Delila Program: ttest

# ttest program

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### Documentation for the ttest program is below, with links to related programs in the "see also" section.

```{   version = 1.12; (* of ttest.p 2015 Jul 20}

(* begin module describe.ttest *)
(*
name
ttest: Student's t-test

synopsis
ttest(ttestp: in, list: out, output: out)

files
ttestp:  parameters to control the program:
A set of 6 lines defines the two distributions:
N                   (integer)  for first distribution
mean                (real)     for first distribution
standard deviation  (real)     for first distribution
N                   (integer)  for second distribution
mean                (real)     for second distribution
standard deviation  (real)     for second distribution

The 7th line is the factor to divide the sample by.  If we have an
Rsequence calculated from a dimeric sequence, then the two halves are NOT
independent.  The correct calculation takes this into account by using
the same N for the one-way sites and by dividing the mean by 2.  Squaring
the standard deviation gives the variance.  This variance is divided by 2
and then square rooted to get the variance of the half sites.  If this
"sample division factor" is 1, then the calculations proceed without
them.  If the factor is 2, then the changes described above are made.

list:  Input values and calculated T value

output: messages to the user

description

This simple program performs the T test computations.

examples

7 OxyR binding site sequences were analzyed for information content
and the standard deviation calculated by the rsim.p program.
This gave 15.4 +/- 1.9 bits for n = 14 sequences.

A randomization experiment was performed and 16 sequences which bind
OxyR were recovered.  These were analyzed as above.
This gave 17.5 +/- 1.2 bits for n = 32 sequences.

Since both the sequences and their complements were used for the
calculation, only half site information should be used.

The ttest p file is:

14        n1: number of samples, sample 1
15.4      m1: mean, sample 1
1.9       s1: standard deviation, sample 1
32        n2: number of samples, sample 2
17.5      m2: mean, sample 2
1.2       s2: standard deviation, sample 2
2         sample division factor.

The resulting list file is:

********************************************************************************
old:
ttest 1.04
sample division by a factor of 2
distribution 1 | distribution 2
number                    14 |             32
mean                 7.70000 |        8.75000
standard dev.        1.34350 |        0.84853

sigma-D =        0.38914
degrees of freedom = 44
t =       -2.69827

This is significant (p < 0.02).  So the randomization did not give a similar
information content to the wild type.
********************************************************************************

ttest 1.08
sample division by a factor of 2
distribution 1 | distribution 2
number                    14 |             32
mean                 7.70000 |        8.75000
standard dev.        1.34350 |        0.84853

sigma-D =        0.38914
degrees of freedom = 44
t =       -2.69827
p =        0.99508

documentation

@book{Press1989,
author = "W. H. Press
and B. P. Flannery
and S. A. Teukolsky
and W. T. Vetterling",
title = "Numerical Recipies in Pascal.
The Art of Scientific Computing",
publisher = "Cambridge University Press",
address = "Cambridge",
year = "1989"}

@article{Schneider.oxyr,
author = "T. D. Schneider",
title = "Reading of {DNA} Sequence Logos:
Prediction of Major Groove Binding
by Information Theory",
journal = "Meth. Enzym.",
volume = "274",
pages = "445-455",
year = "1996"}

Given a t value from a Student's t test, and the
degrees of freedom, df, return the probability for a two tailed test.
The code was originally in java script, from:

Richard Lowry
Department of Psychology
Vassar College
Poughkeepsie, NY  12604-0396  USA
office:  (914)437-7381
fax:  (914)437-7538
lowry@vassar.edu
http://faculty.vassar.edu/~lowry/VassarStats.html

The original functional html containing this code
is given below the Pascal.

It was translated to Pascal by Tom Schneider.

A concise description of the t-test is given on page 1256 of:

@article{Bulyk.Church2002,
author = "M. L. Bulyk
and P. L. Johnson
and G. M. Church",
title = "{Nucleotides of transcription factor binding sites exert
interdependent effects on the binding affinities of transcription
factors}",
journal = "Nucleic Acids Res.",
volume = "30",
pages = "1255--1261",
pmid = "11861919",
pmcid = "PMC101241",
year = "2002"}

see also
rseq.p, rsim.p, multtest.p

http://www.statsol.com/tools/stattools/ttestindependenttool.html
http://faculty.vassar.edu/~lowry/VassarStats.html

Bulyk.Church2002:
http://www.ncbi.nlm.nih.gov/pubmed/11861919

author
Thomas Dana Schneider

bugs

technical notes

*)
(* end module describe.ttest *)
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