source: project/wiki/eggref/4/statistics @ 20489

Still under testing!

== Introduction

This library is a port of [[http://compbio.uchsc.edu/Hunter_lab/Hunter/|Larry Hunter]]'s Lisp statistics library to chicken scheme.

The library provides a number of formulae and methods taken from the book "Fundamentals of Biostatistics" by Bernard Rosner (5th edition).

== Provided Functions

=== Utilities

*    average-rank
*   beta-incomplete
*    bin-and-count
*   combinations
*    factorial
*    find-critical-value
*    fisher-z-transform
*    gamma-incomplete
*    gamma-ln
*    permutations
*    random-normal

; (random-pick items) : given a list of {{items}}, returns a random item.
; (random-sample n items) : given a number of items to select, {{n}}, and a list of items to select from, {{items}}, returns a random sample without replacement of size {{n}}.
; (sign n) : given a number {{n}}, returns 0, 1 or -1 according to if {{n}} is zero, positive or negative.
; (square n) : given a number {{n}}, returns the square of {{n}}.

=== Descriptive statistics

These functions provide information on a given list of numbers.  Note, the list of items does not have to be sorted.

; (mean items) : given a list of numbers, {{items}}, returns the arithmetic mean of the items (the sum of the numbers divided by the number of numbers).
 (mean '(1 2 3 4 5)) => 3
; (median items) : given a list of numbers, {{items}}, returns the value which separates the upper and lower halves of the list of numbers.
 (median '(1 2 3 4)) => 5/2
; (mode items) : given a list of numbers, {{items}}, returns two '''values'''.  The first is a list of the ''modes'' and the second is the frequency.  (A mode of a list of numbers is the most frequently occurring value.)
 > (mode '(1 2 3 4))
 (1 2 3 4)
 1
 > (mode '(1 2 2 3 4))
 (2)
 2
 > (mode '(1 2 2 3 3 4))
 (2 3)
 2
; (geometric-mean items) : given a list of numbers, {{items}}, returns the geometric mean of the items (the result of multiplying the items together and then taking the nth root, where n is the number of items).
 (geometric-mean '(1 2 3 4 5)) => 2.60517108469735
; (range items) : given a list of numbers, {{items}}, returns the difference between the biggest and the smallest value.
 (range '(5 1 2 3 4)) => 4
; (percentile items percent) : given a list of numbers, {{items}}, and a percentage, {{percent}}, returns the item closest to the percent value if the items are sorted into order; the returned item may be in the list, or the average of adjacent values.
 (percentile '(1 2 3 4) 50) => 5/2
 (percentile '(1 2 3 4) 67) => 3
; (variance items) : given a list of numbers, {{items}}, returns the variance of the numbers.
; (standard-deviation items) : given a list of numbers, {{items}}, returns the standard deviation of the numbers.
; (coefficient-of-variation items) : given a list of numbers, {{items}}, returns 100 * (std-dev / mean) of the items.
 (coefficient-of-variation '(1 2 3 4)) => 51.6397779494322
; (standard-error-of-the-mean items) : given a list of numbers, {{items}}, returns std-dev / sqrt(length items).
  (standard-error-of-the-mean '(1 2 3 4)) => 0.645497224367903
; (mean-sd-n items) : given a list of numbers, {{items}}, returns three '''values''', one for the mean, one for the standard deviation, and one for the length of the list.
 > (mean-sd-n '(1 2 3 4))
 5/2
 1.29099444873581
 4

=== Distributional functions

*    binomial-probability
*    binomial-cumulative-probability
*    binomial-ge-probability
*    binomial-le-probability
*    poisson-probability
*    poisson-cumulative-probability
*    poisson-ge-probability
*    normal-pdf
*    convert-to-standard-normal
*    phi
*    z
*    t-distribution
*    chi-square
*    chi-square-cdf

===  Confidence intervals

*    binomial-probability-ci
*    poisson-mu-ci
*    normal-mean-ci
*    normal-mean-ci-on-sequence
*    normal-variance-ci
*    normal-variance-ci-on-sequence
*    normal-sd-ci
*    normal-sd-ci-on-sequence

=== Hypothesis testing

====  (parametric)

*    z-test
*    z-test-on-sequence
*    t-test-one-sample
*    t-test-one-sample-on-sequence
*    t-test-paired
*    t-test-paired-on-sequences
*    t-test-two-sample
*    t-test-two-sample-on-sequences
*    f-test
*    chi-square-test-one-sample
*    binomial-test-one-sample
*    binomial-test-two-sample
*    fisher-exact-test
*    mcnemars-test
*    poisson-test-one-sample

==== (non parametric)

*    sign-test
*    sign-test-on-sequence
*    wilcoxon-signed-rank-test
*    wilcoxon-signed-rank-test-on-sequences
*    chi-square-test-rxc
*    chi-square-test-for-trend

=== Sample size estimates

*    t-test-one-sample-sse
*    t-test-two-sample-sse
*    t-test-paired-sse
*    binomial-test-one-sample-sse
*    binomial-test-two-sample-sse
*    binomial-test-paired-sse
*    correlation-sse

=== Correlation and regression

*    linear-regression
*    correlation-coefficient
*    correlation-test-two-sample
*    correlation-test-two-sample-on-sequences
*    spearman-rank-correlation

=== Significance test functions

*    t-significance
*    f-significance 


== Authors

[[http://wiki.call-cc.org/users/peter-lane|Peter Lane]] wrote the scheme version of this library.  The original Lisp version was written by [[http://compbio.uhsc.edu/Hunter_lab/Hunter/|Larry Hunter]].

== License

GPL version 3.0.

== Requirements

Needs srfi-1, srfi-25, srfi-69, vector-lib, numbers, extras, foreign, format

Uses the GNU scientific library for basic numeric processing, so requires libgsl, libgslcblas and the development files for libgsl. 

== Version History

trunk, for testing