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=head1 Synopsis

Get basic R statistical functions working in Perl as if they were part of List::Util, like C<min>, C<max>, C<sum>, etc.
I've used Artificial Intelligence tools such as Claude, Gemini, and Grok to write this as well as using my own gray matter.
There are other similar tools on CPAN, but I want speed and a form like List::Util, which I've gotten here with the help of AI, which often required many attempts to do correctly.
This is meant to call subroutines directly through eXternal Subroutines (XS) for performance and portability.

There B<are> other modules on CPAN that can do B<PARTS> of this, but this works the way that I B<want> it to.

=head1 Functions/Subroutines

=head2 aov

 aov(
 {
     yield => [5.5, 5.4, 5.8, 4.5, 4.8, 4.2],
     ctrl  => [1,     1,   1,   0,   0,   0]
 },
 'yield ~ ctrl');

which returns

 {
     ctrl        {
         Df          1,
         "F value"   25.6000000000001,
         "Mean Sq"   1.70666666666667,
         Pr(>F)      0.00718232855871859,
         "Sum Sq"    1.70666666666667
     },
     Residuals   {
         Df          4,
         "Mean Sq"   0.0666666666666665,
         "Sum Sq"    0.266666666666666
    }
 }

You can also perform Two-Way ANOVA with categorical interactions using the C<*> operator. The parser will implicitly evaluate the main effects alongside the interaction:

 my $res_2way = aov($data_2way, 'len ~ supp * dose');

It is robust against rank deficiency; collinear terms will gracefully receive 0 degrees of freedom and 0 sum of squares, matching R's behavior.

=head2 chisq_test

 my @test_data = ([762, 327, 468], [484, 239, 477]);
 my $test_data = chisq_test(\@test_data);

which outputs:

 {
 data.name   "Perl ArrayRef",
 expected    [
     [0] [
             [0] 703.671381936888,
             [1] 319.645266594124,
             [2] 533.683351468988
         ],
     [1] [
             [0] 542.328618063112,
             [1] 246.354733405876,
             [2] 411.316648531012
         ]
 ],
 method      "Pearson's Chi-squared test",
 observed    [
     [0] [
             [0] 762,
             [1] 327,
             [2] 468
         ],
     [1] [
             [0] 484,
             [1] 239,
             [2] 477
         ]
 ],
 p.value     2.95358918321176e-07,
 parameter   {
     df   2
 },
 statistic   {
     X-squared   30.0701490957547
 }
 }

It also supports 1D arrays for Goodness of Fit tests:

 my $chisq_1d = chisq_test([10, 20, 30]);

For 2x2 matrices, Yates' Continuity Correction is applied automatically, exactly like in R.

=head2 cor

 cor($array1, $array2, $method = 'pearson'),

that is, C<pearson> is the default and will be used if C<$method> is not specified.

Just like R, C<pearson>, C<spearman>, and C<kendall> are available

If you provide an array of arrays (a matrix), C<cor> will compute the correlation matrix automatically. 

=head2 cor_test

 my $result = cor_test(
         'x'         => $x,
         'y'         => $y,
         alternative => 'two.sided'
         method      => 'pearson',
         continuity  => 1
     );

C<cor_test> safely handles C<undef> (or C<NA>) values seamlessly by computing over pairwise complete observations. 

=head2 cov

 cov($array1, $array2, 'pearson')

or

 cov($array1, $array2, 'spearman')

or

 cov($array1, $array2, 'kendall')

=head2 fisher_test

=head3 array reference entry

 my $array_data = [
     [10, 2],
     [3, 15]
 ];
 my $res1 = fisher_test($array_data);

which returns a hash reference:

 {
 alternative   "two.sided",
 conf_int      [
     [0] 2.75338278824932,
     [1] 301.462337971516
 ],
 estimate      {
     "odds ratio"   21.3053175567504
 },
 method        "Fisher's Exact Test for Count Data",
 p_value       0.00053672411914343

}

=head3 hash reference entry

 $ft = fisher_test( {
     Guess => {
         Milk => 3, Tea => 1
     },
     Truth => {
         Milk => 1, Tea => 3
     }
 });

I have the p-value calculated very precisely, but there are some inexactness (approximately 1% for the confidence intervals) which I couldn't rectify.  The answers are very close to R besides the p-value, where they are identical.

=head2 glm

takes a hash of an array as input

 my %tooth_growth = (
     dose => [qw(0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0
 1.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5
 0.5 0.5 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 2.0 2.0 2.0 2.0 2.0 2.0 2.0
 2.0 2.0 2.0)],
     len  => [qw(4.2 11.5  7.3  5.8  6.4 10.0 11.2 11.2  5.2  7.0 16.5 16.5 15.2 17.3 22.5
 17.3 13.6 14.5 18.8 15.5 23.6 18.5 33.9 25.5 26.4 32.5 26.7 21.5 23.3 29.5
 15.2 21.5 17.6  9.7 14.5 10.0  8.2  9.4 16.5  9.7 19.7 23.3 23.6 26.4 20.0
 25.2 25.8 21.2 14.5 27.3 25.5 26.4 22.4 24.5 24.8 30.9 26.4 27.3 29.4 23.0)],
     supp => [qw(VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC VC
 VC VC VC VC VC OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ
 OJ OJ OJ OJ OJ OJ OJ OJ OJ OJ)]
 );
 
 my $glm_teeth = glm(
     data    => \%tooth_growth,
     formula => 'len ~ dose + supp',
     family  => 'gaussian'
 );

I'm not completely confident that this is working perfectly, though I've gotten this subroutine to work for simple cases.

In addition to the C<gaussian> default, it fully supports logistic regression using the C<binomial> family parameter via Iteratively Reweighted Least Squares (IRLS):

 my $glm_bin = glm(formula => 'am ~ wt + hp', data => \%mtcars, family => 'binomial');

=head2 hist

Computes the histogram of the given data values, operating in single $O(N)$ pass performance. It returns the bin counts, computed breaks, midpoints, and density. 

 my $res = hist([1, 2, 2, 3, 3, 3, 4, 4, 5], breaks => 4);

If C<breaks> is not explicitly provided, it defaults to calculating the number of bins using Sturges' formula.

=head2 kruskal_test

Essentially the test determines if all groups have the same median (same distribution) (an excellent review is at https://library.virginia.edu/data/articles/getting-started-with-the-kruskal-wallis-test)

Performs a Kruskal-Wallis rank sum test, see 
https://www.rdocumentation.org/packages/stats/versions/3.6.2/topics/kruskal.test

=head3 R-like array entry

 my @xk = (2.9, 3.0, 2.5, 2.6, 3.2); # normal subjects
 my @yk = (3.8, 2.7, 4.0, 2.4);      # with obstructive airway disease
 my @zk = (2.8, 3.4, 3.7, 2.2, 2.0); # with asbestosis
 my @x = (@xk, @yk, @zk);
 my @g = (
     (map {'Normal subjects'} 0..4),
     (map {'Subjects with obstructive airway disease'} 0..3),
     map {'Subjects with asbestosis'} 0..4
 );
 my $t0 = Time::HiRes::time();
 my $kt = kruskal_test(\@x, \@g);
 my $t1 = Time::HiRes::time();
 printf("Kruskal calculation in %g seconds.\n", $t1-$t0);
 p $kt;

=head3 hash of array entry

 my %x = (
 'normal.subjects' => [2.9, 3.0, 2.5, 2.6, 3.2],
 'obs. airway disease' => [3.8, 2.7, 4.0, 2.4],
 'asbestosis' => [2.8, 3.4, 3.7, 2.2, 2.0]
 );
 $t0 = Time::HiRes::time();
 $kt = kruskal_test(\%x);
 $t1 = Time::HiRes::time();
 printf("Kruskal calculation via HoA in %g seconds.\n", $t1-$t0);
 p $kt;

=head2 ks_test

The Kolmogorov-Smirnov test, which tests whether or not two arrays/lists of data are part of the same distribution is implemented simply:

 $ks = ks_test(\@x, \@y, alternative => 'greater');

returning a hash reference.

Also, a single array can be tested against a normal distribution:

 $ks = ks_test($ksx, 'pnorm');

The p-value precision is about 1e-8, which I want to improve, but am not sure how.

=head2 lm

This is the linear models function.

 $lm = lm(formula =>  'mpg ~ wt + hp', data => $mtcars);

where C<$mtcars> is a hash of hashes

C<lm> also supports generating interaction terms directly within the formula using the C<*> operator:

 my $lm = lm(formula => 'mpg ~ wt * hp^2', data => \%mtcars);

If your data contains missing numbers (C<NA> or C<undef>), C<lm> handles listwise deletion dynamically to ensure mathematical integrity before fitting.

the dot operator also works:

 $lm = lm(formula => 'y ~ .', data => $dot_data);

=head2 matrix

 my $mat1 = matrix(
     data => [1..6],
     nrow => 2
 );

You can also pass C<< byrow =E<gt> 1 >> if you want the matrix populated row-wise instead of column-wise.

=head2 mean

 mean(1,2,3);

or

 my @arr = 1..8;
 mean(@arr, 4, 5)

or

 mean([1,1], [2,2]) # 1.5

=head2 median

works like mean, taking array references and arrays:

 median( $test_data[$i][0] )

=head2 p_adjust

Returns array of false-discovery-rate-corrected p-values, where methods available are "holm", "hochberg", "hommel", "bonferroni", "BH", "BY", "fdr"

 my @q = p_adjust(\@pvalues, $method);

=head2 power_t_test

 $test_data = power_t_test(
     n   => 30,  delta     => 0.5, 
     sd  => 1.0, sig_level => 0.05
 );

It also allows configuring the test type (C<< type =E<gt> 'one.sample' >>, C<'two.sample'>, C<'paired'>) and alternative hypothesis (C<< alternative =E<gt> 'one.sided' >>). You can also pass C<< strict =E<gt> 1 >> to strictly evaluate both tails of the distribution.

=head2 quantile

Calculates sample quantiles using R's continuous Type 7 interpolation. 

 my $quantile = quantile('x' => [1..99], probs => [0.05, 0.1, 0.25]);

If the C<probs> parameter is omitted, it behaves identically to R by defaulting to the 0, 25, 50, 75, and 100 percentiles (C<c(0, .25, .5, .75, 1)>). The returned hash keys match R's standardized naming convention (e.g., C<"25%">, C<"33.3%">).

=head2 rbinom

Create a binomial distribution of numbers

 my $binom = rbinom( n => $n, prob => 0.5, size => 9);

It hooks directly into Perl's internal PRNG system, respecting C<srand()> seeds. 

=head2 read_table

I've tried to make this as simple as possible, trying to follow from R:

 my $test_data = read_table('t/HepatitisCdata.csv');

output types can be AOH (aoa), HOA (hoa), HOH (hoh)

 read_table($filename, 'output.type' => 'aoh');
 
 read_table($filename, 'output.type' => 'hoa');

and, like Text::CSV_XS, filters can be applied in order to save RAM on big files:

 $test_data = read_table(
     't/HepatitisCdata.csv',
     filter => {
         Sex => sub {$_ eq 'f'} # where "Sex" is the column name, and "$_" is the value for that column
     },
     'output.type' => 'aoh'
 );

=head2 rnorm

Make a normal distribution of numbers, with pre-set mean C<mean>, standard deviation C<sd>, and number C<n>.

 my ($rmean, $sd, $n) = (10, 2, 9999);
 my $normals = rnorm( n => $n, mean => $rmean, sd => $sd);

=head2 runif

=head3 named arguments

Make a distribution of approximately uniform distribution

 my $unif = runif( n => $n, min => 0, max => 1);

where C<n> is the number of items, the values are between C<min> and C<max>

=head3 positional args

this is to match R's behavior:

 runif( 9 )

will make 9 numbers in [0,1]

 runif(9, 0, 99)

will match C<n>, C<min>, and C<max> respectively

=head2 scale

 my @scaled_results = scale(1..5);

You can also pass an options hash to disable centering or scaling:

 my @scaled_results = scale(1..5, { center => false, scale => true });

It fully supports matrix operations. By passing an array of arrays, C<scale> processes the data column by column independently:

 my $scaled_mat = scale([[1, 2], [3, 4], [5, 6]]);

=head2 sd

 my $stdev = sd(2,4,4,4,5,5,7,9);

Correct answer is 2.1380899352994;

=head2 seq

Works as closely as I can to R's seq, which is very similar to Perl's C<for> loops.  Returns an array, not an array reference.

=head3 Example 1: Standard integer sequence

 say 'seq(1, 5):';
 my @seq = seq(1, 5);
 say join(', ', @seq), "\n";
 
 say 'seq(1, 2, 0.25):';
 @seq = seq(1, 2, 0.25);

=head3 Example 2: Fractional steps

 say 'seq(1, 2, 0.25):';
 @seq = seq(1, 2, 0.25);
 say join(", ", @seq), "\n";
 for (my $idx = 2; $idx >= 1; $idx -= 0.25) { # count down to pop
     is_approx(pop @seq, $idx, "seq item $idx with fractional step");
 }

=head3 Example 3: Negative steps

 say 'seq(10, 5, -1):';
 @seq = seq(10, 5, -1);
 say join(", ", @seq), "\n";
 for (my $idx = 5; $idx <= 10; $idx++) { # count down to pop
     is_approx(pop @seq, $idx, "seq item $idx with negative step");
 }

=head2 shapiro_test

tests to see if an array reference is normally distributed, returns a p-value and a statistic

 my $shapiro = shapiro_test(
     [1..5]
 );

and returns the hash reference:

 {
 p.value     0.589650577093106,
 p_value     0.589650577093106,
 statistic   0.960870680168535,
 W           0.960870680168535
 }

=head2 t_test

There are 1-sample and 2-sample t-tests:

 my $t_test = t_test( $test_data[$i][$j], mu => mean( $test_data[$i][$j] ));

or 2-sample:

 $t_test = t_test(
     $test_data[3][0],
     $test_data[3][1],
     paired => true
 );

returns a hash reference, which looks like:

 conf_int     => [
     -0.06672889, 0.25672889
 ],
 df        => 5,
 estimate  => 0.095,
 p_value   => 0.19143688433660,
 statistic => 1.50996688705414

the two groups compared can be specified, though not necessarily, as C<x> and C<y>, just like in R:

 $t_test = t_test(
     'x' => test_data[3][0],
     'y' => $test_data[3][1],
     paired => true
 );

=head2 var

as simple as possible:

 var(2, 4, 5, 8, 9)

=head2 wilcox_test

 $test_data = wilcox_test(
     [1.83,  0.50,  1.62,  2.48, 1.68, 1.88, 1.55, 3.06, 1.30],
     [0.878, 0.647, 0.598, 2.05, 1.06, 1.29, 1.06, 3.14, 1.29]
 );

It fully supports paired tests (C<< paired =E<gt> true >>) and can calculate exact p-values (the default for $N < 50$ without ties). If ties are encountered, it automatically switches to an approximation with continuity correction.

=head2 write_table

mimics R's "write.table", with data as first argument to subroutine, and output file as second

 write_table(\@data_aoh, $tmp_file, sep => "\t", 'row.names' => true);

You can also precisely filter and reorder which columns are written by passing an array reference to C<col.names>:

 write_table(\@data, $tmp_file, sep => "\t", 'col.names' => ['c', 'a']);