1About

Statistical functions in Common Lisp.Version 1.01July 27, 2001

• Sourced from: http://nostoc.stanford.edu/jeff/cllib/utils.lisp
• CLiki: http://www.cliki.net/Stats

Documentation from lhstats.lisp:

This comes in large part from Larry Hunter but has been significantly augmented by Jeff Shrager, partly from his own stats libraries, and partly from open source stuff borrowed from around the web. Citations and acknowledgements are given where possible.

Patches welcome (preferably via pull requests at https://github.com/mrc/lhstats)

2Larry Hunter's Code

Statistical functions in Common Lisp. Version 1.01 July 27, 2001

This code is copyright (c) 2000 by Larry Hunter (Larry.Hunter@uchsc.edu) except where otherwise noted.

Thanks to Paul Cohen for the original CLASP package. Thanks also to bug reports from Rob St. Amant.

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA

The formulas and methods used are largely taken from Bernard Rosner, "Fundamentals of Biostatistics," 5th edition. "Rosner x" is a page number. Some numeric functions were taken from CLASP, a 1994 common lisp package that implemented some of the statistical functions from "Numeric recipes in C" For CLASP functions, see copyright notice below.

These abreviations used in function and variable names:

ci	confidence interval
cdf	cumulative density function
ge	greater than or equal to
le	less than or equal to
pdf	probability density function
sd	standard deviation
rxc	rows by columns
sse	sample size estimate

3Functions provided

3.1Descriptive statistics

Mean, median, mode, geometric mean, range, percentile, variance,standard-deviation (sd), coefficient-of-variation,standard-error-of-the-mean

3.2Distributional functions

3.2.1Poisson & Binomial

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

3.3Confidence Intervals

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

3.4Hypothesis tests (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, chi-square-test-one-sample, f-test,binomial-test-one-sample, binomial-test-two-sample, fisher-exact-test,mcnemars-test, poisson-test-one-sample

3.5Hypothesis tests (non-parametric)

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

3.6Sample size estimates

t-test-one-sample-sse, t-test-two-sample-sset-test-paired-sse, binomial-test-one-sample-sse,binomial-test-two-sample-sse,binomial-test-paired-sse, correlation-sse

3.7Correlation and Regression

linear-regression, correlation-coefficient,correlation-test-two-sample, spearman-rank-correlation

3.8Significance test functions

t-significance, f-significance (chi square significance is calculatedfrom chi-square-cdf in various ways depending on the problem).

3.9Utilities

random-sample, random-pick, bin-and-count, fishers-z-transform,mean-sd-n, square, choose, permutations, round-float