mnshankar/two-factorial-anova

Analysis of Variance with 2 independent variables (balanced, with interaction)

, _(*1)

Classic two-factorial ANOVA (With Replication)

This package is used to output simple 2 factor ANOVA (Analysis of Variables) parameters using PHP. (AKA: Two-Way ANOVA, Two-Way Crossed ANOVA), _(*2)

Installation

Add the ANOVA package as a dependency to your composer.json file:, _(*3)

{
    "require": {
        "mnshankar/two-factorial-anova": "1.0"
    }
}

Usage

Initialize the factorial array for processing as follows: NOTE: Order in which data is passed in is important, _(*4)

*+-------------+------------------+-----------------------+
*|             |             1st Factor                   |
*|             |       1          |          2            |
*|             |                  |                       |
*+--------------------------------------------------------+
*|             |                  |                       |
*|             |       1          |          4            |
*|  2  A       |       2          |          5            |
*|  n          |       3          |          6            |
*|  d          |                  |                       |
*|             |                  |                       |
*|--F----------+------------------------------------------+
*|  a          |                  |                       |
*|  c          |                  |                       |
*|  t          |       7          |          10           |
*|  o  B       |       8          |          11           |
*|  r          |       9          |          12           |
*|             |                  |                       |
*+-------------+------------------+-----------------------+

 $obj = new ANOVA(
            array(1,2,3,4,5,6,7,8,9,10,11,12),3
        );

The above example is converting a 12 element array into a 2*2 factorial array containing 3 elements in each cell. The first parameter to the constructor is the input array and the second parameter is the number of replications (defaults to 3), _(*5)

The various ANOVA parameters can then be calculated as follows:, _(*6)

$obj->computeR();   //array of row sums
$obj->computeC();   //array of column sums
$obj->MSC();        //Mean square of columns
$obj->MSR();        //Mean square of rows
$obj->MSRC();       //Mean square interaction rc
$obj->MSE();        //Mean square residuals
$obj->Fc();         //F stat Column
$obj->Fr();         //F stat row
$obj->Frc();        //F stat interaction rc
$obj->Pc();         //P value Column
$obj->Pr();         //P value row
$obj->Prc();        //P value interaction rc

Reference

NIST/SEMATECH e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/ppc/section2/ppc232.htm, 5/4/2015., _(*7)

I acknowledge with thanks, input from Dr. Ying Zhang, Ph.D Professor & Director of Education Department of Biostatistics IU Fairbanks School of Public Health and IU School of Medicine, _(*8)