NAME¶
PDL::Stats::Basic -- basic statistics and related utilities such as standard
deviation, Pearson correlation, and t-tests.
DESCRIPTION¶
The terms FUNCTIONS and METHODS are arbitrarily used to refer to methods that
are threadable and methods that are NOT threadable, respectively.
Does not have mean or median function here. see SEE ALSO.
SYNOPSIS¶
use PDL::LiteF;
use PDL::NiceSlice;
use PDL::Stats::Basic;
my $stdv = $data->stdv;
or
my $stdv = stdv( $data );
FUNCTIONS¶
stdv¶
Signature: (a(n); float+ [o]b())
Sample standard deviation.
stdv does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
stdv_unbiased¶
Signature: (a(n); float+ [o]b())
Unbiased estimate of population standard deviation.
stdv_unbiased does handle bad values. It will set the bad-value flag of all
output piddles if the flag is set for any of the input piddles.
var¶
Signature: (a(n); float+ [o]b())
Sample variance.
var does handle bad values. It will set the bad-value flag of all output piddles
if the flag is set for any of the input piddles.
var_unbiased¶
Signature: (a(n); float+ [o]b())
Unbiased estimate of population variance.
var_unbiased does handle bad values. It will set the bad-value flag of all
output piddles if the flag is set for any of the input piddles.
Signature: (a(n); float+ [o]b())
Standard error of the mean. Useful for calculating confidence intervals.
# 95% confidence interval for samples with large N
$ci_95_upper = $data->average + 1.96 * $data->se;
$ci_95_lower = $data->average - 1.96 * $data->se;
se does handle bad values. It will set the bad-value flag of all output piddles
if the flag is set for any of the input piddles.
Signature: (a(n); float+ [o]b())
Sum of squared deviations from the mean.
ss does handle bad values. It will set the bad-value flag of all output piddles
if the flag is set for any of the input piddles.
skew¶
Signature: (a(n); float+ [o]b())
Sample skewness, measure of asymmetry in data. skewness == 0 for normal
distribution.
skew does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
skew_unbiased¶
Signature: (a(n); float+ [o]b())
Unbiased estimate of population skewness. This is the number in GNumeric
Descriptive Statistics.
skew_unbiased does handle bad values. It will set the bad-value flag of all
output piddles if the flag is set for any of the input piddles.
kurt¶
Signature: (a(n); float+ [o]b())
Sample kurtosis, measure of "peakedness" of data. kurtosis == 0 for
normal distribution.
kurt does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
kurt_unbiased¶
Signature: (a(n); float+ [o]b())
Unbiased estimate of population kurtosis. This is the number in GNumeric
Descriptive Statistics.
kurt_unbiased does handle bad values. It will set the bad-value flag of all
output piddles if the flag is set for any of the input piddles.
cov¶
Signature: (a(n); b(n); float+ [o]c())
Sample covariance. see
corr for ways to call
cov does handle bad values. It will set the bad-value flag of all output piddles
if the flag is set for any of the input piddles.
cov_table¶
Signature: (a(n,m); float+ [o]c(m,m))
Square covariance table. Gives the same result as threading using
cov but
it calculates only half the square, hence much faster. And it is easier to use
with higher dimension pdls.
Usage:
# 5 obs x 3 var, 2 such data tables
perldl> $a = random 5, 3, 2
perldl> p $cov = $a->cov_table
[
[
[ 8.9636438 -1.8624472 -1.2416588]
[-1.8624472 14.341514 -1.4245366]
[-1.2416588 -1.4245366 9.8690655]
]
[
[ 10.32644 -0.31311789 -0.95643674]
[-0.31311789 15.051779 -7.2759577]
[-0.95643674 -7.2759577 5.4465141]
]
]
# diagonal elements of the cov table are the variances
perldl> p $a->var
[
[ 8.9636438 14.341514 9.8690655]
[ 10.32644 15.051779 5.4465141]
]
for the same cov matrix table using
cov,
perldl> p $a->dummy(2)->cov($a->dummy(1))
cov_table does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
corr¶
Signature: (a(n); b(n); float+ [o]c())
Pearson correlation coefficient. r = cov(X,Y) / (stdv(X) * stdv(Y)).
Usage:
perldl> $a = random 5, 3
perldl> $b = sequence 5,3
perldl> p $a->corr($b)
[0.20934208 0.30949881 0.26713007]
for square corr table
perldl> p $a->corr($a->dummy(1))
[
[ 1 -0.41995259 -0.029301192]
[ -0.41995259 1 -0.61927619]
[-0.029301192 -0.61927619 1]
]
but it is easier and faster to use
corr_table.
corr does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
corr_table¶
Signature: (a(n,m); float+ [o]c(m,m))
Square Pearson correlation table. Gives the same result as threading using
corr but it calculates only half the square, hence much faster. And it
is easier to use with higher dimension pdls.
Usage:
# 5 obs x 3 var, 2 such data tables
perldl> $a = random 5, 3, 2
perldl> p $a->corr_table
[
[
[ 1 -0.69835951 -0.18549048]
[-0.69835951 1 0.72481605]
[-0.18549048 0.72481605 1]
]
[
[ 1 0.82722569 -0.71779883]
[ 0.82722569 1 -0.63938828]
[-0.71779883 -0.63938828 1]
]
]
for the same result using
corr,
perldl> p $a->dummy(2)->corr($a->dummy(1))
This is also how to use
t_corr and
n_pair with such a table.
corr_table does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
t_corr¶
Signature: (r(); n(); [o]t())
$corr = $data->corr( $data->dummy(1) );
$n = $data->n_pair( $data->dummy(1) );
$t_corr = $corr->t_corr( $n );
use PDL::GSL::CDF;
$p_2tail = 2 * (1 - gsl_cdf_tdist_P( $t_corr->abs, $n-2 ));
t significance test for Pearson correlations.
t_corr does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
n_pair¶
Signature: (a(n); b(n); int [o]c())
Returns the number of good pairs between 2 lists. Useful with
corr (esp.
when bad values are involved)
n_pair does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
corr_dev¶
Signature: (a(n); b(n); float+ [o]c())
$corr = $a->dev_m->corr_dev($b->dev_m);
Calculates correlations from
dev_m vals. Seems faster than doing
corr from original vals when data pdl is big
corr_dev does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
t_test¶
Signature: (a(n); b(m); float+ [o]t(); [o]d())
my ($t, $df) = t_test( $pdl1, $pdl2 );
use PDL::GSL::CDF;
my $p_2tail = 2 * (1 - gsl_cdf_tdist_P( $t->abs, $df ));
Independent sample t-test, assuming equal var.
t_test does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
t_test_nev¶
Signature: (a(n); b(m); float+ [o]t(); [o]d())
Independent sample t-test, NOT assuming equal var. ie Welch two sample t test.
Df follows Welch-Satterthwaite equation instead of Satterthwaite (1946, as
cited by Hays, 1994, 5th ed.). It matches GNumeric, which matches R.
my ($t, $df) = $pdl1->t_test( $pdl2 );
t_test_nev does handle bad values. It will set the bad-value flag of all output
piddles if the flag is set for any of the input piddles.
t_test_paired¶
Signature: (a(n); b(n); float+ [o]t(); [o]d())
Paired sample t-test.
t_test_paired does handle bad values. It will set the bad-value flag of all
output piddles if the flag is set for any of the input piddles.
binomial_test¶
Signature: (x(); n(); p_expected(); [o]p())
Binomial test. One-tailed significance test for two-outcome distribution. Given
the number of success, the number of trials, and the expected probability of
success, returns the probability of getting this many or more successes.
Usage:
# assume a fair coin, ie. 0.5 probablity of getting heads
# test whether getting 8 heads out of 10 coin flips is unusual
my $p = binomial_test( 8, 10, 0.5 ); # 0.0107421875. Yes it is unusual.
METHODS¶
rtable¶
Reads either file or file handle*. Returns observation x variable pdl and var
and obs ids if specified. Ids in perl @ ref to allow for non-numeric ids.
Other non-numeric entries are treated as missing, which are filled with
$opt{MISSN} then set to BAD*. Can specify num of data rows to read from top
but not arbitrary range.
*If passed handle, it will not be closed here.
*PDL::Bad::setvaltobad only works consistently with the default TYPE double
before PDL-2.4.4_04.
Default options (case insensitive):
V => 1, # verbose. prints simple status
TYPE => double,
C_ID => 1, # boolean. file has col id.
R_ID => 1, # boolean. file has row id.
R_VAR => 0, # boolean. set to 1 if var in rows
SEP => "\t", # can take regex qr//
MISSN => -999, # this value treated as missing and set to BAD
NROW => '', # set to read specified num of data rows
Usage:
Sample file diet.txt:
uid height weight diet
akw 72 320 1
bcm 68 268 1
clq 67 180 2
dwm 70 200 2
($data, $idv, $ido) = rtable 'diet.txt';
# By default prints out data info and @$idv index and element
reading diet.txt for data and id... OK.
data table as PDL dim o x v: PDL: Double D [4,3]
0 height
1 weight
2 diet
Another way of using it,
$data = rtable( \*STDIN, {TYPE=>long} );
group_by¶
Returns pdl reshaped according to the specified factor variable. Most useful
when used in conjunction with other threading calculations such as average,
stdv, etc. When the factor variable contains unequal number of cases in each
level, the returned pdl is padded with bad values to fit the level with the
most number of cases. This allows the subsequent calculation (average, stdv,
etc) to return the correct results for each level.
Usage:
# simple case with 1d pdl and equal number of n in each level of the factor
pdl> p $a = sequence 10
[0 1 2 3 4 5 6 7 8 9]
pdl> p $factor = $a > 4
[0 0 0 0 0 1 1 1 1 1]
pdl> p $a->group_by( $factor )->average
[2 7]
# more complex case with threading and unequal number of n across levels in the factor
pdl> p $a = sequence 10,2
[
[ 0 1 2 3 4 5 6 7 8 9]
[10 11 12 13 14 15 16 17 18 19]
]
pdl> p $factor = qsort $a( ,0) % 3
[
[0 0 0 0 1 1 1 2 2 2]
]
pdl> p $a->group_by( $factor )
[
[
[ 0 1 2 3]
[10 11 12 13]
]
[
[ 4 5 6 BAD]
[ 14 15 16 BAD]
]
[
[ 7 8 9 BAD]
[ 17 18 19 BAD]
]
]
ARRAY(0xa2a4e40)
# group_by supports perl factors, multiple factors
# returns factor labels in addition to pdl in array context
pdl> p $a = sequence 12
[0 1 2 3 4 5 6 7 8 9 10 11]
pdl> $odd_even = [qw( e o e o e o e o e o e o )]
pdl> $magnitude = [qw( l l l l l l h h h h h h )]
pdl> ($a_grouped, $label) = $a->group_by( $odd_even, $magnitude )
pdl> p $a_grouped
[
[
[0 2 4]
[1 3 5]
]
[
[ 6 8 10]
[ 7 9 11]
]
]
pdl> p Dumper $label
$VAR1 = [
[
'e_l',
'o_l'
],
[
'e_h',
'o_h'
]
];
which_id¶
Lookup specified var (obs) ids in $idv ($ido) (see
rtable) and return
indices in $idv ($ido) as pdl if found. The indices are ordered by the
specified subset. Useful for selecting data by var (obs) id.
my $ind = which_id $ido, ['smith', 'summers', 'tesla'];
my $data_subset = $data( $ind, );
# take advantage of perl pattern matching
# e.g. use data from people whose last name starts with s
my $i = which_id $ido, [ grep { /^s/ } @$ido ];
my $data_s = $data($i, );
SEE ALSO¶
PDL::Basic (hist for frequency counts)
PDL::Ufunc (sum, avg, median, min, max, etc.)
PDL::GSL::CDF (various cumulative distribution functions)
REFERENCES¶
Hays, W.L. (1994). Statistics (5th ed.). Fort Worth, TX: Harcourt Brace College
Publishers.
AUTHOR¶
Copyright (C) 2009 Maggie J. Xiong <maggiexyz users.sourceforge.net>
All rights reserved. There is no warranty. You are allowed to redistribute this
software / documentation as described in the file COPYING in the PDL
distribution.