ANOVA Statistical Programming with PHP

ANOVA Statistical Programming with PHP
Pages: 1, 2, 3, 4

Step 3: Show Box Plot

Early in your analysis you should graph your data so that you are being guided by proper overall intuitions about your data. A commonly recommended way to visualize ANOVA data is to use side-by-side box plots for each treatment level. To generate these box plots we need to compute a five-number summary for each treatment level, consisting of the minimum value, first quartile, median, third quartile, and maximum value. The showBoxPlot($params) method computes these summary values and uses them to generate the treatment-level box plots.

Test Score by Anxiety Level
Figure 2 — box plot of test anxiety data

The showBoxPlot($params) method is actually a wrapper around JpGraph library methods. The $params argument allows us to supply parameter values needed to fine tune JpGraph's output as you can see if you examine the method source code:

<?php
/**
* The showBoxPlot method is a wrapper for JPGRAPH methods.  
* The JpGraph constant defining to the root of the JpGraph
* library is specified in the config.php file.  
*
* I only do very basic $params array handling in this method.  There
* is a lot of room for improvement in making parameter handling more
* extensive (i.e., so you have more control over aspects of your plot)
* and more intelligent.
*/
function showBoxPlot($params=array()) {
  include_once JPGRAPH . "/src/JpGraph.php";
  include_once JPGRAPH . "/src/jpgraph_stock.php";

  $summary = $this->getFiveNumberSummary();
  $yData   = array();

  foreach($this->levels AS $level) {
    // Data must be in the format : q1, q3, min, max, median.
    $plot_parts = array("q1","q3","min","max","median");

    foreach($plot_parts AS $part) {
      $yData[] = $summary[$level][$part];
    }
  }

  $figureTitle = $params["figureTitle"];
  $xTitle      = $params["xTitle"];
  $yTitle      = $params["yTitle"];

  if(!isset($figureTitle))
    $figureTitle = "Figure 1";

  if(!isset($xTitle))
    $xTitle = "x-level";    

  if(!isset($yTitle)) 
    $yTitle = "y-level";        

  $plotWidth  = 400;
  $plotHeight = 300;
  $yMin       = $params["yMin"];
  $yMax       = $params["yMax"];
  $yTicks     = $params["yTicks"];
  $yMargin    = 35;
  $xMargin    = 15;
  $xLabels    = $this->levels;

  $graph = new Graph($plotWidth, $plotHeight);

  $graph->SetFrame(false);
  $graph->SetMarginColor('white');
  $graph->title->Set($figureTitle);
  $graph->SetScale("textlin", $yMin, $yMax);
  $graph->yscale->ticks->Set($yTicks);
  $graph->xaxis->SetTickLabels($xLabels);
  $graph->xaxis->SetTitle($xTitle,"center");
  $graph->xaxis->SetTitleMargin($xMargin);
  $graph->yaxis->SetTitle($yTitle, "center");
  $graph->yaxis->SetTitleMargin($yMargin);

  // Create a new box plot.
  $bp = new BoxPlot($yData);

  // Indent bars so they don’t start and end at the edge of the plot area.
  $bp->SetCenter();

  // Width of the bars in pixels.
  $bp->SetWidth(25);

  // Set bar colors
  $bp->SetColor('black','white','black','white');

  // Set median colors
  $bp->SetMedianColor('black','black');
  $graph->Add($bp);

  if (isset($params["outputFile"])) {
    $outputFile = $params["outputFile"];
    $graph_name = "temp/$outputfile";      
  } else {
    $graph_name = "temp/boxplot.png";
  }

  $graph->Stroke($graph_name);

  echo "<img src='$graph_name' vspace='15' alt='$figureTitle'>";      
}
?>

Step 4: Show Descriptive Statistics

Another report that we will want to see early in our analysis is a descriptive statistics report. The descriptive statistics table comes directly from the showDescriptiveStatistics() method.

Table 2. Show Descriptive Statistics

Anxiety Levels