Synopsis

Get basic statistical functions working in Perl as if they were part of List::Util, like min, max, 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 are other modules on CPAN that can do PARTS of this, but this works the way that I want it to.

Functions/Subroutines

add_data

Add data to an existing hash or array reference. This function acts as the equivalent of adding new rows, as well as an ljoin (described below). It dynamically infers your target data structure, handles deeply nested records, and seamlessly coerces mismatched data shapes to preserve the structural integrity of your primary reference.

Hash of Hashes (HoH)

When the target is a Hash of Hashes, incoming hash keys update existing rows, and new keys create new rows.

$data = { 'Jack Smith' => { age => 30 } };

$n = { 
    'Jack Smith' => {    # Update existing (Hash)
        dept => 'Engineering'
     },
    'Jane Doe'   => { age => 25, dept => 'Sales' }, # Add new (Hash)
    'Invalid'    => 'Not a reference'               # Edge case safety
};

add_data($data, $n);

Resulting Structure:

{
    "Jack Smith":  {
        "age":  30,
        "dept": "Engineering"
    },
    "Jane Doe":    {
        "age":  25,
        "dept": "Sales"
    }
}

Hash of Arrays (HoA)

When the target is a Hash of Arrays, incoming arrays are pushed onto the existing arrays, appending the new elements, similarly to R's rbind.

$data = { 'Project Alpha' => [ 'task1', 'task2' ] };

$n = {
    'Project Alpha' => [ 'task3' ],              # Appends to existing array
    'Project Beta'  => [ 'task1', 'task2' ]      # Creates new array row
};

add_data($data, $n);

Resulting Structure:

{
    "Project Alpha": [ "task1", "task2", "task3" ],
    "Project Beta":  [ "task1", "task2" ]
}

Array of Hashes / Arrays (AoH / AoA)

add_data now natively supports Array references at the root level. When targeting an Array, it iterates through the source array and merges data at the corresponding indices.

$data = [ 
    { id => 1, name => 'Alice' } 
];

$n = [ 
    { role => 'Admin' },             # Updates index 0
    { id => 2, name => 'Bob' }       # Creates index 1
];

add_data($data, $n);

Resulting Structure:

[
    { "id": 1, "name": "Alice", "role": "Admin" },
    { "id": 2, "name": "Bob" }
]

Advanced Structural Coercion & Cross-Merging

add_data strictly enforces the primary structure of your target reference (determined by inspecting its outer and inner bounds). If you mix Array and Hash types, the function automatically coerces the incoming data to match the target.

1. Inner Coercion (Mixing Rows):

Target is HoH: Source Array rows are read in pairs and converted to key-value pairs.
Target is HoA: Source Hash rows are flattened into key-value pairs and pushed onto the array.

2. Root-Level Coercion (Mixing Outer Containers):

Target is Array, Source is Hash: The function evaluates the Hash keys as numeric indices. (e.g., source key "0" merges into target array index [0]). Non-numeric keys are safely ignored.
Target is Hash, Source is Array: The function converts the Array indices into stringified Hash keys. (e.g., source array index [1] merges into target hash key "1").

Source is a mixed Hash. Keys dictate the target array index!

$n = {
    '0' => { y => 20 },                 # Merges into $data->[0]
    '1' => [ 'z', 30 ],                 # Array pair coerced to Hash, creates $data->[1]
    'ignored' => { k => 'v' }           # Ignored: cannot map to an array index
};

add_data($data, $n);

Resulting Structure strictly remains an Array of Hashes:

[
    { "x": 10, "y": 20 },
    { "z": 30 }
]

NB: If add_data is called on a completely empty target reference (e.g., $data = {} or $data = []), it will intelligently infer the required inner structure (Hashes vs Arrays) by inspecting the first valid row of the source data.

aov

Warning: assumes normal distribution

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 * 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.

Input Parameters

| Parameter | Type | Default | Description | Example | | --- | --- | --- | --- | --- | | data_sv | HashRef or ArrayRef | (Required) | The dataset to analyze. Accepts a Hash of Arrays (HoA) or Array of Hashes (AoH). If no formula is provided, it must be an HoA to allow automatic stacking (mimicking R's stack() on a named list). | | formula_sv | String | undef | A symbolic description of the model to be fitted. If omitted, the formula automatically defaults to 'Value ~ Group' and the input data is stacked. | 'yield ~ N * P' |

Output Variables

The function returns a single HashRef containing the evaluated statistical results. Because the keys map dynamically to the terms parsed from your formula, the structure will vary based on your inputs.

| Parameter | Type | Default | Description | Example | | --- | --- | --- | --- | --- | | (Term Name) | HashRef | undef | A nested hash for each independent term in the formula (e.g., 'Group', 'N:P'), containing its ANOVA table statistics. | {'Df' => 1, 'Sum Sq' => 14.2, 'Mean Sq' => 14.2, 'F value' => 25.81, 'Pr(>F)' => 0.0004} | | Residuals | HashRef | undef | A nested hash containing the residual (error) statistics for the fitted model. | {'Df' => 10, 'Sum Sq' => 5.5, 'Mean Sq' => 0.55} | | group_stats | HashRef | undef | A nested hash containing descriptive statistics (mean and size / count) for every column evaluated in the original unstacked data structure. | {'mean' => {'A' => 2.1, 'B' => 5.4}, 'size' => {'A' => 10, 'B' => 10}} |

omitting formula

As of version 0.07, in the case of an omitted formula, stacking is done:

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

is the equivalent of:

yield <- c(5.5, 5.4, 5.8, 4.5, 4.8, 4.2)
ctrl <- c(1,     1,   1,   0,   0,   0)

# Combine them into a named list (the R equivalent of your hash)
my_list <- list(yield = yield, ctrl = ctrl)

# Convert the list into a "long" dataframe
# This creates two columns: "values" and "ind" (the group name)
my_data <- stack(my_list)

# Rename columns for clarity (optional but good practice)
colnames(my_data) <- c("Value", "Group")
anova_model <- aov(Value ~ Group, data = my_data)
summary(anova_model)

in R

chisq_test

The chisq_test function performs chi-squared contingency table tests and goodness-of-fit tests. It natively accepts both arrays and hashes (1D and 2D) and mathematically mirrors R's chisq.test(), returning a structured hash reference of the results.

For 2x2 matrices, Yates' Continuity Correction is applied automatically.

Accepted Inputs

| Input Type | Data Structure | Applied Test | | --- | --- | --- | | 1D Array | [ $v1, $v2, ... ] | Chi-squared test for given probabilities | | 2D Array | [ [ $v1, $v2 ], [ $v3, $v4 ] ] | Pearson's Chi-squared test (Yates' correction if 2x2) | | 1D Hash | { key1 => $v1, key2 => $v2 } | Chi-squared test for given probabilities | | 2D Hash | { row1 => { c1 => $v1, c2 => $v2 } } | Pearson's Chi-squared test (Yates' correction if 2x2) |

Output Object Structure

The function returns a single Hash Reference containing the following key-value pairs. The internal structure of expected and observed will always identically match the structure of your input.

| Key | Data Type | Description | | --- | --- | --- | | data.name | String | Identifies the input type (e.g., "Perl ArrayRef" or "Perl HashRef"). | | expected | Array/Hash Ref | The expected frequencies, matching the geometry of the input. | | method | String | The specific statistical test applied. | | observed | Array/Hash Ref | The original data passed to the function. | | p.value | Float | The calculated p-value of the test. | | parameter | Hash Ref | Contains the degrees of freedom (df). | | statistic | Hash Ref | Contains the test statistic (X-squared). |

1. Two-Dimensional Array

Passing an Array of Arrays (AoA) triggers a standard Pearson's Chi-squared test. If the input is exactly a 2x2 matrix, Yates' continuity correction is applied automatically.

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

Output:

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

2. One-Dimensional Array (Goodness of Fit)

Passing a flat Array Reference triggers a Goodness of Fit test, assuming equal expected probabilities across all items.

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

Output:

{
    'data.name' => 'Perl ArrayRef',
    'expected'  => [ 20, 20, 20 ],
    'method'    => 'Chi-squared test for given probabilities',
    'observed'  => [ 10, 20, 30 ],
    'p.value'   => 0.00673794699908547,
    'parameter' => { 'df' => 2 },
    'statistic' => { 'X-squared' => 10 }
}

3. Two-Dimensional Hash (Pearson's Chi-squared)

Passing a Hash of Hashes (HoH) applies the exact same logic as a 2D Array, but preserves your nested string keys in the output. This is particularly useful when mapping data extracted directly from JSON, databases, or categorical mappings.

my $data = {
    GroupA => { Success => 10, Failure => 15 },
    GroupB => { Success => 20, Failure => 5  }
};

my $res = chisq_test($data);

Output:

{
    'data.name' => 'Perl HashRef',
    'expected'  => {
    'GroupA' => { 'Failure' => 10, 'Success' => 15 },
    'GroupB' => { 'Failure' => 10, 'Success' => 15 }
},
'method'    => "Pearson's Chi-squared test with Yates' continuity correction",
    'observed'  => {
    'GroupA' => { 'Failure' => 15, 'Success' => 10 },
    'GroupB' => { 'Failure' => 5,  'Success' => 20 }
    },
    'p.value'   => 0.00937475878430379,
    'parameter' => { 'df' => 1 },
    'statistic' => { 'X-squared' => 6.75 }
}

4. One-Dimensional Hash (Goodness of Fit)

Flat Hash References evaluate Goodness of Fit while preserving your categorical keys in the expected and observed output blocks.

my $data = { 
	Apples  => 10, 
	Oranges => 20, 
	Bananas => 30 
};

my $res = chisq_test($data);

col2col

my $result = col2col( $data, $command );
my $result = col2col( $data, $command, $cols );   # restrict the "from" columns

Compares every column against every other column in a dataset and returns a hash of hashes:

$result->{ $col_a }{ $col_b }   # outcome of comparing column A with column B

The diagonal is skipped (a column is never compared with itself), so each inner hash holds an entry for every other column.

$data may be given in any of three shapes — array of hashes, hash of arrays, or hash of hashes — and col2col detects which one it received.

$command is usually a block (anonymous sub) that compares the two columns. The two columns are passed to the block in @_, so you read them as $_[0] and $_[1]:

my $result = col2col( \%data, sub { cor( $_[0], $_[1], 'spearman' ) } );

$_[0] and $_[1] are array refs holding the two columns. There are no package globals, so nothing you declare in your own script (a $c1, an $a, etc.) can ever clash, and you need no our/use vars declarations. If you prefer names, unpack into your own lexicals first:

my $result = col2col( \%data, sub { my ( $c1, $c2 ) = @_; cor( $c1, $c2, 'spearman' ) } );

Pass the columns as explicit scalars. Because the built-ins are prototyped, write cor( $_[0], $_[1], 'spearman' ), not cor( @_, 'spearman' ) — a prototyped sub forces @_ into scalar context, collapsing it to the element count (2) instead of the two columns. (&cor( @_, 'spearman' ) also works, since the & sigil bypasses the prototype, but the explicit form is clearer.)

As a shorthand, $command may instead be a bare function name (a string), which is treated as fn( $col_a, $col_b ):

my $result = col2col( \%data, 'cor' );   # same as sub { cor( $_[0], $_[1] ) }

Whatever the block or function returns is stored verbatim.

Undefined values are always removed pairwise. For each pair, any row where either column is undef or non-numeric is dropped, so the two columns are always aligned and the same length — exactly what correlation needs, and a sound (complete-case) basis for the two-sample tests too. If you need a column's full set of values regardless of the other column, clean it yourself inside the block.

Restricting which columns are compared

By default every column is compared against every other, which is N * (N-1) calls. When you only care about how one column, or a handful, relates to the rest, pass an optional third argument: a column name, or an array ref of names. Only those columns are then used as the first ($col_a, outer-key) side of each comparison; each is still compared against every other column. This runs faster and returns a smaller result, because the work and the output shrink to (chosen columns) * (N-1).

How does just "age" relate to every other column?

my $r = col2col( $data, sub { cor( $_[0], $_[1] ) }, 'age' );
print $r->{age}{weight}, "\n";    # only the "age" row is present
# $r has no {height}{...} or {weight}{...} rows

# A handful of columns of interest, each vs everything else
my $r2 = col2col( $data, sub { cor( $_[0], $_[1] ) }, [ 'age', 'height' ] );
# $r2 has exactly the {age}{...} and {height}{...} rows

The result is identical to the corresponding rows of an unrestricted run, only the rows you didn't ask for are omitted. Naming a column that isn't in the data is a fatal error, so typos surface immediately. Omitting the argument (or passing undef) keeps the original every-column-vs-every-column behavior.

array of hash input

Row-major: an array ref whose elements are hash refs ($data->[$row]{$col}). Column names are the union of the keys seen across all rows.

my $rows = [
    { height => 170, weight => 65, age => 31 },
    { height => 182, weight => 84, age => 45 },
    { height => 168, weight => 60, age => 29 },
    { height => 191, weight => 92, age => 52 },
    { height => 175, weight => 71, age => 38 },
];

my $cor = col2col( $rows, 'cor' );

print $cor->{height}{weight}, "\n";   # Pearson r between height and weight
print $cor->{weight}{age},    "\n";

hash of array input

Column-major: a hash ref whose values are array refs ($data->{$col}[$row]). The keys are the column names. This is the most direct shape — each value is already a column.

my $data = {
    height => [ 170, 182, 168, 191, 175 ],
    weight => [  65,  84,  60,  92,  71 ],
    age    => [  31,  45,  29,  52,  38 ],
};

my $cov = col2col( $data, 'cov' );

print $cov->{height}{weight}, "\n";   # sample covariance

Undefined entries are skipped. For cor/cov/cor_test they are dropped pairwise, so the pair below is compared on its three complete rows only:

my $data = {
    a => [ 1,      2,     3,  4,  5 ],
    b => [ 2,  undef,     6,  8, 10 ],   # row 1 dropped for any pair touching b
};

my $cor = col2col( $data, 'cor' );
print $cor->{a}{b}, "\n";              # correlation over rows 0,2,3,4

hash of hash input

Row-major and keyed: a hash ref whose values are hash refs ($data->{$row}{$col}). The outer keys label the rows (e.g. sample IDs); the inner keys are the column names (the union across all rows).

my $samples = {
    s1 => { height => 170, weight => 65, age => 31 },
    s2 => { height => 182, weight => 84, age => 45 },
    s3 => { height => 168, weight => 60, age => 29 },
    s4 => { height => 191, weight => 92, age => 52 },
    s5 => { height => 175, weight => 71, age => 38 },
};

my $cor = col2col( $samples, 'cor' );

print $cor->{age}{weight}, "\n";

Because pairing is done within each row, the (unordered) row-key order does not affect the result — all three shapes above give the same numbers.

Examples with different `Stats::LikeR` functions

The same dataset can be run through any comparison function just by changing the block. Using the hash-of-arrays $data from above:

# Correlation coefficients (Pearson) — returns a number per pair
my $r = col2col( $data, sub { cor( $_[0], $_[1] ) } );
print $r->{height}{weight}, "\n";

# Covariance — returns a number per pair
my $c = col2col( $data, sub { cov( $_[0], $_[1] ) } );

# Correlation test — returns whatever cor_test returns
# (e.g. estimate, statistic, p_value) for each pair
my $ct = col2col( $data, sub { cor_test( $_[0], $_[1] ) } );
print $ct->{height}{weight}{p_value}, "\n";

# Welch two-sample t-test between every pair of columns
my $t = col2col( $data, sub { t_test( $_[0], $_[1] ) } );
say $t->{height}{age}{p_value};

# Two-sample Kolmogorov–Smirnov test
my $ks = col2col( $data, sub { ks_test( $_[0], $_[1] ) } );
print $ks->{height}{age}{statistic}, "\n";

# Other two-sample comparisons work the same way
my $w  = col2col( $data, sub { wilcox_test( $_[0], $_[1] ) } );   # Wilcoxon rank-sum
my $f  = col2col( $data, sub { var_test( $_[0], $_[1] ) } );      # F test for equal variances
my $kw = col2col( $data, sub { kruskal_test( $_[0], $_[1] ) } );  # Kruskal–Wallis

# For the no-argument case, a bare function name is a handy shorthand:
my $r2 = col2col( $data, 'cor' );   # same as sub { cor( $_[0], $_[1] ) }

Passing arguments

Because the block is just ordinary Perl, you pass arguments exactly the way you would call the function directly:

# Spearman instead of the default Pearson correlation (method is cor's 3rd arg)
my $sp = col2col( $data, sub { cor( $_[0], $_[1], 'spearman' ) } );

# Whatever extra arguments a function takes, pass them inline. For example, if
# t_test accepts a trailing paired flag, t_test($x, $y, $paired):
my $tp = col2col( $data, sub { t_test( $_[0], $_[1], 1 ) } );

# Combine results, scale them, call several functions — anything goes:
my $scaled = col2col( $data, sub { cor( $_[0], $_[1] ) * 100 } );

Custom subroutine

The block can run any analysis you like; $_[0] and $_[1] are the two columns (array refs, pairwise complete cases) and the return value is stored verbatim.

# Mean difference between every pair of columns
my $diff = col2col( $data, sub {
    my ( $x, $y ) = @_;
    my $mx = 0; $mx += $_ for @$x; $mx /= @$x;
    my $my = 0; $my += $_ for @$y; $my /= @$y;
    return $mx - $my;
} );

print $diff->{height}{weight}, "\n";

# Wrap a built-in and post-process its result — it reads like a normal call
my $pct = col2col( $data, sub { cor( $_[0], $_[1] ) * 100 } );

cor

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

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

Just like R, pearson, spearman, and kendall are available

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

cor_test

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

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

cov

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

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

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

dnorm

gives the density of the normal distribution, with the specified mean and standard deviation.

In other words, the predicted height of the value x, given a mean, standard deviation, and whether or not to use a log value.

returns a single scalar/number if a single value is given, otherwise returns an array reference.

Usage:

dnorm(4) # assumes a mean of 0 and standard deviation of 1

but default mean, standard deviation, and log can be passed as parameters:

$x = dnorm(0, mean => 0, sd => 2, 'log' => 0);

fisher_test

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
}

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.

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'
);

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

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

Input Parameters

| Parameter | Type | Default | Description | Example | | --- | --- | --- | --- | --- | | formula | String | None (Required) | A symbolic description of the model to be fitted. Supports operators like +, :, *, ^, and -1 (to remove the intercept). | 'am ~ wt + hp', 'y ~ x - 1' | | data | HashRef or ArrayRef | None (Required) | The dataset containing the variables used in the formula. Accepts either a Hash of Arrays (HoA) or an Array of Hashes (AoH). | \%mtcars, [{x => 1, y => 2}, ...] | | family | String | 'gaussian' | A description of the error distribution and link function to be used in the model. Currently supports 'gaussian' (identity link) and 'binomial' (logit link). | 'binomial' |

Output variables

| Variable | Type | Description | Example | | --- | --- | --- | --- | | aic | Double | Akaike's Information Criterion for the fitted model. | 123.45 | | boundary | Integer (Boolean) | 1 if the fitted values computationally reached the 0 or 1 boundary (specific to the binomial family), 0 otherwise. | 0 | | coefficients | HashRef | A hash mapping the expanded model term names to their estimated coefficient values. | {'Intercept' => 1.5, 'wt' => -0.5} | | converged | Integer (Boolean) | 1 if the Iteratively Reweighted Least Squares (IRLS) algorithm converged within the maximum iterations, 0 otherwise. | 1 | | deviance | Double | The residual deviance of the fitted model. | 15.2 | | deviance.resid | HashRef | A hash mapping data row names to their computed deviance residuals. | {'Mazda RX4' => 0.12} | | df.null | Integer | The residual degrees of freedom for the null model. | 31 | | df.residual | Integer | The residual degrees of freedom for the fitted model. | 30 | | family | String | The statistical family used to fit the model. | "gaussian" | | fitted.values | HashRef | A hash mapping data row names to the fitted mean values (the model's predictions on the scale of the response). | {'Mazda RX4' => 0.85} | | iter | Integer | The number of IRLS iterations performed before convergence or hitting the iteration limit. | 4 | | null.deviance | Double | The deviance for the null model (a baseline model containing only an intercept, or an offset of 0 if the intercept is removed). | 43.5 | | rank | Integer | The numeric rank of the fitted linear model (the number of estimated, non-aliased parameters). | 2 | | summary | HashRef | A nested hash mapping each term to its detailed summary statistics, including Estimate, Std. Error, t value / z value, and Pr(> t ) / Pr(> z ). Aliased parameters return "NaN". | {'wt' => {'Estimate' => -0.5, 'Std. Error' => 0.1, ...}} | | terms | ArrayRef | An ordered list of the expanded term names included in the model matrix. | ['Intercept', 'wt', 'hp'] |

group_by

Take a hash of arrays, hash of hashes, or array of hashes, and group a column by another column.

my $aoh_data = [
    { 'Gender' => 'Male',   'Testosterone, total (nmol/L)' => 20.5 },
    { 'Gender' => 'Female', 'Testosterone, total (nmol/L)' => 1.8 },
    { 'Gender' => 'Male',   'Testosterone, total (nmol/L)' => 18.2 },
    { 'Gender' => 'Female' } # Intentional missing target value
];

as well as

$hoh_data = {
    'Patient_A' => { 'Gender' => 'Male',   'Testosterone, total (nmol/L)' => 20.5 },
    'Patient_B' => { 'Gender' => 'Female', 'Testosterone, total (nmol/L)' => 1.8 },
    'Patient_C' => { 'Gender' => 'Male',   'Testosterone, total (nmol/L)' => 18.2 },
    'Patient_D' => { 'Gender' => 'Female' }, # Intentional missing target value
    'Patient_E' => { 'Gender' => 'Female', 'Testosterone, total (nmol/L)' => undef } # Explicit undef
    };

and

my $hoa_data = {
    'Gender'                       => ['Male', 'Female', 'Male', 'Female'],
    'Testosterone, total (nmol/L)' => [22.1,   2.5,      19.4,   undef   ]
};

then run the function thus:

group_by( $hoa_data, 'Testosterone, total (nmol/L)', 'Gender');

The output can be thought of like a hash, with the first string broken down by the second.

all become hash of arrays:

{
    Female   [
        [0] 1.8
    ],
    Male     [
        [0] 18.2,
        [1] 20.5
    ]
}

returns an empty array of hashes if neither target nor group keys are found.

Filtering

Data can be further broken down with filter/subs like in read_table:

my $testosterone = group_by($d, # group testosterone by "Gender"
    'Testosterone, total (nmol/L)',
    'Gender',
    { 'Race/Hispanic origin w/ NH Asian' => sub { $_ eq $n } },# filter
    { 'Testosterone, total (nmol/L)' => sub { $_ ne 'NA' } } # filter
);

where each filter filters on the columns, e.g. second hash keys.

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

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

hash of array entry

I feel that this is better, and more easily read, than what you get in R:

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]
);
$kt = kruskal_test(\%x);

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 $kt = kruskal_test(\@x, \@g);

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.

ljoin

Consider a hash: $h{$row}{$col}, and another hash $i{$row}{$col}. ljoin will add information for $col in %i for each $row to %h, where $row exists in both %h and %i

For example,

{
"Jack Smith"   {
    age   30
}
}

and a second hash, { "Jack Smith" { dept "Engineering" }, "Jane Doe" { age 25 } }

in this case, running ljoin(\%h, \%i) will modify %h to result:

{
"Jack Smith"   {
    age    30,
    dept   "Engineering"
}
}

lm

This is the linear models function.

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

where $mtcars is a hash of hashes

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

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

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

the dot operator also works:

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

matrix

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

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

As of version 0.10, parameters do not need to be named, so that matrix works more like R:

my $d = matrix(rnorm(32000), 1000, 32);

works as data, nrow, and ncol

max

max(1,2,3);

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

as of version 0.02, max will die if any undefined values are provided

mean

mean(1,2,3);

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

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

as of version 0.02, mean will die if any undefined values are provided

median

works like mean, taking array references and arrays:

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

as of version 0.02, median will die if any undefined values are provided

min

min(1,2,3);

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

as of version 0.02, min will die if any undefined values are provided

mode

Takes either an array or an array reference, and returns an array of the most common scalars (numbers or strings)

@arr = mode([1,3,3,3]); # returns (3)

@arr = mode('a','a','c','c','z'); # returns ('a', 'c')

oneway_test

Like ANOVA/aov but does not assume normality

hash of array input

$test_data = oneway_test({
	yield => [5.5, 5.4, 5.8, 4.5, 4.8, 4.2],
	ctrl  => [1,     1,   1,   0,   0,   0]
});

which will output a hash reference:

{
Group         {
    Df          1,
    "F value"   177.504798464491,
    "Mean Sq"   61.6533333333333,
    Pr(>F)      1.31343255160843e-07,
    "Sum Sq"    61.6533333333333
},
group_stats   {
    mean   {
        ctrl    0.5,
        yield   5.03333333333333
    },
    size   {
        ctrl    6,
        yield   6
    }
},
Residuals     {
    Df          9.81767348326473,
    "Mean Sq"   0.353783749200256,
    "Sum Sq"    3.47333333333333
}

}

array of array input

oneway_test([
   [5.5, 5.4, 5.8, 4.5, 4.8, 4.2],
   [1,     1,   1,   0,   0,   0]
	]);

which will output a nearly identical hash reference as for hash of arrays:

{
Group         {
    Df          1,
    "F value"   177.504798464491,
    "Mean Sq"   61.6533333333333,
    Pr(>F)      1.31343255160843e-07,
    "Sum Sq"    61.6533333333333
},
group_stats   {
    mean   {
        "Index 0"   5.03333333333333,
        "Index 1"   0.5
    },
    size   {
        "Index 0"   6,
        "Index 1"   6
    }
},
Residuals     {
    Df          9.81767348326473,
    "Mean Sq"   0.353783749200256,
    "Sum Sq"    3.47333333333333
}
}

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);

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 (type => 'one.sample', 'two.sample', 'paired') and alternative hypothesis (alternative => 'one.sided'). You can also pass strict => 1 to strictly evaluate both tails of the distribution.

prcomp

Principal Component Analysis

Options

Results

Returned Data Structure

The prcomp function returns a HashRef containing the following keys representing the results of the Principal Component Analysis:

| Key | Type | Description | | :--- | :--- | :--- | | sdev | ArrayRef[Number] | The standard deviations of the principal components. Mathematically, these are the square roots of the eigenvalues of the covariance matrix. | | rotation | ArrayRef[ArrayRef] | A 2D array representing the matrix of variable loadings (the eigenvectors). Each inner array represents a row, and the columns correspond to the principal components. | | x | ArrayRef[ArrayRef] | A 2D array containing the rotated data (often referred to as PCA scores). This is the original data projected onto the principal components. Note: Only present if the retx option is true. | | center | ArrayRef[Number] or 0 | The centering values used (typically the column means). Returns false (0) if centering was disabled. | | scale | ArrayRef[Number] or 0 | The scaling values used (typically the column standard deviations). Returns false (0) if scaling was disabled. | | varnames | ArrayRef[String] | The sorted names of the original variables. Note: Only present if the input data was a Hash of Arrays (HoA) or a Hash of Hashes (HoH). |

Using array of arrays

my $aoa = [ 
    [2, 4], 
    [4, 2], 
    [6, 6] 
];

my $pca = prcomp($aoa);

which returns

{
    center     [
        [0] 4,
        [1] 4
    ],
    rotation   [
        [0] [
                [0] 0.707106781186547,
                [1] 0.707106781186548
            ],
        [1] [
                [0] 0.707106781186548,
                [1] -0.707106781186547
            ]
    ],
    scale      0,
    sdev       [
        [0] 2.44948974278318,
        [1] 1.4142135623731
    ],
    x          [
        [0] [
                [0] -1.41421356237309,
                [1] -1.4142135623731
            ],
        [1] [
                [0] -1.4142135623731,
                [1] 1.41421356237309
            ],
        [2] [
                [0] 2.82842712474619,
                [1] 2.22044604925031e-16
            ]
    ]
}

Hash of Arrays

my $hoa = { B => [4, 2, 6], A => [2, 4, 6] };
my $pca = prcomp($hoa);

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

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 srand() seeds.

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');

options

| Option | Description | Example | | -------- | ------- | ------- | |comment | Comment character, by default # | comment = % or whatever| |output.type| data type for output: array of hash, hash of array, or hash of hash | 'output.type' => 'aoh'| |filter| Only take in rows with a certain filter | filter => { Sex => sub {$_ eq 'f'} }| |row.names | include row names in retrieved data; off by default | | |sep | field separator character; synonym with delim| sep => "\t" | | delim| field separator character; synonym with sep| delim => "\t" |

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'
);

the default delimiter is , Suffixes .csv and .tsv are automatically detected from file names, but if specified, are overridden by delim and/or sep. sep is given priority.

rnorm

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

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

runif

Make an approximately uniform distribution into an array

named arguments

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

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

positional args

this is to match R's behavior:

runif( 9 )

will make 9 numbers in [0,1]

runif(9, 0, 99)

will match n, min, and max respectively

sample

take a sample of hash or array slices.

my $h = sample(\%h, 4); # take 4 hash keys and their values into $h

or, alternatively, with arrays:

my $arr = sample(\@arr, 3); # take 3 indices of an array

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 => 1 });

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

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

sd

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

Correct answer is 2.1380899352994

sd can accept both array references as well as arrays:

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

As of version 0.02, sd will croak/die if any undefined values are provided.

seq

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

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);

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");
}

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");
}

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
}

sum

returns sum, but using both arrays and array references.

my $test_data = [1..8];
sum($test_data)

which I prefer, compared to List::Util's required casting into an array:

sum(@{ $test_data });

which passing a reference is shorter and much easier to read. Stats::LikeR, however, will work for both

as of version 0.02, sum will cause the script to die if any undefined values are provided

summary

Analogous to R's summary, but does not deal with outputs from other functions. summary only describes data as it is entered. An option nrows or its synonym nrow specifies the maximum number of rows that will print.

array of array input

my @arr;
foreach my $i (0..18) {
	push @arr, runif(22);
}

and then summary(\@arr), or summary(@arr)

---------------------------------------------------------------------------
Index  # values      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
---------------------------------------------------------------------------
     0       22   0.04312     0.286    0.4975    0.5121    0.7296    0.9633 
     1       22   0.05932    0.1483     0.495    0.4737    0.7699    0.9371 
     2       22   0.02742    0.1588    0.4045    0.4325    0.6682    0.9878 
     3       22  0.009233    0.2552    0.5398    0.5147    0.7755    0.9808 
     4       22   0.06727    0.2432    0.5019    0.4855    0.7121    0.9043 
     5       22  0.001032    0.1646    0.3021    0.3727    0.5704    0.9556

hash of array input

$test_data = summary(
	{
		A => runif(9),
		B => runif(9)
	},
);

t_test

There are 1-sample and 2-sample t-tests, from one or two arrays:

my $t_test = t_test( $array1, mu => 0.2334 );

or 2-sample:

$t_test = t_test(
	$array1,	$array2,
    paired => 1
);

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 x and y, just like in R:

$t_test = t_test(
	'x' => $array1, 'y' => $array2,
    paired => 1
);

Parameters

Return Hash

transpose

Transposes a two-dimensional data structure, swapping rows and columns. Accepts either an array of arrays or a hash of hashes. Returns a new reference of the same type; the input is never modified.

Array of array input

Takes a reference to an array of array references and returns a new AoA where output[j][i] = input[i][j].

my $matrix = [[1, 2, 3], [4, 5, 6]];
my $t = transpose($matrix);
# [[1, 4],
#  [2, 5],
#  [3, 6]]

All rows must be the same length; a ragged input is a fatal error. undef is valid as an element value and is preserved exactly. An empty outer array or an array of empty rows both return [].

Dies if:

any inner element is not an array reference
rows differ in length (ragged array)

Hash of hash input

Takes a reference to a hash of hash references and returns a new HoH where output{col}{row} = input{row}{col}.

my $table = { alice => { score => 97, grade => 'A' }, bob   => { score => 84, grade => 'B' } };
my $t = transpose($table);
# { score => { alice => 97,  bob => 84  },
#   grade => { alice => 'A', bob => 'B' } }

Inner keys do not need to be uniform across rows. If a given column key appears in only some rows, the output hash for that column will simply contain only those rows — no padding or undef-filling is performed.

my $sparse = {
a => { x => 1, y => 2 },
b => { x => 3, z => 4 } };

my $t = transpose($sparse);
# { x => { a => 1, b => 3 },
#   y => { a => 2 },
#   z => { b => 4 } }

An empty outer hash or an outer hash whose inner hashes are all empty both return {}.

Dies if any inner element is not a hash reference

value_counts

Count the values in a given data set, return a hash reference showing how many times each particular value is present.

Scalar

$hash = value_counts('c');

returns { c => 1 }

Array reference

value_counts(['a','b','b']);

returns { a => 1, b => 2}

Array

my $value_counts = value_counts('a','b','b');

like an array reference above, returns { a => 1, b => 2}

Hash

my $value_counts = value_counts( { A => 'a', B => 'a', C => 'b' } );

returns { a => 2, b => 1}

Hash of array

my $value_counts = value_counts({ 'a' => ['j', 't', 't'], 'b' => ['j', 't', 'v']});

without a key (like above), the occurences of j, t, and v are counted.

With a key, like a for above, only values within that hash key are counted:

my $vc = value_counts({ 'a' => ['j', 't', 't'], 'b' => ['j', 't', 'v']}, 'a');

Hash of hash (table)

$hash = value_counts( {
    A => {
        a => 'x',
        b => 'z'
    },
    B => {
        a => 'x'
    },
    C => {
        a => 'y'
    }
}, 'a');

the column, or second hash key, that you wish to count, is specified at the command line

var

as simple as possible:

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

as of version 0.02, var will die if any undefined values are provided

like min, max, etc., var can accept array references, to make code simpler:

my $ref = \@arr;
var($ref) = var(@arr)

var_test

As described by R: Performs an F test to compare the variances of two samples from normal populations

use Stats::LikeR;

my @x = (2.9, 3.0, 2.5, 2.6, 3.2);
my @y = (3.8, 2.7, 4.0, 2.4);

my $vt = var_test(\@x, \@y);

also, conf_level can be set:

$vt = var_test(\@x, \@y, conf_level => 0.99);

as well as a ratio (from R: the hypothesized ratio of the population variances of x and y:

$test_data = var_test(\@xk, \@yk, ratio => 2);

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 (paired => 1) 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.

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' => 1);

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

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

undefined variables are printed as NA by default, but can be set as you wish using undef.val

write_table(\%data_hoa, '/tmp/undef.val.tsv', sep => "\t", 'undef.val' => 'nan')

as of version 0.07, write_table determines comma and tab-separated delimiters from the filename, but will override if sep or delim are explicitly set.

Args can also be accepted:

write_table( 'data' => \%flat, 'file' => $f );

changes

0.12

add_data can also take hash of arrays, and various mixes of data types

ljoin: Addition of restrict keywords in many places; should improve CPU performance

Better POD formatting, correction of output hash for README's add_data

chisq_test can now accept hash of hashes as input

new transpose function for switching 2D hash keys and 2D array indices, and col2col for comparing columns against columns

removed unused function from C helpers

value_counts: addition of restrict keywords in preinit, should improve CPU performance

MANIFEST.skip changed to MANIFEST.SKIP to improve CPAN testing

using is_deeply for tests of transpose, which may or may not work with CPAN testers (experimental)

Added function name to warnings, so I actually know which function is producing the error

write_table can also take file and data as args, in addition to positions

fixed write_table as it could hang if given empty col.names or row.names

Added __EXTENSIONS__ to source XS file for better CPAN testing

0.11

better POD formatting for tables

addition of MANIFEST.skip to get better testing results on CPAN

glm: bugfix for when there is no intercept in the formula, new test cases in t/glm.t

write_table now accepts simple hashes as input, in addition to hash of arrays, hash of hashes, and arrays of hashes

Better documentation for t-test

0.10

changes to compilation for CPAN, trying to get this work on Windows

Addition of prcomp and value_counts

matrix will work without key names, just like in R. Testing for matrix has improved.

0.09

context changes in XS dTHX, pTHX_, and aTHX_ to get better CPAN testing results

restrict keywords added to lm to increase speed

0.08

Speed improvement in summary of hashes.

Addition of add_data, dnorm, group_by, ljoin, and mode functions

Chi-squared function no longer has Perl wrapper, and all code is in XS, which should result in a minor speed increase with 1 less function call.

Compiler changes for GNU source and inclusion of strings.h, to ensure more CPAN testing works better.

read_table now returns hash-of-hash in {row}{column}

0.07

Addition of summary function.

Formulas can now be omitted from aov, resulting in a stacked calculation as R would think.

Addition of oneway_test for multi-group comparisons that does not assume normality like aov does.

read_table and write_table now automatically set separators for .csv files as , and .tsv files as "\t", respectively, so these values no longer need to be specified separately from the file name.

0.06

Changed compiler options so that Solaris will work

signed integers changed to unsigned in glm

Added restrict keywords to power_t_test, and made int to unsigned int

0.05

Leak testing for sample

removal of Data::Printer dependency for easier CPAN testing

switched several unsigned int variable to I32 so that clang doesn't complain

added restrict keyword for sample

0.04

addition of sample function

GNU source, to maximize compatibility and ease installation

removal of JSON dependency to ease installation

0.03

Compatibility back to Perl 5.10

0.02

back-compatible to Perl 5.10, instead of original 5.40, ensuring more people can use it

added var_test

mean, min, sum, median, var, and max die with undefined values, and print the offending indices

"group_stats" added to aov, for TukeyHSD in the future

"cor" dies when given data with standard deviation of 0

write_table now has undef.val option, which shows how undefined values are printed to tables, which is NA by default.

	Global
`s`	Focus search bar
`?`	Bring up this help dialog

	GitHub
`g` `p`	Go to pull requests
`g` `i`	Go to GitHub issues (only if GitHub is preferred repository)

	POD
`g` `a`	Go to author
`g` `c`	Go to changes
`g` `i`	Go to issues
`g` `d`	Go to dist
`g` `r`	Go to repository/SCM
`g` `s`	Go to source
`g` `b`	Go to file browse

Search terms
module: (e.g. module:Plugin)
distribution: (e.g. distribution:Dancer auth)
author: (e.g. author:SONGMU Redis)
version: (e.g. version:1.00)

Synopsis

Functions/Subroutines

add_data

Hash of Hashes (HoH)

Hash of Arrays (HoA)

Array of Hashes / Arrays (AoH / AoA)

Advanced Structural Coercion & Cross-Merging

Source is a mixed Hash. Keys dictate the target array index!

aov

Input Parameters

Output Variables

omitting formula

chisq_test

Accepted Inputs

Output Object Structure

1. Two-Dimensional Array

2. One-Dimensional Array (Goodness of Fit)

3. Two-Dimensional Hash (Pearson's Chi-squared)

4. One-Dimensional Hash (Goodness of Fit)

col2col

Restricting which columns are compared

array of hash input

hash of array input

hash of hash input

Examples with different Stats::LikeR functions

Passing arguments

Custom subroutine

cor

cor_test

cov

dnorm

fisher_test

array reference entry

hash reference entry

glm

Input Parameters

Output variables

group_by

Filtering

hist

kruskal_test

hash of array entry

R-like array entry

ks_test

ljoin

lm

matrix

max

mean

median

min

mode

oneway_test

hash of array input

array of array input

p_adjust

power_t_test

prcomp

Options

Results

Returned Data Structure

Using array of arrays

Hash of Arrays

quantile

rbinom

read_table

options

rnorm

runif

named arguments

positional args

sample

scale

sd

seq

Standard integer sequence

Fractional steps

Negative steps

shapiro_test

sum

Examples with different `Stats::LikeR` functions