Math
|
|
|
|
<?php
/*
* This is a statistic class that accepts one or two unidimensional arrays of data.
* It returns a stat array using the getStats() method.
* If only one array is sent, it will return the min,max, sum, median, average and standard
* deviation for this array. If two arrays are sent, in addition to these values for both
* arrays, a linear regression line is computed: m is the slope b is the Yaxis intersect,
* r is the correlation, a measure of the quality of the data fit by the regression line (r=1
* being a perfect fit) and t is the "t"test, to test whether the association between X and Y
* data is real or merely apparent, I leave the user to interpret this test himself. (See the
* tutorial and the table at: http://www.bmj.com/collections/statsbk/apptabb.html).
* The regression line will be calculated only if both arrays have the same number of samples.
* Note that it is the responsibility of the user to make sure that his data are in linear form
* (For the linear regression to work, Median and Average values should be close).
* I tried to use the histogram class wrote by Jesus Castagnetto as an inheritance for
* this script, but it was too complicated since that I needed two arrays. Probably the other
* way around, using Stat1 as an inheritance for an histogram class, will be easier now.
* Tested with PHP4 beta 4.
* (c) Alain M. Samoun 3/12/00 alain@samoun.com
* License: Same as the GNU's Free Software Foundation or the open source PHP license as you
prefer;-).
This library 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
Lesser General Public License for more details.
*/
class Stat1 {
/* variables */
var $N,$NY,$MINX,$MAXX,$MAXY,$MINY,$AVGX,$AVGY,$STDVX,$STDVY,$SUMX,$SUMY,$SUMX2,$SUMY2,$SUMXY;
var $X = array(),$Y = array();
var $MEDX,$MEDY,$DEV,$m,$b,$r;
var $STATS = array();
/* Constructor */
function Stat1($X="", $Y="",$DEV=0, $title="") {
if ($X && $Y && $title) {
$this->create($X,$Y,$title);
}
}
/* Create the class */
function create($X,$Y,$title="") {
/* Check if we got a valid set of data*/
(($this->N = count($X)) > 1) or die("Not enough data, number of values : ".$this->N."n");
/* initialize values */
$this->MINX = (float) min($X);
$this->MAXX= (float) max($X);
/* Compute X Median */
# Sort values in array X
$XX = $X;
sort ($XX);
if ($this->N%2 == 0){
$this->MEDX = (($XX[($this->N)/2])+($XX[-1+($this->N/2)]))/2;
}else{
$this->MEDX = $XX[floor($this->N/2)];
}
$this->NY = count($Y);
$this->MINY = (float) min($Y);
$this->MAXY= (float) max($Y);
/* Compute Y Median */
# Sort values in array Y
$YY = $Y;
sort ($YY);
if ($this->NY%2 == 0){
$this->MEDY = (($YY[($this->NY)/2])+($YY[-1+($this->NY/2)]))/2;
}else{
$this->MEDY = $YY[floor($this->NY/2)];
}
$this->setTitle($title);
/* stats */
for ($i = 0; $i < $this->N ; $i++) {
$this->SUMX += (float) $X[$i];
$this->SUMX2 += (float) pow($X[$i],2);
$this->SUMXY += (float) $X[$i]* (float)$Y[$i];
}
$this->AVGX = (float) $this->SUMX/ (float) $this->N;
$this->STDVX = (float) sqrt(($this->SUMX2 - $this->N*pow($this->AVGX,2))/(float)($this->N - 1));
for ($i = 0; $i < $this->NY ; $i++) {
$this->SUMY += (float) $Y[$i];
$this->SUMY2 += (float) pow($Y[$i],2);
}
$this->AVGY = (float) $this->SUMY/ (float)$this->NY;
$this->STDVY = (float) sqrt(($this->SUMY2 - $this->NY*pow($this->AVGY,2))/(float)($this->NY - 1));
if ($this->NY == $this->N){
$this->DEV = (float) (($this->SUMX2 * $this->N)- ($this->SUMX * $this->SUMX));
$this->m = (float)(($this->SUMXY * $this->N)- ($this->SUMX * $this->SUMY))/$this->DEV;
$this->b = (float)(($this->SUMX2 * $this->SUMY)- ($this->SUMXY * $this->SUMX))/$this->DEV;
$this->r = (float) ($this->SUMXY -($this->N * $this->AVGX * $this->AVGY))/(($this->N-1)*$this->STDVX * $this->STDVY);
$this->t = (float) $this->r * sqrt(($this->N -2)/(1- pow($this->r,2)));
}
/* make the STATS array */
$this->STATS = array (
N=>$this->N,
NY=>$this->NY,
MINX=>$this->MINX,
MAXX=>$this->MAXX,
SUMX=>$this->SUMX,
MEDX=>$this->MEDX,
AVGX=>$this->AVGX,
STDVX=>$this->STDVX,
MINY=>$this->MINY,
MAXY=>$this->MAXY,
SUMY=>$this->SUMY,
MEDY=>$this->MEDY,
AVGY=>$this->AVGY,
STDVY=>$this->STDVY,
m=>$this->m,
b=>$this->b,
r=>$this->r,
t=>$this->t
);
}
/* sets the Title */
function setTitle($title) {
$this->TITLE=$title;
}
/* send back STATS array */
function getStats() {
return $this->STATS;
}
/* simple printStats */
function printStats() {
$s = "Statistics for : ".$this->TITLE."n";
$s .= "Number of data in X axis: $this->N n";
$s .= sprintf("Min = %-2.4ftMax = %-2.4ftAvg = %-2.4ftMED = %-2.4ftStDev = %-2.4f n",$this->MINX,$this->MAXX,$this->AVGX,$this->MEDX, $this->STDVX );
$s .= "nNumber of data in Y axis: $this->NY n";
$s .= sprintf("Min = %-2.4ftMax = %-2.4ftAvg = %-2.4ftMED = %-2.4ftStDev = %-2.4f n",$this->MINY,$this->MAXY,$this->AVGY,$this->MEDY, $this->STDVY );
if($this->NY ==$this->N){
$s .= "nLinear regression line: n";
if ($this->b >=0){
$s .= "Y = $this->m X + $this->b with correlation (r)= $this->rn "t"test (df=$this->N-2) = $this->t";
}else{
$s .= "Y = $this->m X $this->b with correlation (r)= $this->rn "t"test (df=$this->N-2) = $this->t";
}
}
echo $s;
}
} /* end of Stat1 class */
?>
|
|
|
Usage Example
|
<?
/*
* Sample test code for the Statistic and the Linear Least square regression class: Stat1
* Alain M. Samoun 3/12/00
*/
echo "
<HTML>
<BODY BGCOLOR="white">
<PRE>
";
require("Stat1.php");
/* create two arrays for testing*/
$X= array( 110, 116, 124, 129, 131, 138, 142, 150, 153, 155, 156, 159, 164, 168, 174);
$Y= array( 44, 31, 43, 45, 56, 79, 57, 56, 58, 92, 78, 64, 88, 112, 101);
/* create an instance w/o initialization */
$h = new Stat1;
/* do the calculation and print the results */
$h->create($X,$Y,"Test Stat1");
$h->printStats();
/* access the result arrays directly*/
$result = $h->getStats();
echo "nnresult is of type: ".gettype($result)."n";
while (list($key,$val) = each($result)) {
echo $key."t".$val."n";
}
echo"
</PRE>
</BODY></HTML>"
?>
|
|
|
Rate This Script
|
|
|
|
Store
Your email: