m';'m'};
 
- ## 90% equal-tailed percentile bootstrap confidence intervals for
- ## the variance
+ % 90% equal-tailed percentile bootstrap confidence intervals for
+ % the variance
  bootclust (data, 1999, {@var, 1}, 0.1, clustid);

Produces the following output

Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -258,18 +258,18 @@ 
Demonstration 4

 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -9.818       +33.48       +105.5       +215.6
+ +171.5 -9.464 +33.90 +104.1 +214.8

Demonstration 5

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% BCa bootstrap confidence intervals for the variance
+ % 90% BCa bootstrap confidence intervals for the variance
  bootclust (data, 1999, {@var, 1}, [0.05 0.95]);

Produces the following output

Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -280,24 +280,24 @@ 
Demonstration 5

  Resampling method: Balanced, bootstrap cluster resampling 
  Number of resamples: 1999 
  Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 90% (12.0%, 98.7%)
+ Nominal coverage (and the percentiles used): 90% (12.2%, 98.7%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -6.833       +41.90       +115.1       +261.9
+ +171.5 -6.800 +41.10 +115.4 +261.1

Demonstration 6

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
  clustid = {'a';'a';'b';'b';'a';'c';'c';'d';'e';'e';'e';'f';'f'; ...
             'g';'g';'g';'h';'h';'i';'i';'j';'j';'k';'l';'m';'m'};
 
- ## 90% BCa bootstrap confidence intervals for the variance
+ % 90% BCa bootstrap confidence intervals for the variance
  bootclust (data, 1999, {@var, 1}, [0.05 0.95], clustid);

Produces the following output

Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -308,21 +308,21 @@ 
Demonstration 6

  Resampling method: Balanced, bootstrap cluster resampling 
  Number of resamples: 1999 
  Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 90% (12.8%, 98.7%)
+ Nominal coverage (and the percentiles used): 90% (12.9%, 98.7%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -9.726       +33.28       +123.1       +228.8
+ +171.5 -9.876 +32.85 +123.2 +228.9

Demonstration 7

The following code

 
- ## Input dataset
+ % Input dataset
  y = randn (20,1); x = randn (20,1); X = [ones(20,1), x];
 
- ## 90% BCa confidence interval for regression coefficients 
+ % 90% BCa confidence interval for regression coefficients 
  bootclust ({y,X}, 1999, @(y,X) X\y, [0.05 0.95]); % Could also use @regress

Produces the following output

Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -337,19 +337,19 @@ 
Demonstration 7

 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +0.2164      +0.03162     +0.2372      -0.2505      +0.5444    
- +0.02405     +0.03589     +0.2652      -0.4380      +0.4111
+ +0.01658 -0.02123 +0.2032 -0.3300 +0.3262 + -0.2459 -0.002949 +0.1725 -0.5289 +0.03772

Demonstration 8

The following code

 
- ## Input dataset
+ % Input dataset
  y = randn (20,1); x = randn (20,1); X = [ones(20,1), x];
  clustid = [1;1;1;1;2;2;2;3;3;3;3;4;4;4;4;4;5;5;5;6];
 
- ## 90% BCa confidence interval for regression coefficients 
+ % 90% BCa confidence interval for regression coefficients 
  bootclust ({y,X}, 1999, @(y,X) X\y, [0.05 0.95], clustid);

Produces the following output

Summary of nonparametric cluster bootstrap estimates of bias and precision
@@ -364,24 +364,24 @@ 
Demonstration 8

 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- -0.06313     -0.01992     +0.1748      -0.3865      +0.1868    
- -0.3765      +0.003190    +0.1941      -0.6577      -0.02047
+ -0.07271 -0.01387 +0.2734 -0.5017 +0.3980 + +0.1061 +0.09242 +0.1964 -0.2119 +0.3748

Demonstration 9

The following code

 
- ## Input bivariate dataset
+ % Input bivariate dataset
  x = [576 635 558 578 666 580 555 661 651 605 653 575 545 572 594].';
  y = [3.39 3.3 2.81 3.03 3.44 3.07 3 3.43 ...
       3.36 3.13 3.12 2.74 2.76 2.88 2.96].';
  clustid = [1;1;3;1;1;2;2;2;2;3;1;3;3;3;2];
 
- ## 95% BCa bootstrap confidence intervals for the correlation coefficient
+ % 95% BCa bootstrap confidence intervals for the correlation coefficient
  bootclust ({x, y}, 1999, @cor, [], clustid);
 
- ## Please be patient, the calculations will be completed soon...
+ % Please be patient, the calculations will be completed soon...

Produces the following output

Summary of nonparametric cluster bootstrap estimates of bias and precision
 ******************************************************************************
@@ -391,11 +391,11 @@ 
Demonstration 9

  Resampling method: Balanced, bootstrap cluster resampling 
  Number of resamples: 1999 
  Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 95% (2.1%, 97.1%)
+ Nominal coverage (and the percentiles used): 95% (1.6%, 96.5%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +0.7764      -0.02447     +0.1423      +0.4174      +0.9981
+ +0.7764 -0.02425 +0.1437 +0.3909 +0.9902

Package: statistics-resampling

diff --git a/docs/function/bootknife.html b/docs/function/bootknife.html index 7ee9ff3e..5f2ade0e 100644 --- a/docs/function/bootknife.html +++ b/docs/function/bootknife.html @@ -206,11 +206,11 @@

Demonstration 1

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 95% expanded BCa bootstrap confidence intervals for the mean
+ % 95% expanded BCa bootstrap confidence intervals for the mean
  bootknife (data, 1999, @mean);

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
@@ -222,25 +222,25 @@ 
Demonstration 1

  Number of resamples (outer): 1999 
  Number of resamples (inner): 0 
  Confidence interval (CI) type: Expanded bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 95% (1.4%, 97.3%)
+ Nominal coverage (and the percentiles used): 95% (1.2%, 97.0%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +29.65       -3.553e-15   +2.624       +23.64       +34.48
+ +29.65 +0.000 +2.617 +23.16 +34.38

Demonstration 2

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 95% calibrated percentile bootstrap confidence intervals for the mean
+ % 95% calibrated percentile bootstrap confidence intervals for the mean
  bootknife (data, [1999, 199], @mean);
 
- ## Please be patient, the calculations will be completed soon...
+ % Please be patient, the calculations will be completed soon...

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
 ******************************************************************************
@@ -251,26 +251,26 @@ 
Demonstration 2

  Number of resamples (outer): 1999 
  Number of resamples (inner): 199 
  Confidence interval (CI) type: Calibrated percentile
- Nominal coverage (and the percentiles used): 95% (1.1%, 97.3%)
+ Nominal coverage (and the percentiles used): 95% (1.3%, 97.4%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +29.65       +4.974e-14   +2.674       +23.47       +34.60
+ +29.65 -9.948e-14 +2.694 +23.40 +34.47

Demonstration 3

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 95% calibrated percentile bootstrap confidence intervals for the median
- ## with smoothing.
+ % 95% calibrated percentile bootstrap confidence intervals for the median
+ % with smoothing.
  bootknife (data, [1999, 199], @smoothmedian);
 
- ## Please be patient, the calculations will be completed soon...
+ % Please be patient, the calculations will be completed soon...

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
 ******************************************************************************
@@ -281,23 +281,23 @@ 
Demonstration 3

  Number of resamples (outer): 1999 
  Number of resamples (inner): 199 
  Confidence interval (CI) type: Calibrated percentile
- Nominal coverage (and the percentiles used): 95% (2.1%, 97.9%)
+ Nominal coverage (and the percentiles used): 95% (1.9%, 97.3%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +30.86       -0.01637     +2.909       +24.67       +37.00
+ +30.86 -0.02125 +3.072 +24.30 +36.93

Demonstration 4

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% equal-tailed percentile bootstrap confidence intervals for
- ## the variance
+ % 90% equal-tailed percentile bootstrap confidence intervals for
+ % the variance
  bootknife (data, 1999, {@var, 1}, 0.1);

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
@@ -313,18 +313,18 @@ 
Demonstration 4

 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -6.849       +42.29       +96.62       +236.4
+ +171.5 -6.566 +42.18 +97.13 +235.9

Demonstration 5

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% BCa bootstrap confidence intervals for the variance
+ % 90% BCa bootstrap confidence intervals for the variance
  bootknife (data, 1999, {@var, 1}, [0.05 0.95]);

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
@@ -336,26 +336,26 @@ 
Demonstration 5

  Number of resamples (outer): 1999 
  Number of resamples (inner): 0 
  Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 90% (13.0%, 98.9%)
+ Nominal coverage (and the percentiles used): 90% (11.4%, 98.5%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -6.736       +42.56       +117.4       +265.3
+ +171.5 -6.673 +42.16 +112.9 +255.5

Demonstration 6

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% calibrated equal-tailed percentile bootstrap confidence intervals for
- ## the variance.
+ % 90% calibrated equal-tailed percentile bootstrap confidence intervals for
+ % the variance.
  bootknife (data, [1999, 199], {@var, 1}, 0.1);
 
- ## Please be patient, the calculations will be completed soon...
+ % Please be patient, the calculations will be completed soon...

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
 ******************************************************************************
@@ -370,21 +370,21 @@ 
Demonstration 6

 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -6.246       +44.64       +85.85       +251.0
+ +171.5 -7.484 +43.15 +86.54 +249.2

Demonstration 7

The following code

 
- ## Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41].';
 
- ## 90% calibrated percentile bootstrap confidence intervals for the variance
+ % 90% calibrated percentile bootstrap confidence intervals for the variance
  bootknife (data, [1999, 199], {@var, 1}, [0.05, 0.95]);
 
- ## Please be patient, the calculations will be completed soon...
+ % Please be patient, the calculations will be completed soon...

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
 ******************************************************************************
@@ -395,21 +395,21 @@ 
Demonstration 7

  Number of resamples (outer): 1999 
  Number of resamples (inner): 199 
  Confidence interval (CI) type: Calibrated percentile
- Nominal coverage (and the percentiles used): 90% (12.3%, 99.4%)
+ Nominal coverage (and the percentiles used): 90% (11.2%, 99.4%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +171.5       -6.765       +42.26       +118.0       +288.2
+ +171.5 -7.238 +46.48 +112.2 +274.3

Demonstration 8

The following code

 
- ## Input dataset
+ % Input dataset
  y = randn (20,1); x = randn (20,1); X = [ones(20,1), x];
 
- ## 90% BCa confidence interval for regression coefficients 
+ % 90% BCa confidence interval for regression coefficients 
  bootknife ({y,X}, 1999, @(y,X) X\y, [0.05 0.95]); % Could also use @regress

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
@@ -425,23 +425,23 @@ 
Demonstration 8

 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +0.2257      +0.01272     +0.2753      -0.2639      +0.6355    
- +0.01235     +0.001187    +0.2198      -0.3413      +0.3731
+ +0.04178 -0.004920 +0.2227 -0.3313 +0.3933 + -0.07522 -0.003103 +0.1416 -0.3371 +0.1291

Demonstration 9

The following code

 
- ## Input bivariate dataset
+ % Input bivariate dataset
  x = [576 635 558 578 666 580 555 661 651 605 653 575 545 572 594].';
  y = [3.39 3.3 2.81 3.03 3.44 3.07 3 3.43 ...
       3.36 3.13 3.12 2.74 2.76 2.88 2.96].'; 
 
- ## 95% BCa bootstrap confidence intervals for the correlation coefficient
+ % 95% BCa bootstrap confidence intervals for the correlation coefficient
  bootknife ({x, y}, 1999, @cor);
 
- ## Please be patient, the calculations will be completed soon...
+ % Please be patient, the calculations will be completed soon...

Produces the following output

Summary of nonparametric bootstrap estimates of bias and precision
 ******************************************************************************
@@ -452,35 +452,40 @@ 
Demonstration 9

  Number of resamples (outer): 1999 
  Number of resamples (inner): 0 
  Confidence interval (CI) type: Bias-corrected and accelerated (BCa) 
- Nominal coverage (and the percentiles used): 95% (0.5%, 93.5%)
+ Nominal coverage (and the percentiles used): 95% (0.6%, 93.9%)
 
 Bootstrap Statistics: 
  original     bias         std_error    CI_lower     CI_upper  
- +0.7764      -0.004412    +0.1341      +0.3519      +0.9460
+ +0.7764 -0.004729 +0.1386 +0.3191 +0.9531

Demonstration 10

The following code

  
- ## Calculating confidence intervals for the coefficients from logistic 
- ## regression using an example with an ordinal response from:
- ## https://uk.mathworks.com/help/stats/mnrfit.html
+ % Calculating confidence intervals for the coefficients from logistic 
+ % regression using an example with an ordinal response from:
+ % https://uk.mathworks.com/help/stats/mnrfit.html
  
- ##>>>>>>>>> This code block must be run first in Octave only >>>>>>>>>>>>
+ %>>>>>>>>> This code block must be run first in Octave only >>>>>>>>>>>>
+
  try
    pkg load statistics
    load carbig
+   info = ver;
+   if ( str2num ({info.Version}{strcmp({info.Name},'statistics')}(1:3)) < 1.5)
+     error ('statistics package version must be > 1.5')
+   end
    if (~ exist ('mnrfit', 'file'))
-     ## Octave Statistics package does not currently have the mnrfit function,
-     ## so we will use it's logistic_regression function for fitting ordinal
-     ## models instead. 
+     % Octave Statistics package does not currently have the mnrfit function,
+     % so we will use it's logistic_regression function for fitting ordinal
+     % models instead. 
      function [B, DEV] = mnrfit (X, Y, varargin)
-       ## Note that the if the outcome has more than two levels, the
-       ## logistic_regression function is only suitable when the outcome 
-       ## is ordinal, so we would need to use append 'model', 'ordinal'
-       ## as a name-value pair in MATLAB when executing it's mnrfit
-       ## function (see below)
+       % Note that the if the outcome has more than two levels, the
+       % logistic_regression function is only suitable when the outcome 
+       % is ordinal, so we would need to use append 'model', 'ordinal'
+       % as a name-value pair in MATLAB when executing it's mnrfit
+       % function (see below)
        [INTERCEPT, SLOPE, DEV] = logistic_regression (Y - 1, X, false);
        B = cat (1, INTERCEPT, SLOPE);
      end
@@ -491,24 +496,25 @@ 
Demonstration 10

    fprintf ('\nSkipping this demo...')
    fprintf ('\nRequired features of the statistics package not found.\n\n');
  end
- ##<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
+
+ %<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
 
  if (stats_pkg)
 
-   ##>>>>>>>>>>>>>>>>>>> This code block is the demo >>>>>>>>>>>>>>>>>>>>>>
+   %>>>>>>>>>>>>>>>>>>> This code block is the demo >>>>>>>>>>>>>>>>>>>>>>
 
-   ## This demo requires the statistics package in Octave (equivalent to
-   ## the Statistics and Machine Learning Toolbox in Matlab)
+   % This demo requires the statistics package in Octave (equivalent to
+   % the Statistics and Machine Learning Toolbox in Matlab)
 
-   ## Create the dataset
+   % Create the dataset
    load carbig
    X = [Acceleration Displacement Horsepower Weight];
 
-   ## The responses 1 - 4 correspond to the following classification:
-   ## 1:  9 - 19 miles per gallon
-   ## 2: 19 - 29 miles per gallon
-   ## 3: 29 - 39 miles per gallon
-   ## 4: 39 - 49 miles per gallon
+   % The responses 1 - 4 correspond to the following classification:
+   % 1:  9 - 19 miles per gallon
+   % 2: 19 - 29 miles per gallon
+   % 3: 29 - 39 miles per gallon
+   % 4: 39 - 49 miles per gallon
    miles = [1,1,1,1,1,1,1,1,1,1,NaN,NaN,NaN,NaN,NaN,1,1,NaN,1,1,2,2,1,2, ...
             2,2,2,2,2,2,2,1,1,1,1,2,2,2,2,NaN,2,1,1,2,1,1,1,1,1,1,1,1,1, ...
             2,2,1,2,2,3,3,3,3,2,2,2,2,2,2,2,1,1,1,1,1,1,1,1,1,2,1,1,1,1, ...
@@ -524,26 +530,27 @@ 
Demonstration 10

             3,3,3,3,3,3,3,3,3,3,3,3,3,2,NaN,3,2,2,2,2,2,1,2,2,3,3,3,2,2, ...
             2,3,3,3,3,3,3,3,3,3,3,3,2,3,2,2,3,3,2,2,4,3,2,3]';
 
-   ## Bootsrap confidence intervals for each logistic regression coefficient
+   % Bootsrap confidence intervals for each logistic regression coefficient
    bootknife ({X, miles}, 1999, ...
                @(X, miles) mnrfit (X, miles, 'model', 'ordinal'));
 
-   ## Where the first 3 rows are the intercept terms, and the last 4 rows
-   ## are the slope coefficients. For each predictor, the slope coefficient
-   ## corresponds to how a unit change in the predictor impacts on the odds,
-   ## which are proportional across the (ordered) catagories, where each
-   ## log-odds in each case is:
-   ##
-   ##       ln ( ( P[below] ) / ( P[above] ) )
-   ##
-   ## Therefore, a positive slope value indicates that a unit increase in the
-   ## predictor increases the odds of running at fewer miles per gallon.
-
-   ## Note that ordinal and multinomial logistic regression (appropriate
-   ## for ordinal and nominal responses respectively) would be equivalent
-   ## for any binary outcome
-
-   ##<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
+   % Where the first 3 rows are the intercept terms, and the last 4 rows
+   % are the slope coefficients. For each predictor, the slope coefficient
+   % corresponds to how a unit change in the predictor impacts on the odds,
+   % which are proportional across the (ordered) catagories, where each
+   % log-odds in each case is:
+   %
+   %       ln ( ( P[below] ) / ( P[above] ) )
+   %
+   % i.e. in mnrfit, the reference class is the higher of the two classes.
+   % Therefore, a positive slope value indicates that a unit increase in the
+   % predictor increases the odds of running at fewer miles per gallon.
+
+   % Note that ordinal and multinomial logistic regression (appropriate
+   % for ordinal and nominal responses respectively) would be equivalent
+   % for any binary outcome
+
+   %<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<
  
  end

Produces the following output

@@ -560,121 +567,121 @@

Demonstration 10

Bootstrap Statistics: original bias std_error CI_lower CI_upper - -16.69 -0.5336 +2.127 -20.36 -12.02 - -11.72 -0.3730 +1.862 -15.05 -7.826 - -8.061 -0.2695 +1.761 -11.12 -4.182 - +0.1048 +0.005780 +0.09083 -0.08086 +0.2788 - +0.01034 +0.0007234 +0.006842 -0.001846 +0.02452 - +0.06452 +0.002460 +0.01682 +0.03245 +0.09611 - +0.001664 +2.718e-06 +0.0007383 +0.0001822 +0.003085 + -16.69 -0.5173 +2.132 -20.46 -12.62 + -11.72 -0.3624 +1.869 -15.04 -7.914 + -8.061 -0.2634 +1.761 -11.28 -4.540 + +0.1048 +0.005527 +0.09053 -0.07227 +0.2799 + +0.01034 +0.0007151 +0.006584 -0.002616 +0.02307 + +0.06452 +0.002392 +0.01661 +0.03127 +0.09507 + +0.001664 +2.962e-06 +0.0007398 +0.0002144 +0.003082

Demonstration 11

The following code

 
- ## Air conditioning failure times (x) in Table 1.2 of Davison A.C. and
- ## Hinkley D.V (1997) Bootstrap Methods And Their Application. (Cambridge
- ## University Press)
-
- ## AIM: to construct 95% nonparametric bootstrap confidence intervals for
- ## the mean failure time from the sample x (n = 12). The mean(x,1) = 108.1 
- ## and exact intervals based on an exponential model are [65.9, 209.2].
-
- ## Calculations using the 'bootstrap' and 'resample' packages in R
- ##
- ## x <- c(3, 5, 7, 18, 43, 85, 91, 98, 100, 130, 230, 487);
- ##
- ## library (bootstrap)  # Functions from Efron and Tibshirani (1993)
- ## set.seed(1);
- ## ci1 <- boott (x, mean, nboott=19999, nbootsd=499, perc=c(.025,.975))
- ## set.seed(1); 
- ## ci2a <- bcanon (x, 19999, mean, alpha = c(0.025,0.975))
- ##
- ## library (resample)  # Functions from Hesterberg, Tim (2014)
- ## bootout <- bootstrap (x, mean, R=19999, seed=1)
- ## ci2b <- CI.bca (bootout, confidence=0.95, expand=FALSE)
- ## ci3 <- CI.bca (bootout, confidence=0.95, expand=TRUE)
- ## ci4 <- CI.percentile (bootout, confidence=0.95, expand=FALSE)
- ## ci5 <- CI.percentile (bootout, confidence=0.95, expand=TRUE)
- ##
- ## Confidence intervals from 'bootstrap' and 'resample' packages in R
- ##
- ## method                                |   0.05 |   0.95 | length | shape |  
- ## --------------------------------------|--------|--------|--------|-------|
- ## ci1  - bootstrap-t (bootstrap)        |   45.2 |  301.6 |  256.4 |  3.08 |
- ## ci2a - BCa (bootstrap)                |   57.1 |  226.5 |  169.4 |  2.32 |
- ## ci2b - BCa (resample)                 |   57.5 |  223.4 |  165.9 |  2.27 |
- ## ci3  - expanded BCa (resample)        |   52.0 |  252.5 |  200.0 |  2.57 |
- ## ci4  - percentile (resample)          |   47.7 |  191.8 |  144.1 |  1.39 |
- ## ci5  - expanded percentile (resample) |   41.1 |  209.0 |  167.9 |  1.51 |
-
- ## Calculations using the 'statistics-resampling' package for Octave/Matlab
- ##
- ## x = [3 5 7 18 43 85 91 98 100 130 230 487]';
- ## boot (1,1,false,1); ci3 = bootknife (x, 19999, @mean, [.025,.975]);
- ## boot (1,1,false,1); ci5 = bootknife (x, 19999, @mean, 0.05);
- ## boot (1,1,false,1); ci6 = bootknife (x, [19999,499], @mean, [.025,.975]);
- ##
- ## Confidence intervals from 'statistics-resampling' package for Octave/Matlab
- ##
- ## method                                |  0.025 |  0.975 | length | shape |
- ## --------------------------------------|--------|--------|--------|-------|
- ## ci3  - expanded BCa                   |   51.4 |  255.6 |  204.2 |  2.60 |
- ## ci5  - expanded percentile            |   37.3 |  207.4 |  170.1 |  1.40 |
- ## ci6  - calibrated                     |   50.3 |  245.3 |  194.9 |  2.37 |
- ## --------------------------------------|--------|--------|--------|-------|
- ## parametric - exact                    |   65.9 |  209.2 |  143.3 |  3.40 |
- ##
- ## Simulation results for constructing 95% confidence intervals for the
- ## mean of populations with different distributions. The simulation was
- ## of 1000 random samples of size 12 (analagous to the situation above).
- ## Simulation performed using the bootsim script with nboot of 1999 (for
- ## single bootstrap) or [1999,199] (for double bootstrap).
- ##
- ## --------------------------------------------------------------------------
- ## expanded BCa
- ## --------------------------------------------------------------------------
- ## Population                 | coverage |  lower |  upper | length | shape |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ## Normal N(0,1)              |    94.8% |   2.7% |   2.5% |   1.22 |  0.99 |
- ## Folded normal |N(0,1)|     |    94.9% |   1.8% |   3.3% |   0.75 |  1.34 |
- ## Laplace exp(1) - exp(1)    |    92.0% |   3.1% |   4.9% |   1.67 |  0.99 |
- ## Log-normal exp(N(0,1))     |    87.4% |   0.6% |  12.0% |   1.95 |  1.82 |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ##
- ## --------------------------------------------------------------------------
- ## expanded percentile
- ## --------------------------------------------------------------------------
- ## Population                 | coverage |  lower |  upper | length | shape |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ## Normal N(0,1)              |    94.8% |   2.2% |   3.0% |   1.22 |  1.00 |
- ## Folded normal |N(0,1)|     |    92.1% |   1.5% |   6.4% |   0.71 |  1.10 |
- ## Laplace exp(1) - exp(1)    |    94.7% |   1.9% |   3.4% |   1.61 |  1.00 |
- ## Log-normal exp(N(0,1))     |    86.4% |   0.1% |  13.5% |   1.74 |  1.24 |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ##
- ## --------------------------------------------------------------------------
- ## calibrated percentile (equal-tailed)
- ## --------------------------------------------------------------------------
- ## Population                 | coverage |  lower |  upper | length | shape |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ## Normal N(0,1)              |    95.5% |   2.9% |   1.6% |   1.30 |  1.00 |
- ## Folded normal |N(0,1)|     |    95.1% |   0.8% |   4.1% |   0.79 |  1.14 |
- ## Laplace exp(1) - exp(1)    |    94.7% |   2.3% |   3.0% |   1.76 |  0.99 |
- ## Log-normal exp(N(0,1))     |    88.8% |   0.3% |  10.9% |   1.99 |  1.39 |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ##
- ## --------------------------------------------------------------------------
- ## calibrated percentile
- ## --------------------------------------------------------------------------
- ## Population                 | coverage |  lower |  upper | length | shape |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ## Normal N(0,1)              |    95.5% |   3.1% |   1.4% |   1.28 |  1.01 |
- ## Folded normal |N(0,1)|     |    95.5% |   0.9% |   3.6% |   0.75 |  1.40 |
- ## Laplace exp(1) - exp(1)    |    93.3% |   3.4% |   3.3% |   1.74 |  1.02 |
- ## Log-normal exp(N(0,1))     |    89.4% |   0.9% |   9.7% |   1.97 |  1.78 |
- ## ---------------------------|----------|--------|--------|--------|-------|
+ % Air conditioning failure times (x) in Table 1.2 of Davison A.C. and + % Hinkley D.V (1997) Bootstrap Methods And Their Application. (Cambridge + % University Press) + + % AIM: to construct 95% nonparametric bootstrap confidence intervals for + % the mean failure time from the sample x (n = 12). The mean(x,1) = 108.1 + % and exact intervals based on an exponential model are [65.9, 209.2]. + + % Calculations using the 'bootstrap' and 'resample' packages in R + % + % x <- c(3, 5, 7, 18, 43, 85, 91, 98, 100, 130, 230, 487); + % + % library (bootstrap) % Functions from Efron and Tibshirani (1993) + % set.seed(1); + % ci1 <- boott (x, mean, nboott=19999, nbootsd=499, perc=c(.025,.975)) + % set.seed(1); + % ci2a <- bcanon (x, 19999, mean, alpha = c(0.025,0.975)) + % + % library (resample) % Functions from Hesterberg, Tim (2014) + % bootout <- bootstrap (x, mean, R=19999, seed=1) + % ci2b <- CI.bca (bootout, confidence=0.95, expand=FALSE) + % ci3 <- CI.bca (bootout, confidence=0.95, expand=TRUE) + % ci4 <- CI.percentile (bootout, confidence=0.95, expand=FALSE) + % ci5 <- CI.percentile (bootout, confidence=0.95, expand=TRUE) + % + % Confidence intervals from 'bootstrap' and 'resample' packages in R + % + % method | 0.05 | 0.95 | length | shape | + % --------------------------------------|--------|--------|--------|-------| + % ci1 - bootstrap-t (bootstrap) | 45.2 | 301.6 | 256.4 | 3.08 | + % ci2a - BCa (bootstrap) | 57.1 | 226.5 | 169.4 | 2.32 | + % ci2b - BCa (resample) | 57.5 | 223.4 | 165.9 | 2.27 | + % ci3 - expanded BCa (resample) | 52.0 | 252.5 | 200.0 | 2.57 | + % ci4 - percentile (resample) | 47.7 | 191.8 | 144.1 | 1.39 | + % ci5 - expanded percentile (resample) | 41.1 | 209.0 | 167.9 | 1.51 | + + % Calculations using the 'statistics-resampling' package for Octave/Matlab + % + % x = [3 5 7 18 43 85 91 98 100 130 230 487]'; + % boot (1,1,false,1); ci3 = bootknife (x, 19999, @mean, [.025,.975]); + % boot (1,1,false,1); ci5 = bootknife (x, 19999, @mean, 0.05); + % boot (1,1,false,1); ci6 = bootknife (x, [19999,499], @mean, [.025,.975]); + % + % Confidence intervals from 'statistics-resampling' package for Octave/Matlab + % + % method | 0.025 | 0.975 | length | shape | + % --------------------------------------|--------|--------|--------|-------| + % ci3 - expanded BCa | 51.4 | 255.6 | 204.2 | 2.60 | + % ci5 - expanded percentile | 37.3 | 207.4 | 170.1 | 1.40 | + % ci6 - calibrated | 50.3 | 245.3 | 194.9 | 2.37 | + % --------------------------------------|--------|--------|--------|-------| + % parametric - exact | 65.9 | 209.2 | 143.3 | 3.40 | + % + % Simulation results for constructing 95% confidence intervals for the + % mean of populations with different distributions. The simulation was + % of 1000 random samples of size 12 (analagous to the situation above). + % Simulation performed using the bootsim script with nboot of 1999 (for + % single bootstrap) or [1999,199] (for double bootstrap). + % + % -------------------------------------------------------------------------- + % expanded BCa + % -------------------------------------------------------------------------- + % Population | coverage | lower | upper | length | shape | + % ---------------------------|----------|--------|--------|--------|-------| + % Normal N(0,1) | 94.8% | 2.7% | 2.5% | 1.22 | 0.99 | + % Folded normal |N(0,1)| | 94.9% | 1.8% | 3.3% | 0.75 | 1.34 | + % Laplace exp(1) - exp(1) | 92.0% | 3.1% | 4.9% | 1.67 | 0.99 | + % Log-normal exp(N(0,1)) | 87.4% | 0.6% | 12.0% | 1.95 | 1.82 | + % ---------------------------|----------|--------|--------|--------|-------| + % + % -------------------------------------------------------------------------- + % expanded percentile + % -------------------------------------------------------------------------- + % Population | coverage | lower | upper | length | shape | + % ---------------------------|----------|--------|--------|--------|-------| + % Normal N(0,1) | 94.8% | 2.2% | 3.0% | 1.22 | 1.00 | + % Folded normal |N(0,1)| | 92.1% | 1.5% | 6.4% | 0.71 | 1.10 | + % Laplace exp(1) - exp(1) | 94.7% | 1.9% | 3.4% | 1.61 | 1.00 | + % Log-normal exp(N(0,1)) | 86.4% | 0.1% | 13.5% | 1.74 | 1.24 | + % ---------------------------|----------|--------|--------|--------|-------| + % + % -------------------------------------------------------------------------- + % calibrated percentile (equal-tailed) + % -------------------------------------------------------------------------- + % Population | coverage | lower | upper | length | shape | + % ---------------------------|----------|--------|--------|--------|-------| + % Normal N(0,1) | 95.5% | 2.9% | 1.6% | 1.30 | 1.00 | + % Folded normal |N(0,1)| | 95.1% | 0.8% | 4.1% | 0.79 | 1.14 | + % Laplace exp(1) - exp(1) | 94.7% | 2.3% | 3.0% | 1.76 | 0.99 | + % Log-normal exp(N(0,1)) | 88.8% | 0.3% | 10.9% | 1.99 | 1.39 | + % ---------------------------|----------|--------|--------|--------|-------| + % + % -------------------------------------------------------------------------- + % calibrated percentile + % -------------------------------------------------------------------------- + % Population | coverage | lower | upper | length | shape | + % ---------------------------|----------|--------|--------|--------|-------| + % Normal N(0,1) | 95.5% | 3.1% | 1.4% | 1.28 | 1.01 | + % Folded normal |N(0,1)| | 95.5% | 0.9% | 3.6% | 0.75 | 1.40 | + % Laplace exp(1) - exp(1) | 93.3% | 3.4% | 3.3% | 1.74 | 1.02 | + % Log-normal exp(N(0,1)) | 89.4% | 0.9% | 9.7% | 1.97 | 1.78 | + % ---------------------------|----------|--------|--------|--------|-------|

gives an example of how 'bootknife' is used.

Demonstration 12

@@ -682,122 +689,122 @@

Demonstration 12

The following code

 
- ## Spatial Test Data (A) from Table 14.1 of Efron and Tibshirani (1993)
- ## An Introduction to the Bootstrap in Monographs on Statistics and Applied 
- ## Probability 57 (Springer)
-
- ## AIM: to construct 90% nonparametric bootstrap confidence intervals for
- ## var(A,1), where var(A,1) = 171.5 and n = 23, and exact intervals based
- ## on Normal theory are [118.4, 305.2].
- ##
- ## (i.e. (n - 1) * var (A, 0) ./ chi2inv (1 - [0.05; 0.95], n - 1))
-
- ## Calculations using the 'boot' and 'bootstrap' packages in R
- ## 
- ## library (boot)       # Functions from Davison and Hinkley (1997)
- ## A <- c(48,36,20,29,42,42,20,42,22,41,45,14,6, ...
- ##        0,33,28,34,4,32,24,47,41,24,26,30,41);
- ## n <- length(A)
- ## var.fun <- function (d, i) { 
- ##        # Function to compute the population variance
- ##        n <- length (d); 
- ##        return (var (d[i]) * (n - 1) / n) };
- ## boot.fun <- function (d, i) {
- ##        # Compute the estimate
- ##        t <- var.fun (d, i);
- ##        # Compute sampling variance of the estimate using Tukey's jackknife
- ##        n <- length (d);
- ##        U <- empinf (data=d[i], statistic=var.fun, type="jack", stype="i");
- ##        var.t <- sum (U^2 / (n * (n - 1)));
- ##        return ( c(t, var.t) ) };
- ## set.seed(1)
- ## var.boot <- boot (data=A, statistic=boot.fun, R=19999, sim='balanced')
- ## ci1 <- boot.ci (var.boot, conf=0.90, type="norm")
- ## ci2 <- boot.ci (var.boot, conf=0.90, type="perc")
- ## ci3 <- boot.ci (var.boot, conf=0.90, type="basic")
- ## ci4 <- boot.ci (var.boot, conf=0.90, type="bca")
- ## ci5 <- boot.ci (var.boot, conf=0.90, type="stud")
- ##
- ## library (bootstrap)  # Functions from Efron and Tibshirani (1993)
- ## set.seed(1);
- ## ci4a <- bcanon (A, 19999, var.fun, alpha=c(0.05,0.95))
- ## set.seed(1); 
- ## ci5a <- boott (A, var.fun, nboott=19999, nbootsd=499, perc=c(.05,.95))
- ##
- ## Confidence intervals from 'boot' and 'bootstrap' packages in R
- ##
- ## method                                |   0.05 |   0.95 | length | shape |  
- ## --------------------------------------|--------|--------|--------|-------|
- ## ci1  - normal                         |  109.6 |  246.7 |  137.1 |  1.21 |
- ## ci2  - percentile                     |   97.9 |  234.8 |  136.9 |  0.86 |
- ## ci3  - basic                          |  108.3 |  245.1 |  136.8 |  1.16 |
- ## ci4  - BCa                            |  116.0 |  260.7 |  144.7 |  1.60 |
- ## ci4a - BCa                            |  115.8 |  260.6 |  147.8 |  1.59 |
- ## ci5  - bootstrap-t                    |  112.0 |  291.8 |  179.8 |  2.02 |
- ## ci5a - bootstrap-t                    |  116.1 |  290.9 |  174.7 |  2.16 |
- ## --------------------------------------|--------|--------|--------|-------|
- ## parametric - exact                    |  118.4 |  305.2 |  186.8 |  2.52 |
- ##
- ## Summary of bias statistics from 'boot' package in R
- ##
- ## method                             | original |    bias | bias-corrected |
- ## -----------------------------------|----------|---------|----------------|
- ## single bootstrap                   |   171.53 |   -6.58 |         178.11 |
- ## -----------------------------------|----------|---------|----------------|
- ## parametric - exact                 |   171.53 |   -6.86 |         178.40 |
-
- ## Calculations using the 'statistics-resampling' package for Octave/Matlab
- ##
- ## A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
- ##      0 33 28 34 4 32 24 47 41 24 26 30 41].';
- ## boot (1,1,false,1); ci2 = bootknife (A,19999,{@var,1},0.1);
- ## boot (1,1,false,1); ci4 = bootknife (A,19999,{@var,1},[0.05,0.95]);
- ## boot (1,1,false,1); ci6a = bootknife (A,[19999,499],{@var,1},0.1);
- ## boot (1,1,false,1); ci6b = bootknife (A,[19999,499],{@var,1},[0.05,0.95]);
- ##
- ## Confidence intervals from 'statistics-resampling' package for Octave/Matlab
- ##
- ## method                                |   0.05 |   0.95 | length | shape |
- ## --------------------------------------|--------|--------|--------|-------|
- ## ci2  - percentile (equal-tailed)      |   96.1 |  237.0 |  140.9 |  0.87 |
- ## ci4  - BCa                            |  115.9 |  264.6 |  148.7 |  1.68 |
- ## ci6a - calibrated (equal-tailed)      |   82.6 |  254.4 |  171.8 |  0.93 |
- ## ci6b - calibrated                     |  113.4 |  284.9 |  171.5 |  1.95 |
- ## --------------------------------------|--------|--------|--------|-------|
- ## parametric - exact                    |  118.4 |  305.2 |  186.8 |  2.52 |
- ##
- ## Simulation results for constructing 90% confidence intervals for the
- ## variance of a population N(0,1) from 1000 random samples of size 26
- ## (analagous to the situation above). Simulation performed using the
- ## bootsim script with nboot of 1999 (for single bootstrap) or [1999,499]
- ## (for double bootstrap).
- ##
- ## method                     | coverage |  lower |  upper | length | shape |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ## percentile (equal-tailed)  |    81.9% |   1.3% |  16.8% |   0.78 |  0.91 |
- ## BCa                        |    85.6% |   5.2% |   9.2% |   0.87 |  1.84 |
- ## calibrated (equal-tailed)  |    90.0% |   0.1% |   9.9% |   1.01 |  1.04 |
- ## calibrated                 |    90.3% |   4.5% |   5.2% |   0.99 |  2.21 |
- ## ---------------------------|----------|--------|--------|--------|-------|
- ## parametric - exact         |    90.8% |   3.7% |   5.5% |   0.99 |  2.52 |
-
- ## Summary of bias statistics from 'boot' package in R
- ##
- ## method                             | original |    bias | bias-corrected |
- ## -----------------------------------|----------|---------|----------------|
- ## single bootstrap                   |   171.53 |   -6.70 |         178.24 |
- ## double bootstrap                   |   171.53 |   -7.12 |         178.65 |
- ## -----------------------------------|----------|---------|----------------|
- ## parametric - exact                 |   171.53 |   -6.86 |         178.40 |
-
- ## The equivalent methods for constructing bootstrap intervals in the 'boot'
- ## and 'bootstrap' packages (in R) and the statistics-resampling package (in
- ## Octave/Matlab) produce intervals with very similar end points, length and
- ## shape. However, all intervals calculated using the 'statistics-resampling'
- ## package are slightly longer than the equivalent intervals calculated in
- ## R because the 'statistics-resampling' package uses bootknife resampling.
- ## The scale of the sampling distribution for small samples is approximated
- ## better by bootknife (rather than bootstrap) resampling.
+ % Spatial Test Data (A) from Table 14.1 of Efron and Tibshirani (1993) + % An Introduction to the Bootstrap in Monographs on Statistics and Applied + % Probability 57 (Springer) + + % AIM: to construct 90% nonparametric bootstrap confidence intervals for + % var(A,1), where var(A,1) = 171.5 and n = 23, and exact intervals based + % on Normal theory are [118.4, 305.2]. + % + % (i.e. (n - 1) * var (A, 0) ./ chi2inv (1 - [0.05; 0.95], n - 1)) + + % Calculations using the 'boot' and 'bootstrap' packages in R + % + % library (boot) % Functions from Davison and Hinkley (1997) + % A <- c(48,36,20,29,42,42,20,42,22,41,45,14,6, ... + % 0,33,28,34,4,32,24,47,41,24,26,30,41); + % n <- length(A) + % var.fun <- function (d, i) { + % % Function to compute the population variance + % n <- length (d); + % return (var (d[i]) * (n - 1) / n) }; + % boot.fun <- function (d, i) { + % % Compute the estimate + % t <- var.fun (d, i); + % % Compute sampling variance of the estimate using Tukey's jackknife + % n <- length (d); + % U <- empinf (data=d[i], statistic=var.fun, type="jack", stype="i"); + % var.t <- sum (U^2 / (n * (n - 1))); + % return ( c(t, var.t) ) }; + % set.seed(1) + % var.boot <- boot (data=A, statistic=boot.fun, R=19999, sim='balanced') + % ci1 <- boot.ci (var.boot, conf=0.90, type="norm") + % ci2 <- boot.ci (var.boot, conf=0.90, type="perc") + % ci3 <- boot.ci (var.boot, conf=0.90, type="basic") + % ci4 <- boot.ci (var.boot, conf=0.90, type="bca") + % ci5 <- boot.ci (var.boot, conf=0.90, type="stud") + % + % library (bootstrap) % Functions from Efron and Tibshirani (1993) + % set.seed(1); + % ci4a <- bcanon (A, 19999, var.fun, alpha=c(0.05,0.95)) + % set.seed(1); + % ci5a <- boott (A, var.fun, nboott=19999, nbootsd=499, perc=c(.05,.95)) + % + % Confidence intervals from 'boot' and 'bootstrap' packages in R + % + % method | 0.05 | 0.95 | length | shape | + % --------------------------------------|--------|--------|--------|-------| + % ci1 - normal | 109.6 | 246.7 | 137.1 | 1.21 | + % ci2 - percentile | 97.9 | 234.8 | 136.9 | 0.86 | + % ci3 - basic | 108.3 | 245.1 | 136.8 | 1.16 | + % ci4 - BCa | 116.0 | 260.7 | 144.7 | 1.60 | + % ci4a - BCa | 115.8 | 260.6 | 147.8 | 1.59 | + % ci5 - bootstrap-t | 112.0 | 291.8 | 179.8 | 2.02 | + % ci5a - bootstrap-t | 116.1 | 290.9 | 174.7 | 2.16 | + % --------------------------------------|--------|--------|--------|-------| + % parametric - exact | 118.4 | 305.2 | 186.8 | 2.52 | + % + % Summary of bias statistics from 'boot' package in R + % + % method | original | bias | bias-corrected | + % -----------------------------------|----------|---------|----------------| + % single bootstrap | 171.53 | -6.58 | 178.11 | + % -----------------------------------|----------|---------|----------------| + % parametric - exact | 171.53 | -6.86 | 178.40 | + + % Calculations using the 'statistics-resampling' package for Octave/Matlab + % + % A = [48 36 20 29 42 42 20 42 22 41 45 14 6 ... + % 0 33 28 34 4 32 24 47 41 24 26 30 41].'; + % boot (1,1,false,1); ci2 = bootknife (A,19999,{@var,1},0.1); + % boot (1,1,false,1); ci4 = bootknife (A,19999,{@var,1},[0.05,0.95]); + % boot (1,1,false,1); ci6a = bootknife (A,[19999,499],{@var,1},0.1); + % boot (1,1,false,1); ci6b = bootknife (A,[19999,499],{@var,1},[0.05,0.95]); + % + % Confidence intervals from 'statistics-resampling' package for Octave/Matlab + % + % method | 0.05 | 0.95 | length | shape | + % --------------------------------------|--------|--------|--------|-------| + % ci2 - percentile (equal-tailed) | 96.1 | 237.0 | 140.9 | 0.87 | + % ci4 - BCa | 115.9 | 264.6 | 148.7 | 1.68 | + % ci6a - calibrated (equal-tailed) | 82.6 | 254.4 | 171.8 | 0.93 | + % ci6b - calibrated | 113.4 | 284.9 | 171.5 | 1.95 | + % --------------------------------------|--------|--------|--------|-------| + % parametric - exact | 118.4 | 305.2 | 186.8 | 2.52 | + % + % Simulation results for constructing 90% confidence intervals for the + % variance of a population N(0,1) from 1000 random samples of size 26 + % (analagous to the situation above). Simulation performed using the + % bootsim script with nboot of 1999 (for single bootstrap) or [1999,499] + % (for double bootstrap). + % + % method | coverage | lower | upper | length | shape | + % ---------------------------|----------|--------|--------|--------|-------| + % percentile (equal-tailed) | 81.9% | 1.3% | 16.8% | 0.78 | 0.91 | + % BCa | 85.6% | 5.2% | 9.2% | 0.87 | 1.84 | + % calibrated (equal-tailed) | 90.0% | 0.1% | 9.9% | 1.01 | 1.04 | + % calibrated | 90.3% | 4.5% | 5.2% | 0.99 | 2.21 | + % ---------------------------|----------|--------|--------|--------|-------| + % parametric - exact | 90.8% | 3.7% | 5.5% | 0.99 | 2.52 | + + % Summary of bias statistics from 'boot' package in R + % + % method | original | bias | bias-corrected | + % -----------------------------------|----------|---------|----------------| + % single bootstrap | 171.53 | -6.70 | 178.24 | + % double bootstrap | 171.53 | -7.12 | 178.65 | + % -----------------------------------|----------|---------|----------------| + % parametric - exact | 171.53 | -6.86 | 178.40 | + + % The equivalent methods for constructing bootstrap intervals in the 'boot' + % and 'bootstrap' packages (in R) and the statistics-resampling package (in + % Octave/Matlab) produce intervals with very similar end points, length and + % shape. However, all intervals calculated using the 'statistics-resampling' + % package are slightly longer than the equivalent intervals calculated in + % R because the 'statistics-resampling' package uses bootknife resampling. + % The scale of the sampling distribution for small samples is approximated + % better by bootknife (rather than bootstrap) resampling.

gives an example of how 'bootknife' is used.

diff --git a/docs/function/bootlm.html b/docs/function/bootlm.html index 8ac68572..05cd4c14 100644 --- a/docs/function/bootlm.html +++ b/docs/function/bootlm.html @@ -455,20 +455,20 @@

Demonstration 1

The following code

 
- ## Two-sample unpaired test on independent samples (equivalent to Welch's
- ## t-test). 
+ % Two-sample unpaired test on independent samples (equivalent to Welch's
+ % t-test). 
 
  score = [54 23 45 54 45 43 34 65 77 46 65]';
  gender = {'male' 'male' 'male' 'male' 'male' 'female' 'female' 'female' ...
            'female' 'female' 'female'}';
 
- ## 95% confidence intervals and p-values for the difference in mean score
- ## between males and females (computed by wild bootstrap)
+ % 95% confidence intervals and p-values for the difference in mean score
+ % between males and females (computed by wild bootstrap)
  STATS = bootlm (score, gender, 'display', 'on', 'varnames', 'gender', ...
                  'dim', 1, 'posthoc','trt_vs_ctrl');
 
- ## 95% credible intervals for the estimated marginal means of the scores by
- ## males and females (computed by Bayesian bootstrap)
+ % 95% credible intervals for the estimated marginal means of the scores by
+ % males and females (computed by Bayesian bootstrap)
  STATS = bootlm (score, gender, 'display', 'on', 'varnames', 'gender', ...
                  'dim', 1, 'method', 'bayesian', 'prior', 'auto');

Produces the following output

@@ -480,7 +480,7 @@

Demonstration 1

name mean CI_lower CI_upper p-adj -------------------------------------------------------------------------------- -female - male +10.80 -8.591 +30.19 .252 +female - male +10.80 -8.650 +30.25 .243 MODEL FORMULA (based on Wilkinson's notation): @@ -491,8 +491,8 @@

Demonstration 1

name mean CI_lower CI_upper N -------------------------------------------------------------------------------- -male +44.20 +32.89 +53.57 5 -female +55.00 +42.05 +67.39 6 +male +44.20 +32.51 +53.02 5 +female +55.00 +42.56 +67.82 6

and the following figure

@@ -507,23 +507,23 @@

Demonstration 2

The following code

 
- ## Two-sample paired test on dependent or matched samples equivalent to a
- ## paired t-test.
+ % Two-sample paired test on dependent or matched samples equivalent to a
+ % paired t-test.
 
  score = [4.5 5.6; 3.7 6.4; 5.3 6.4; 5.4 6.0; 3.9 5.7]';
  treatment = {'before' 'after'; 'before' 'after'; 'before' 'after';
               'before' 'after'; 'before' 'after'}';
  subject = {'GS' 'GS'; 'JM' 'JM'; 'HM' 'HM'; 'JW' 'JW'; 'PS' 'PS'}';
 
- ## 95% confidence intervals and p-values for the difference in mean score
- ## before and after treatment (computed by wild bootstrap)
+ % 95% confidence intervals and p-values for the difference in mean score
+ % before and after treatment (computed by wild bootstrap)
  STATS = bootlm (score(:), {subject(:), treatment(:)}, ...
                             'model', 'linear', 'display', 'on', ...
                             'varnames', {'subject','treatment'}, ...
                             'dim', 2, 'posthoc','trt_vs_ctrl');
 
- ## 95% credible intervals for the estimated marginal means of the scores
- ## before and after treatment (computed by Bayesian bootstrap)
+ % 95% credible intervals for the estimated marginal means of the scores
+ % before and after treatment (computed by Bayesian bootstrap)
  STATS = bootlm (score(:), {subject(:), treatment(:)}, ...
                             'model', 'linear', 'display', 'on', ...
                             'varnames', {'subject','treatment'}, ...
@@ -537,7 +537,7 @@ 
Demonstration 2

 
 name                                   mean        CI_lower    CI_upper    p-adj
 --------------------------------------------------------------------------------
-after - before                         +1.460      +0.6424     +2.278       .002
+after - before                         +1.460      +0.6513     +2.269       .002
 
 
 MODEL FORMULA (based on Wilkinson's notation):
@@ -548,8 +548,8 @@ 
Demonstration 2

 
 name                                   mean        CI_lower    CI_upper        N
 --------------------------------------------------------------------------------
-before                                 +4.560      +4.119      +5.010          5
-after                                  +6.020      +5.586      +6.477          5
+before +4.560 +4.108 +5.000 5 +after +6.020 +5.577 +6.478 5

and the following figure

@@ -564,8 +564,8 @@

Demonstration 3

The following code

 
- ## One-way design. The data is from a study on the strength of structural
- ## beams, in Hogg and Ledolter (1987) Engineering Statistics. NY: MacMillan
+ % One-way design. The data is from a study on the strength of structural
+ % beams, in Hogg and Ledolter (1987) Engineering Statistics. NY: MacMillan
 
  strength = [82 86 79 83 84 85 86 87 74 82 ...
             78 75 76 77 79 79 77 78 82 79]';
@@ -573,13 +573,13 @@ 
Demonstration 3

           'al1','al1','al1','al1','al1','al1', ...
           'al2','al2','al2','al2','al2','al2'}';
 
- ## 95% confidence intervals and p-values for the differences in mean strength
- ## of three alloys (computed by wild bootstrap)
+ % 95% confidence intervals and p-values for the differences in mean strength
+ % of three alloys (computed by wild bootstrap)
  STATS = bootlm (strength, alloy, 'display', 'on', 'varnames', 'alloy', ...
                  'dim', 1, 'posthoc','pairwise');
 
- ## 95% credible intervals for the estimated marginal means of the strengths
- ## of each of the alloys (computed by Bayesian bootstrap)
+ % 95% credible intervals for the estimated marginal means of the strengths
+ % of each of the alloys (computed by Bayesian bootstrap)
  STATS = bootlm (strength, alloy, 'display', 'on', 'varnames', 'alloy', ...
                  'dim', 1, 'method','bayesian', 'prior', 'auto');

Produces the following output

@@ -591,9 +591,9 @@

Demonstration 3

name mean CI_lower CI_upper p-adj -------------------------------------------------------------------------------- -st - al1 +7.000 +3.874 +10.13 <.001 -st - al2 +5.000 +2.548 +7.452 <.001 -al1 - al2 -2.000 -4.870 +0.8702 .170 +st - al1 +7.000 +3.868 +10.13 <.001 +st - al2 +5.000 +2.542 +7.458 <.001 +al1 - al2 -2.000 -4.870 +0.8703 .170 MODEL FORMULA (based on Wilkinson's notation): @@ -604,9 +604,9 @@

Demonstration 3

name mean CI_lower CI_upper N -------------------------------------------------------------------------------- -st +84.00 +82.12 +85.73 8 -al1 +77.00 +74.89 +79.34 6 -al2 +79.00 +77.77 +80.47 6 +st +84.00 +82.09 +85.68 8 +al1 +77.00 +74.93 +79.40 6 +al2 +79.00 +77.72 +80.44 6

and the following figure

@@ -621,9 +621,9 @@

Demonstration 4

The following code

 
- ## One-way repeated measures design. The data is from a study on the number
- ## of words recalled by 10 subjects for three time condtions, in Loftus &
- ## Masson (1994) Psychon Bull Rev. 1(4):476-490, Table 2.
+ % One-way repeated measures design. The data is from a study on the number
+ % of words recalled by 10 subjects for three time condtions, in Loftus &
+ % Masson (1994) Psychon Bull Rev. 1(4):476-490, Table 2.
 
  words = [10 13 13; 6 8 8; 11 14 14; 22 23 25; 16 18 20; ...
           15 17 17; 1 1 4; 12 15 17;  9 12 12;  8 9 12];
@@ -632,15 +632,15 @@ 
Demonstration 4

  subject = [ 1  1  1;  2  2  2;  3  3  3;  4  4  4;  5  5  5; ...
              6  6  6;  7  7  7;  8  8  8;  9  9  9; 10 10 10];
 
- ## 95% confidence intervals and p-values for the differences in mean number
- ## of words recalled for the different times (using wild bootstrap).
+ % 95% confidence intervals and p-values for the differences in mean number
+ % of words recalled for the different times (using wild bootstrap).
  STATS = bootlm (words(:), {subject(:), seconds(:)}, ...
                             'model', 'linear', 'display', 'on', ...
                             'varnames', {'subject', 'seconds'}, ...
                             'dim', 2, 'posthoc', 'pairwise');
 
- ## 95% credible intervals for the estimated marginal means of the number of
- ## words recalled for each time (computed using Bayesian bootstrap).
+ % 95% credible intervals for the estimated marginal means of the number of
+ % words recalled for each time (computed using Bayesian bootstrap).
  STATS = bootlm (words(:), {subject(:), seconds(:)}, ...
                             'model', 'linear', 'display', 'on', ...
                             'varnames', {'subject', 'seconds'}, ...
@@ -654,9 +654,9 @@ 
Demonstration 4

 
 name                                   mean        CI_lower    CI_upper    p-adj
 --------------------------------------------------------------------------------
-1 - 2                                  -2.000      -2.733      -1.267      <.001
-1 - 5                                  -3.200      -3.846      -2.554      <.001
-2 - 5                                  -1.200      -2.072      -0.3279      .012
+1 - 2                                  -2.000      -2.738      -1.262      <.001
+1 - 5                                  -3.200      -3.848      -2.552      <.001
+2 - 5                                  -1.200      -2.087      -0.3132      .012
 
 
 MODEL FORMULA (based on Wilkinson's notation):
@@ -667,9 +667,9 @@ 
Demonstration 4

 
 name                                   mean        CI_lower    CI_upper        N
 --------------------------------------------------------------------------------
-1                                      +11.00      +10.64      +11.35         10
-2                                      +13.00      +12.50      +13.45         10
-5                                      +14.20      +13.75      +14.63         10
+1 +11.00 +10.63 +11.34 10 +2 +13.00 +12.51 +13.47 10 +5 +14.20 +13.77 +14.65 10

and the following figure

@@ -684,9 +684,9 @@

Demonstration 5

The following code

 
- ## Balanced two-way design. The data is yield of cups of popped popcorn from
- ## different popcorn brands and popper types, in Hogg and Ledolter (1987)
- ## Engineering Statistics. NY: MacMillan
+ % Balanced two-way design. The data is yield of cups of popped popcorn from
+ % different popcorn brands and popper types, in Hogg and Ledolter (1987)
+ % Engineering Statistics. NY: MacMillan
 
  popcorn = [5.5, 4.5, 3.5; 5.5, 4.5, 4.0; 6.0, 4.0, 3.0; ...
             6.5, 5.0, 4.0; 7.0, 5.5, 5.0; 7.0, 5.0, 4.5];
@@ -699,34 +699,34 @@ 
Demonstration 5

  popper = {'oil', 'oil', 'oil'; 'oil', 'oil', 'oil'; 'oil', 'oil', 'oil'; ...
            'air', 'air', 'air'; 'air', 'air', 'air'; 'air', 'air', 'air'};
 
- ## Check regression coefficients corresponding to brand x popper interaction
+ % Check regression coefficients corresponding to brand x popper interaction
  STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
                             'display', 'on', 'model', 'full', ...
                             'varnames', {'brands', 'popper'});
 
- ## 95% confidence intervals and p-values for the differences in mean yield of
- ## different popcorn brands (computed by wild bootstrap).
+ % 95% confidence intervals and p-values for the differences in mean yield of
+ % different popcorn brands (computed by wild bootstrap).
  STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
                             'display', 'on', 'model', 'full', ...
                             'varnames', {'brands', 'popper'}, ...
                             'dim', 1, 'posthoc', 'pairwise');
 
- ## 95% credible intervals for the estimated marginal means of the yield for
- ## each popcorn brand (computed by Bayesian bootstrap).
+ % 95% credible intervals for the estimated marginal means of the yield for
+ % each popcorn brand (computed by Bayesian bootstrap).
  STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
                             'display', 'on', 'model', 'full', ...
                             'varnames', {'brands', 'popper'}, ...
                             'dim', 1, 'method', 'bayesian', 'prior', 'auto');
 
- ## 95% confidence intervals and p-values for the differences in mean yield
- ## for different popper types (computed by wild bootstrap).
+ % 95% confidence intervals and p-values for the differences in mean yield
+ % for different popper types (computed by wild bootstrap).
  STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
                             'display', 'on', 'model', 'full', ...
                             'varnames', {'brands', 'popper'}, ...
                             'dim', 2, 'posthoc', 'pairwise');
 
- ## 95% credible intervals for the estimated marginal means of the yield for
- ## each popper type (computed by Bayesian bootstrap).
+ % 95% credible intervals for the estimated marginal means of the yield for
+ % each popper type (computed by Bayesian bootstrap).
  STATS = bootlm (popcorn(:), {brands(:), popper(:)}, ...
                             'display', 'on', 'model', 'full', ...
                             'varnames', {'brands', 'popper'}, ...
@@ -740,12 +740,12 @@ 
Demonstration 5

 
 name                                   coeff       CI_lower    CI_upper    p-val
 --------------------------------------------------------------------------------
-(Intercept)                            +5.667      +4.796      +6.537      <.001
-brands_1                               -1.333      -1.890      -0.7768      .010
-brands_2                               -2.167      -3.122      -1.211      <.001
-popper_1                               +1.167      +0.6063     +1.727       .015
-brands:popper_1                        -0.3333     -1.066      +0.3992      .332
-brands:popper_2                        -0.1667     -1.235      +0.9012      .730
+(Intercept)                            +5.667      +4.794      +6.539      <.001
+brands_1                               -1.333      -1.898      -0.7691      .011
+brands_2                               -2.167      -3.123      -1.210      <.001
+popper_1                               +1.167      +0.5958     +1.738       .016
+brands:popper_1                        -0.3333     -1.074      +0.4077      .338
+brands:popper_2                        -0.1667     -1.260      +0.9266      .726
 
 
 MODEL FORMULA (based on Wilkinson's notation):
@@ -757,8 +757,8 @@ 
Demonstration 5

 name                                   mean        CI_lower    CI_upper    p-adj
 --------------------------------------------------------------------------------
 Gourmet - National                     +1.500      +1.131      +1.869      <.001
-Gourmet - Generic                      +2.250      +1.699      +2.801      <.001
-National - Generic                     +0.7500     +0.2131     +1.287       .009
+Gourmet - Generic                      +2.250      +1.710      +2.790      <.001
+National - Generic                     +0.7500     +0.1981     +1.302       .011
 
 
 MODEL FORMULA (based on Wilkinson's notation):
@@ -769,9 +769,9 @@ 
Demonstration 5

 
 name                                   mean        CI_lower    CI_upper        N
 --------------------------------------------------------------------------------
-Gourmet                                +6.250      +6.060      +6.436          6
-National                               +4.750      +4.555      +4.925          6
-Generic                                +4.000      +3.685      +4.328          6
+Gourmet                                +6.250      +6.066      +6.444          6
+National                               +4.750      +4.563      +4.937          6
+Generic                                +4.000      +3.681      +4.316          6
 
 
 MODEL FORMULA (based on Wilkinson's notation):
@@ -782,7 +782,7 @@ 
Demonstration 5

 
 name                                   mean        CI_lower    CI_upper    p-adj
 --------------------------------------------------------------------------------
-oil - air                              -1.000      -1.387      -0.6134     <.001
+oil - air                              -1.000      -1.384      -0.6160     <.001
 
 
 MODEL FORMULA (based on Wilkinson's notation):
@@ -793,8 +793,8 @@ 
Demonstration 5

 
 name                                   mean        CI_lower    CI_upper        N
 --------------------------------------------------------------------------------
-oil                                    +4.500      +4.310      +4.681          9
-air                                    +5.500      +5.315      +5.692          9
+oil +4.500 +4.316 +4.691 9 +air +5.500 +5.309 +5.679 9

and the following figure

@@ -809,10 +809,10 @@

Demonstration 6

The following code

 
- ## Unbalanced two-way design (2x2). The data is from a study on the effects
- ## of gender and a college degree on starting salaries of a sample of company
- ## employees, in Maxwell, Delaney and Kelly (2018): Chapter 7, Table 15. The
- ## starting salaries are in units of 1000 dollars per annum.
+ % Unbalanced two-way design (2x2). The data is from a study on the effects
+ % of gender and a college degree on starting salaries of a sample of company
+ % employees, in Maxwell, Delaney and Kelly (2018): Chapter 7, Table 15. The
+ % starting salaries are in units of 1000 dollars per annum.
 
  salary = [24 26 25 24 27 24 27 23 15 17 20 16, ...
            25 29 27 19 18 21 20 21 22 19]';
@@ -820,12 +820,12 @@ 
Demonstration 6

            'm' 'm' 'm' 'm' 'm' 'm' 'm' 'm' 'm' 'm'}';
  degree = [1 1 1 1 1 1 1 1 0 0 0 0 1 1 1 0 0 0 0 0 0 0]';
 
- ## ANOVA (including the main effect of gender averaged over all levels of
- ## degree). In this order, the variability in salary only attributed to
- ## having a degree is tested first. Then, having accounted for any effect of
- ## degree, we test for whether variability in salary attributed to gender is
- ## significant. Finally, the interaction term tests whether the effect of
- ## gender differs depending on whether the subjects have a degree or not.
+ % ANOVA (including the main effect of gender averaged over all levels of
+ % degree). In this order, the variability in salary only attributed to
+ % having a degree is tested first. Then, having accounted for any effect of
+ % degree, we test for whether variability in salary attributed to gender is
+ % significant. Finally, the interaction term tests whether the effect of
+ % gender differs depending on whether the subjects have a degree or not.
  [STATS, BOOTSTAT, AOVSTAT] = bootlm (salary, {degree, gender}, 'model', ...
                              'full', 'display', 'off', 'varnames', ...
                              {'degree', 'gender'}, 'seed', 1);
@@ -837,22 +837,22 @@ 
Demonstration 6

             AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
  end
 
- ## Since the interaction is not significant (F(1,18) = 0.42, p = 0.567), we
- ## draw our attention to the main effects. We see that employees in this
- ## have significantly different starting salaries depending or not on whether
- ## they have a degree (F(1,18) = 87.20, p < 0.001). We can also see that once
- ## we factor in any differences in salary attributed to having a degree,
- ## there is a significant difference in the salaries of men and women at
- ## this company (F(1,18) = 10.97, p = 0.005). 
-
- ## ANOVA (including the main effect of degree averaged over all levels of
- ## gender). In this order, the variability in salary only attributed to being
- ## male or female is tested first. Then, having accounted for any effect of
- ## gender, we test for whether variability in salary attributed to having a
- ## degree is significant. Finally, the interaction term tests whether the
- ## effect of having a degree or not differs depending on whether the subjects
- ## are male or female. (Note that the result for the interaction is not
- ## affected by the order of the predictors).
+ % Since the interaction is not significant (F(1,18) = 0.42, p = 0.567), we
+ % draw our attention to the main effects. We see that employees in this
+ % have significantly different starting salaries depending or not on whether
+ % they have a degree (F(1,18) = 87.20, p < 0.001). We can also see that once
+ % we factor in any differences in salary attributed to having a degree,
+ % there is a significant difference in the salaries of men and women at
+ % this company (F(1,18) = 10.97, p = 0.005). 
+
+ % ANOVA (including the main effect of degree averaged over all levels of
+ % gender). In this order, the variability in salary only attributed to being
+ % male or female is tested first. Then, having accounted for any effect of
+ % gender, we test for whether variability in salary attributed to having a
+ % degree is significant. Finally, the interaction term tests whether the
+ % effect of having a degree or not differs depending on whether the subjects
+ % are male or female. (Note that the result for the interaction is not
+ % affected by the order of the predictors).
 
  [STATS, BOOTSTAT, AOVSTAT] = bootlm (salary, {gender, degree}, 'model', ...
                              'full', 'display', 'off', 'varnames', ...
@@ -865,12 +865,12 @@ 
Demonstration 6

             AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
  end
 
- ## We can now see in the output that there is no significant difference in
- ## salary between men and women in this company! (F(1,18) = 0.11, p = 0.752).
- ## Why the discrepancy? There still seems to be a significant effect of
- ## having a degree on the salary of people in this company (F(1,18) = 98.06, 
- ## p < 0.001). Lets look at the regression coefficients to see what this
- ## effect of degree is.
+ % We can now see in the output that there is no significant difference in
+ % salary between men and women in this company! (F(1,18) = 0.11, p = 0.752).
+ % Why the discrepancy? There still seems to be a significant effect of
+ % having a degree on the salary of people in this company (F(1,18) = 98.06, 
+ % p < 0.001). Lets look at the regression coefficients to see what this
+ % effect of degree is.
 
  STATS = bootlm (salary, {gender, degree}, 'model', 'full', ...
                              'display', 'on', 'varnames', ...
@@ -878,37 +878,37 @@ 
Demonstration 6

                               'contrasts', 'treatment');
  STATS.levels
  
- ## The order of the factor levels for degree indicates that having a degree
- ## (i.e. a code of 1) is listed first and therefore is the reference level
- ## for our treatment contrast coding. We see then from the second regression 
- ## coefficient that starting salaries in this company are $8K lower for
- ## employees without a college degree. Let's now take a look at the estimated
- ## marginal means.
+ % The order of the factor levels for degree indicates that having a degree
+ % (i.e. a code of 1) is listed first and therefore is the reference level
+ % for our treatment contrast coding. We see then from the second regression 
+ % coefficient that starting salaries in this company are $8K lower for
+ % employees without a college degree. Let's now take a look at the estimated
+ % marginal means.
 
  STATS = bootlm (salary, {gender, degree}, 'model', 'full', ...
                             'display', 'on', 'varnames', ...
                             {'gender', 'degree'}, 'dim', [1, 2], ...
                             'method', 'bayesian','prior', 'auto');
  
- ## Ah ha! So it seems that sample sizes are very unbalanced here, with most
- ## of the women in this sample having a degree, while most of the men not.
- ## Since the regression coefficient indicated that a high starting salary is
- ## an outcome of having a degree, this observation likely explains why
- ## salaries where not significantly different between men and women when we
- ## ran the ANOVA with gender listed first in the model (i.e. not accounting
- ## for whether employees had a college degree). Note that our inferences here
- ## assume that the unbalanced samples sizes are representative of similar
- ## imbalance in the company as a whole (i.e. the population).
-
- ## Since the interaction term (F(1,18) = 0.42) was not significant (p > 0.1),
- ## we might rather consider the hypotheses tested using type II sums-of-
- ## squares without the interaction, which do not depend on the order and have
- ## more power respectively. This is easy to achieve with only 2 predictors,
- ## by repeating the 'bootlm' commands with different predictors added last to
- ## the model (as above) but without any interaction (i.e. setting 'model',
- ## 'linear'). We then take the statistics for the last main effect listed
- ## in each of the ANOVA tables - these then correspond to the ANOVA test for
- ## the respective predictor with type II sums-of-squares. For example:
+ % Ah ha! So it seems that sample sizes are very unbalanced here, with most
+ % of the women in this sample having a degree, while most of the men not.
+ % Since the regression coefficient indicated that a high starting salary is
+ % an outcome of having a degree, this observation likely explains why
+ % salaries where not significantly different between men and women when we
+ % ran the ANOVA with gender listed first in the model (i.e. not accounting
+ % for whether employees had a college degree). Note that our inferences here
+ % assume that the unbalanced samples sizes are representative of similar
+ % imbalance in the company as a whole (i.e. the population).
+
+ % Since the interaction term (F(1,18) = 0.42) was not significant (p > 0.1),
+ % we might rather consider the hypotheses tested using type II sums-of-
+ % squares without the interaction, which do not depend on the order and have
+ % more power respectively. This is easy to achieve with only 2 predictors,
+ % by repeating the 'bootlm' commands with different predictors added last to
+ % the model (as above) but without any interaction (i.e. setting 'model',
+ % 'linear'). We then take the statistics for the last main effect listed
+ % in each of the ANOVA tables - these then correspond to the ANOVA test for
+ % the respective predictor with type II sums-of-squares. For example:
 
  [~, ~, AOVSTAT1] = bootlm (salary, {degree, gender}, 'model', ...
                              'linear', 'display', 'off', 'varnames', ...
@@ -927,15 +927,15 @@ 
Demonstration 6

             AOVSTAT2.DF(2), AOVSTAT2.DFE, AOVSTAT2.F(2), ...
             AOVSTAT2.PVAL(2), AOVSTAT2.MODEL{2});
 
- ## Here is the output from 'anovan' for comparison:
- ## ANOVA TABLE (Type II sums-of-squares):
- ## 
- ## Source             Sum Sq.    d.f.    Mean Sq.  R Sq.            F  Prob>F
- ## --------------------------------------------------------------------------
- ## gender              30.462       1      30.462  0.373        11.31    .003
- ## degree              272.39       1      272.39  0.842       101.13   <.001
- ## Error               51.175      19      2.6934
- ## Total               323.86      21
+ % Here is the output from 'anovan' for comparison: + % ANOVA TABLE (Type II sums-of-squares): + % + % Source Sum Sq. d.f. Mean Sq. R Sq. F Prob>F + % -------------------------------------------------------------------------- + % gender 30.462 1 30.462 0.373 11.31 .003 + % degree 272.39 1 272.39 0.842 101.13 <.001 + % Error 51.175 19 2.6934 + % Total 323.86 21

Produces the following output

ANOVA SUMMARY with gender averaged over levels of degree
 F(1,18) = 87.20, p = 0.0001 for the model: salary ~ 1 + degree
@@ -1008,9 +1008,9 @@ 
Demonstration 7

 
The following code

 
 
- ## One-way design with continuous covariate. The data is from a study of the
- ## additive effects of species and temperature on chirpy pulses of crickets,
- ## from Stitch, The Worst Stats Text eveR
+ % One-way design with continuous covariate. The data is from a study of the
+ % additive effects of species and temperature on chirpy pulses of crickets,
+ % from Stitch, The Worst Stats Text eveR
 
  pulse = [67.9 65.1 77.3 78.7 79.4 80.4 85.8 86.6 87.5 89.1 ...
           98.6 100.8 99.3 101.7 44.3 47.2 47.6 49.6 50.3 51.8 ...
@@ -1022,8 +1022,8 @@ 
Demonstration 7

             'ex' 'ex' 'ex' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' ...
             'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv' 'niv'};
 
- ## Perform ANCOVA (type I sums-of-squares)
- ## Use 'anova' contrasts so that the continuous covariate is centered
+ % Perform ANCOVA (type I sums-of-squares)
+ % Use 'anova' contrasts so that the continuous covariate is centered
  [STATS, BOOTSTAT, AOVSTAT] = bootlm (pulse, {temp, species}, 'model', ...
                            'linear', 'continuous', 1, 'display', 'off', ...
                            'varnames', {'temp', 'species'}, ...
@@ -1036,8 +1036,8 @@ 
Demonstration 7

             AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
  end
 
- ## Perform ANCOVA (type II sums-of-squares)
- ## Use 'anova' contrasts so that the continuous covariate is centered
+ % Perform ANCOVA (type II sums-of-squares)
+ % Use 'anova' contrasts so that the continuous covariate is centered
  [~, ~, AOVSTAT1] = bootlm (pulse, {temp, species}, 'model', ...
                            'linear', 'continuous', 1, 'display', 'off', ...
                            'varnames', {'temp', 'species'}, ...
@@ -1057,21 +1057,21 @@ 
Demonstration 7

             AOVSTAT2.DF(2), AOVSTAT2.DFE, AOVSTAT2.F(2), ...
             AOVSTAT2.PVAL(2), AOVSTAT2.MODEL{2});
 
- ## Estimate regression coefficients using 'anova' contrast coding 
+ % Estimate regression coefficients using 'anova' contrast coding 
  STATS = bootlm (pulse, {temp, species}, 'model', 'linear', ...
                            'continuous', 1, 'display', 'on', ...
                            'varnames', {'temp', 'species'}, ...
                            'contrasts', 'anova');
 
- ## 95% confidence intervals and p-values for the differences in the mean of
- ## chirpy pulses of ex ad niv species (computed by wild bootstrap).
+ % 95% confidence intervals and p-values for the differences in the mean of
+ % chirpy pulses of ex ad niv species (computed by wild bootstrap).
  STATS = bootlm (pulse, {temp, species}, 'model', 'linear', ...
                            'continuous', 1, 'display', 'on', ...
                            'varnames', {'temp', 'species'}, 'dim', 2, ...
                            'posthoc', 'trt_vs_ctrl', 'contrasts', 'anova');
 
- ## 95% credible intervals for the estimated marginal means of chirpy pulses
- ## of ex and niv species (computed by Bayesian bootstrap).
+ % 95% credible intervals for the estimated marginal means of chirpy pulses
+ % of ex and niv species (computed by Bayesian bootstrap).
  STATS = bootlm (pulse, {temp, species}, 'model', 'linear', ...
                            'continuous', 1, 'display', 'on', ...
                            'varnames', {'temp', 'species'}, 'dim', 2, ...
@@ -1134,9 +1134,9 @@ 
Demonstration 8

 
The following code

 
 
- ## Unbalanced three-way design (3x2x2). The data is from a study of the
- ## effects of three different drugs, biofeedback and diet on patient blood
- ## pressure, adapted* from Maxwell, Delaney and Kelly (2018): Ch 8, Table 12
+ % Unbalanced three-way design (3x2x2). The data is from a study of the
+ % effects of three different drugs, biofeedback and diet on patient blood
+ % pressure, adapted* from Maxwell, Delaney and Kelly (2018): Ch 8, Table 12
 
  drug = {'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' ...
          'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X' 'X';
@@ -1157,8 +1157,8 @@ 
Demonstration 8

        180 187 199 170 204 194 162 184 183 156 180 173 ...
        202 228 190 206 224 204 205 199 170 160 179 179];
 
- ## Perform 3-way ANOVA (this design is balanced, thus the order of predictors 
- ## does not make any difference)
+ % Perform 3-way ANOVA (this design is balanced, thus the order of predictors 
+ % does not make any difference)
  [STATS, BOOTSTAT, AOVSTAT] = bootlm (BP(:), {diet(:), drug(:), ...
                                     feedback(:)}, 'seed', 1, ...
                                     'model', 'full', 'display', 'off', ...
@@ -1171,21 +1171,21 @@ 
Demonstration 8

             AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
  end
 
- ## Check regression coefficient corresponding to drug x feedback x diet
+ % Check regression coefficient corresponding to drug x feedback x diet
  STATS = bootlm (BP(:), {diet(:), drug(:), feedback(:)}, ...
                                     'model', 'full', ...
                                     'display', 'on', ...
                                     'varnames', {'diet', 'drug', 'feedback'});
 
- ## 95% confidence intervals and p-values for the differences in mean salary
- ## between males and females (computed by wild bootstrap).
+ % 95% confidence intervals and p-values for the differences in mean salary
+ % between males and females (computed by wild bootstrap).
  STATS = bootlm (BP(:), {diet(:), drug(:), feedback(:)}, 'model', 'full', ...
                                     'display', 'on', 'dim', [1,2,3], ...
                                     'posthoc', 'trt_vs_ctrl', ...
                                     'varnames', {'diet', 'drug', 'feedback'});
 
- ## 95% credible intervals for the estimated marginal means of salaries of
- ## females and males (computed by Bayesian bootstrap).
+ % 95% credible intervals for the estimated marginal means of salaries of
+ % females and males (computed by Bayesian bootstrap).
  STATS = bootlm (BP(:), {diet(:), drug(:), feedback(:)}, 'model', 'full', ...
                                     'display', 'on', 'dim', [1,2,3], ...
                                     'method', 'bayesian', 'prior', 'auto', ...
@@ -1277,9 +1277,9 @@ 
Demonstration 9

 
The following code

 
 
- ## Factorial design with continuous covariate. The data is from a study of
- ## the effects of treatment and exercise on stress reduction score after
- ## adjusting for age. Data from R datarium package).
+ % Factorial design with continuous covariate. The data is from a study of
+ % the effects of treatment and exercise on stress reduction score after
+ % adjusting for age. Data from R datarium package).
 
  score = [95.6 82.2 97.2 96.4 81.4 83.6 89.4 83.8 83.3 85.7 ...
           97.2 78.2 78.9 91.8 86.9 84.1 88.6 89.8 87.3 85.4 ...
@@ -1303,8 +1303,8 @@ 
Demonstration 9

         58 56 57 59 59 60 55 53 55 58 68 62 61 54 59 63 60 67 60 67 ...
         75 54 57 62 65 60 58 61 65 57 56 58 58 58 52 53 60 62 61 61]';
 
- ## ANOVA/ANCOVA statistics
- ## Use 'anova' contrasts so that the continuous covariate is centered
+ % ANOVA/ANCOVA statistics
+ % Use 'anova' contrasts so that the continuous covariate is centered
  [STATS, BOOTSTAT, AOVSTAT] = bootlm (score, {age, exercise, treatment}, ...
                             'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
                             'continuous', 1, 'display', 'off', ...
@@ -1318,15 +1318,15 @@ 
Demonstration 9

             AOVSTAT.PVAL(i), AOVSTAT.MODEL{i});
  end
 
- ## Estimate regression coefficients
+ % Estimate regression coefficients
  STATS = bootlm (score, {age, exercise, treatment}, ...
                             'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
                             'continuous', 1, 'display', 'on', ...
                             'varnames', {'age', 'exercise', 'treatment'}, ...
                             'contrasts', 'anova');
 
- ## 95% confidence intervals and p-values for the differences in mean score
- ## across different treatments and amounts of exercise after adjusting for
+ % 95% confidence intervals and p-values for the differences in mean score
+ % across different treatments and amounts of exercise after adjusting for
  STATS = bootlm (score, {age, exercise, treatment}, ...
                             'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
                             'continuous', 1, 'display', 'on', ...
@@ -1334,9 +1334,9 @@ 
Demonstration 9

                             'dim', [2, 3], 'posthoc', 'trt_vs_ctrl', ...
                             'contrasts', 'anova');
 
- ## 95% credible intervals for the estimated marginal means of scores across
- ## different treatments and amounts of exercise after adjusting for age
- ## (computed by Bayesian bootstrap).
+ % 95% credible intervals for the estimated marginal means of scores across
+ % different treatments and amounts of exercise after adjusting for age
+ % (computed by Bayesian bootstrap).
  STATS = bootlm (score, {age, exercise, treatment}, 'dim', [2, 3], ...
                             'model', [1 0 0; 0 1 0; 0 0 1; 0 1 1], ...
                             'continuous', 1, 'display', 'on', ...
@@ -1410,8 +1410,8 @@ 
Demonstration 10

 
The following code

 
 
- ## Unbalanced one-way design with custom, orthogonal contrasts. Data from
- ## www.uvm.edu/~statdhtx/StatPages/Unequal-ns/Unequal_n%27s_contrasts.html
+ % Unbalanced one-way design with custom, orthogonal contrasts. Data from
+ % www.uvm.edu/~statdhtx/StatPages/Unequal-ns/Unequal_n%27s_contrasts.html
 
  dv =  [ 8.706 10.362 11.552  6.941 10.983 10.092  6.421 14.943 15.931 ...
         22.968 18.590 16.567 15.944 21.637 14.492 17.965 18.851 22.891 ...
@@ -1426,11 +1426,11 @@ 
Demonstration 10

       -0.6002401  0.0000000  0.0  0.5
       -0.6002401  0.0000000  0.0 -0.5];
 
- ## 95% confidence intervals and p-values for linear contrasts 
+ % 95% confidence intervals and p-values for linear contrasts 
  STATS = bootlm (dv, g, 'contrasts', C, 'varnames', 'score', ...
                           'alpha', 0.05, 'display', true);
 
- ## 95% credible intervals for estimated marginal means 
+ % 95% credible intervals for estimated marginal means 
  STATS = bootlm (dv, g, 'contrasts', C, 'varnames', 'score', ...
                           'alpha', 0.05, 'display', true, 'dim', 1, ...
                           'method', 'Bayesian', 'prior', 'auto');

@@ -1477,9 +1477,9 @@ 
Demonstration 11

 
The following code

 
 
- ## Comparing analysis of nested design using ANOVA with clustered resampling.
- ## Two factor nested model example from:
- ## https://www.southampton.ac.uk/~cpd/anovas/datasets/#Chapter2
+ % Comparing analysis of nested design using ANOVA with clustered resampling.
+ % Two factor nested model example from:
+ % https://www.southampton.ac.uk/~cpd/anovas/datasets/#Chapter2
 
  data = [4.5924 7.3809 21.322; -0.5488 9.2085 25.0426; ...
          6.1605 13.1147 22.66; 2.3374 15.2654 24.1283; ...
@@ -1528,8 +1528,8 @@ 
Demonstration 12

 
The following code

 
 
- ## Prediction errors of linear models. Data from Table 9.1, on page 107 of
- ## Efron and Tibshirani (1993) An Introduction to the Bootstrap.
+ % Prediction errors of linear models. Data from Table 9.1, on page 107 of
+ % Efron and Tibshirani (1993) An Introduction to the Bootstrap.
 
  amount = [25.8; 20.5; 14.3; 23.2; 20.6; 31.1; 20.9; 20.9; 30.4; ...
           16.3; 11.6; 11.8; 32.5; 32.0; 18.0; 24.1; 26.5; 25.8; ...
@@ -1551,10 +1551,10 @@ 
Demonstration 12

 
  fprintf ('PREDICTION ERROR of the FULL MODEL = %.2f\n', PRED_ERR.PE(3))
 
- ## Note: The value of prediction error is lower than the 3.00 calculated by
- ## Efron and Tibhirani (1993) using the same refined bootstrap procedure,
- ## because they have used case resampling whereas we have used wild bootstrap
- ## resampling. The equivalent value of Cp (eq. to AIC) statistic is 2.96.

+ % Note: The value of prediction error is lower than the 3.00 calculated by
+ % Efron and Tibhirani (1993) using the same refined bootstrap procedure,
+ % because they have used case resampling whereas we have used wild bootstrap
+ % resampling. The equivalent value of Cp (eq. to AIC) statistic is 2.96.

 
Produces the following output

 
MODEL FORMULA (based on Wilkinson's notation):
 
@@ -1584,7 +1584,7 @@ 
Demonstration 13

 
The following code

 
 
- ## Step-wise regression
+ % Step-wise regression
 
  sr = [11.43;12.07;13.17;05.75;12.88;08.79;00.60;11.90; ...
        04.98;10.78;16.85;03.59;11.24;12.64;12.55;10.67; ...
@@ -1634,15 +1634,15 @@ 
Demonstration 13

 
  PRED_ERR
  
- ## The results from the bootstrap are broadly consistent to the results
- ## obtained for PE, PRESS and RSQ_pred using cross-validation:
- ##
- ##     MODEL                                  PE-CV    PRESS-CV  RSQ_pred-CV
- ##     sr ~ 1                                  20.48    1024.186       -0.041
- ##     sr ~ 1 + pop15                          16.88     843.910       +0.142
- ##     sr ~ 1 + pop15 + pop75                  16.62     830.879       +0.155
- ##     sr ~ 1 + pop15 + pop75 + dpi            16.54     827.168       +0.159
- ##     sr ~ 1 + pop15 + pop75 + dpi + ddpi     15.98     798.939       +0.188

+ % The results from the bootstrap are broadly consistent to the results
+ % obtained for PE, PRESS and RSQ_pred using cross-validation:
+ %
+ %     MODEL                                  PE-CV    PRESS-CV  RSQ_pred-CV
+ %     sr ~ 1                                  20.48    1024.186       -0.041
+ %     sr ~ 1 + pop15                          16.88     843.910       +0.142
+ %     sr ~ 1 + pop15 + pop75                  16.62     830.879       +0.155
+ %     sr ~ 1 + pop15 + pop75 + dpi            16.54     827.168       +0.159
+ %     sr ~ 1 + pop15 + pop75 + dpi + ddpi     15.98     798.939       +0.188

 
Produces the following output

 
PRED_ERR =
 
diff --git a/docs/function/bootmode.html b/docs/function/bootmode.html
index e8e5f523..4926862e 100644
--- a/docs/function/bootmode.html
+++ b/docs/function/bootmode.html
@@ -85,7 +85,7 @@ 
Demonstration 1

 
The following code

 
 
- # Stamp data example used in reference [1] in bootstrap R package
+ % Stamp data example used in reference [1] in bootstrap R package
  x=[0.060;0.064;0.064;0.065;0.066;0.068;0.069;0.069;0.069;0.069;0.069; ...
     0.069;0.069;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070; ...
     0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070;0.070; ...
@@ -131,12 +131,12 @@ 
Demonstration 1

     0.115;0.115;0.117;0.119;0.119;0.119;0.119;0.120;0.120;0.120;0.121; ...
     0.122;0.122;0.123;0.123;0.125;0.125;0.128; 0.129;0.129;0.129;0.130;0.131];
  
- [H1, P1, CRITVAL1] = bootmode(x,1,2000);
+ [H1, P1, CRITVAL1] = bootmode (x,1,2000);
 
- # Repeat function call systematically increasing the number of modes (M) by 
- # 1, until the null hypothesis is accepted (i.e. H0 = 0)
+ % Repeat function call systematically increasing the number of modes (M) by 
+ % 1, until the null hypothesis is accepted (i.e. H0 = 0)
 
- [H2, P2, CRITVAL2] = bootmode(x,2,2000);
+ [H2, P2, CRITVAL2] = bootmode (x,2,2000);
  
  sprintf ('Summary of results:\n') 
  sprintf (cat (2, 'H1 is %u with p = %.3g so reject the null hypothesis', ...
@@ -144,13 +144,13 @@ 
Demonstration 1

  sprintf (cat (2, 'H2 is %u with p = %.3g so accept the null hypothesis', ...
                   ' that there are 2 modes\n'), H2, P2)
  
- # Please be patient, these calculations take a while...

+ % Please be patient, these calculations take a while...

 
Produces the following output

 
ans = Summary of results:
 
 ans = H1 is 1 with p = 0.0005 so reject the null hypothesisthat there is 1 mode
 
-ans = H2 is 0 with p = 0.322 so accept the null hypothesis that there are 2 modes

+ans = H2 is 0 with p = 0.319 so accept the null hypothesis that there are 2 modes

 
 
 
Package: statistics-resampling

diff --git a/docs/function/bootstrp.html b/docs/function/bootstrp.html
index dd28d754..42ab9dee 100644
--- a/docs/function/bootstrp.html
+++ b/docs/function/bootstrp.html
@@ -93,12 +93,12 @@ 
Demonstration 1

 
The following code

 
 
- # Input univariate dataset
+ % Input univariate dataset
  data = [48 36 20 29 42 42 20 42 22 41 45 14 6 ...
          0 33 28 34 4 32 24 47 41 24 26 30 41]';
 
- # Compute 50 bootstrap statistics for the mean and calculate the bootstrap
- # standard arror
+ % Compute 50 bootstrap statistics for the mean and calculate the bootstrap
+ % standard arror
  bootstat = bootstrp (50, @mean, data)
  std (bootstat)

 
Produces the following output

diff --git a/docs/function/bootwild.html b/docs/function/bootwild.html
index 0cc5a69d..4b1c2c52 100644
--- a/docs/function/bootwild.html
+++ b/docs/function/bootwild.html
@@ -152,13 +152,13 @@ 
Demonstration 1

 
The following code

 
 
- ## Input univariate dataset
+ % Input univariate dataset
  heights = [183, 192, 182, 183, 177, 185, 188, 188, 182, 185].';
 
- ## Test statistics and p-values (H0 = 0)
- bootwild(heights);
+ % Test statistics and p-values (H0 = 0)
+ bootwild (heights);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of wild bootstrap null hypothesis significance tests for linear models
 *******************************************************************************
@@ -181,7 +181,7 @@ 
Demonstration 2

 
The following code

 
 
- ## Input bivariate dataset
+ % Input bivariate dataset
  X = [ones(43,1),...
      [01,02,03,04,05,06,07,08,09,10,11,...
       12,13,14,15,16,17,18,19,20,21,22,...
@@ -192,10 +192,10 @@ 
Demonstration 2

      168.0,170.0,178.0,182.0,180.0,183.0,178.0,182.0,188.0,175.0,179.0,...
      183.0,192.0,182.0,183.0,177.0,185.0,188.0,188.0,182.0,185.0]';
 
- ## Compute test statistics and p-values
- bootwild(y,X);
+ % Compute test statistics and p-values
+ bootwild (y, X);
 
- ## Please be patient, the calculations will be completed soon...

+ % Please be patient, the calculations will be completed soon...

 
Produces the following output

 
Summary of wild bootstrap null hypothesis significance tests for linear models
 *******************************************************************************
@@ -211,8 +211,8 @@ 
Demonstration 2

 
 Test Statistics: 
  original     std_err      CI_lower     CI_upper     t-stat      p-val     FPR
- +175.5       +2.502       +170.0       +181.1       +70.1       <.001    .010
- +0.1904      +0.08261     +0.003699    +0.3771      +2.31        .045    .274

+ +175.5       +2.502       +169.8       +181.2       +70.1       <.001    .010
+ +0.1904      +0.08261     +0.003534    +0.3773      +2.31        .047    .280

 
 
 
Package: statistics-resampling

diff --git a/docs/function/images/boot1way_601.png b/docs/function/images/boot1way_601.png
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diff --git a/docs/function/randtest2.html b/docs/function/randtest2.html
index 6ce2477a..1e463905 100644
--- a/docs/function/randtest2.html
+++ b/docs/function/randtest2.html
@@ -151,9 +151,9 @@ 
Demonstration 1

                            @(x, y) log (var (y) ./ var (x)))

Produces the following output

-
pval = 0.3558
-pval = 0.2834
-pval = 0.31423
+
pval = 0.3562
+pval = 0.277
+pval = 0.30584

Demonstration 2

@@ -226,7 +226,7 @@

Demonstration 4

pval = randtest2 ([X GX], [Y GY], true, 5000)

Produces the following output

-
pval = 0.0016
+
pval = 0.0012
 pval =  0.25
diff --git a/docs/function/sampszcalc.html b/docs/function/sampszcalc.html index 057eb839..f5cab096 100644 --- a/docs/function/sampszcalc.html +++ b/docs/function/sampszcalc.html @@ -102,10 +102,10 @@

Demonstration 1

The following code

 
- # The difference between a sample mean from a zero constant (one sample test)
- # or the difference between two dependent means (matched pair). Sample size
- # determined for Cohen's d = 0.8.
- # d effect size
+ % The difference between a sample mean from a zero constant (one sample test)
+ % or the difference between two dependent means (matched pair). Sample size
+ % determined for Cohen's d = 0.8.
+ % d effect size
 
  n = sampszcalc ('t', 0.8)

Produces the following output

@@ -116,8 +116,8 @@

Demonstration 2

The following code

 
- # The difference between two independent means (two groups). Sample size
- # determined for Cohen's d = 0.8.
+ % The difference between two independent means (two groups). Sample size
+ % determined for Cohen's d = 0.8.
 
  n = sampszcalc ('t2', 0.8)

Produces the following output

@@ -128,8 +128,8 @@

Demonstration 3

The following code

 
- # The difference between two independent means (two groups). Sample size
- # determined for Cohen's d = 0.8 and a design effect of 1.5
+ % The difference between two independent means (two groups). Sample size
+ % determined for Cohen's d = 0.8 and a design effect of 1.5
 
  n = sampszcalc ('t2', 0.8, [], [], [], 1.5)

Produces the following output

@@ -140,8 +140,8 @@

Demonstration 4

The following code

 
- # The difference between two independent proportions (two sample test). 
- # Sample size determined for Cohen's h = 0.8 using Normal approximation.
+ % The difference between two independent proportions (two sample test). 
+ % Sample size determined for Cohen's h = 0.8 using Normal approximation.
 
  n = sampszcalc ('z2', 0.8)

Produces the following output

@@ -152,8 +152,8 @@

Demonstration 5

The following code

 
- # The test for Pearson's correlation coefficient (r) equal to 0 (constant),
- # Sample size determined for r effect size = 0.5.
+ % The test for Pearson's correlation coefficient (r) equal to 0 (constant),
+ % Sample size determined for r effect size = 0.5.
 
  n = sampszcalc ('r', 0.5)

Produces the following output

diff --git a/docs/index.html b/docs/index.html index 52427deb..aecb31ab 100644 --- a/docs/index.html +++ b/docs/index.html @@ -28,7 +28,7 @@

About this package

- + diff --git a/docs/readme.html b/docs/readme.html index 68958571..4ba4a332 100644 --- a/docs/readme.html +++ b/docs/readme.html @@ -95,6 +95,12 @@

Installation

MacOS (Intel 64-bit) and Linux (64-bit). Without the MEX files, all functionality of the package is available, but some of the functions run slower.

+

N.B. The package does not yet include any MEX files (for Octave or +Matlab) precompiled for macOS with Apple silicon processors, since the +package developers do not have access to this computer platform. If you +used this package on macOS with an Apple silicon processor (M1-3 chip), +please consider contacting the package maintainer to contribute the MEX +files to this project.

Usage

All help and demos are documented on the ‘Function diff --git a/matlab/statistics-resampling.mltbx b/matlab/statistics-resampling.mltbx index afbfc941d09f0914655860813f67fb7c7193a5ef..1d202dad76dbb31bcc532cf175faa56cad9870cb 100644 GIT binary patch delta 102125 zcmV)9K*hh|yb{*D5)4pF0|XQR000O8=DM*AzX5;dx+qw!RZPF;3;+Q6B>(^o0001H zb8>HQbT49WZ*(qgy;|LJ+r|~X*HfHcC;}Q15=qCk#ky0x-l17qac|2+d1eWC5 zAi!V&QOsmAoxVqJa^0tB-y~1c@9Yl%k`gUDnQ9o5SnQrXKi~P=%`RO|rJ`|}Mup5$ z%0+)s=BdKB3TN{~#1w}`NLfxYjb$VhMY#wIjE|Ny3X?F6_;;2Ss>s7R?dM6Vk)DlrKeX;u`Xr1V^W;W z8n)FG@H|h#NX$f9(EHAHKqrKWmhD-o3K|JZ4=l(+-UzTzh>6HmpjkHP19LZFQi^|; z(`SnS(U4|gk;~f#<1I@~?|wpgwor{7qbw%>ilLJKHylTOOY4g*c9InWDh~^dotoDb2LUgTCS&dOx+d%v%Q+@m*R+4Mw8>u| zUjbo>(0a)Q00(cuBvnz@rb)#Oa3^jf0j9m~-+CRty$wj~@o|roD3l2dwa7D3OtUzk z;g~1YJ~IvzW!Tu9O(n-1OxkJzr)Wc&rx$toc_ek(v1A%c-aooF7=oi0g0tC8mfW~> z#xoKT-iUUV;=i(>4`KANNveMlYnA*_z;bQs7*{CR=y4t{n2O7r&6$kvilaJ2YWTBc z)n2ua7Hn1ERi;sv&$HaHcqEh($)58Pyvl`1Kazp7rlonFK`Dr0fmUYi&nkk#a!Rs^ 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+53,10 @@ Y:\Documents\GitHub\statistics-resampling\inst\boot.m + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexa64 + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexmaci64 + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexw32 + Y:\Documents\GitHub\statistics-resampling\inst\boot.mexw64 Y:\Documents\GitHub\statistics-resampling\inst\boot1way.m Y:\Documents\GitHub\statistics-resampling\inst\bootbayes.m Y:\Documents\GitHub\statistics-resampling\inst\bootcdf.m @@ -70,6 +74,10 @@ Y:\Documents\GitHub\statistics-resampling\inst\sampszcalc.m Y:\Documents\GitHub\statistics-resampling\inst\smoothmad.m Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.m + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexa64 + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexmaci64 + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexw32 + Y:\Documents\GitHub\statistics-resampling\inst\smoothmedian.mexw64

Package Version:5.5.4
Last Release Date:2024-01-04
Last Release Date:2024-01-08
Package Author:Andrew Penn <andy.c.penn@gmail.com>
Package Maintainer:Andrew Penn <andy.c.penn@gmail.com>
License:GPLv3+