TIP: Statistics

Introduction

A few weeks ago, I needed to find the correlation between two variables at my work. I began searching the net 'Net for the words "correlation" and "pearson" but couldn't find any decent piece of code.

Let me define the word correlation first:

"A correlation gives the strength of the relationship between variables" (mathworld.wolfram.com).

A normalized correlation is called the Pearson Value. The Pearson Value ranges between -1 to +1. A correlation of +1 means that there is a perfect positive linear relationship between the variables. If it's -1, there is a perfect negative relationship. 0 means no relationship at all.

To get the covariance and Pearson, you need to get a few things first.

Implementation

Average

You sum up all values and divide the sum by the number of values.

/// <summary>
/// Get average
/// </summary>

public static double GetAverage( double[] data )
{
   int len = data.Length;
   if ( len == 0 )
      throw new Exception("No data");

      double sum = 0;
      for ( int i = 0; i < data.Length; i++ )
      sum += data[i];
   return sum / len;
}

Variance & Standard Deviation

The variance is the squared differences from the average. The standard deviation is the square root of the variance.

/// <summary>
/// Get variance
/// </summary>
public static double GetVariance( double[] data )
{
   int len = data.Length;
   // Get average
   double avg = GetAverage( data );

   double sum = 0;
   for ( int i = 0; i < data.Length; i++ )
      sum += Math.Pow( ( data[i] - avg ), 2 );
   return sum / len;
}


/// <summary>
/// Get standard deviation
/// </summary>
public static double GetStdev( double[] data )
{
   return Math.Sqrt( GetVariance( data ) );
}

Covariance & Pearson

To calculate covariance, you need to get the average and standard deviation for each variable. You sum the multiplication of x - Avg(x) and y - Avg(y) and finally divide it by the length of the variables. To get the Pearson value, you divide the covariance by the multiplication of stDevX and stDevY.

/// <summary>
/// Get correlation
/// </summary>

public static void GetCorrelation( double[] x,
                                   double[] y,
                                   ref double covXY,
                                   ref double pearson)
{
   if ( x.Length != y.Length )
      throw new Exception("Length of sources is different");
   double avgX = GetAverage( x );
   double stdevX = GetStdev( x );
   double avgY = GetAverage( y );
   double stdevY = GetStdev( y );
   int len = x.Length;

   for ( int i = 0; i < len; i++ )
      covXY += ( x[i] - avgX ) * ( y[i] - avgY );
   covXY /= len;
   pearson = covXY / ( stdevX * stdevY );
}


About the Author

Eran Aharonovich

Been a programmer since 1999. Experience in: .Net, C++, C#, VB, VB.NET, ASP, ASP.NET, DLLs, COM etc. www.Noviway.com Israel

Downloads

Comments

  • There are no comments yet. Be the first to comment!

Leave a Comment
  • Your email address will not be published. All fields are required.

Top White Papers and Webcasts

  • Live Event Date: November 20, 2014 @ 2:00 p.m. ET / 11:00 a.m. PT Are you wanting to target two or more platforms such as iOS, Android, and/or Windows? You are not alone. 90% of enterprises today are targeting two or more platforms. Attend this eSeminar to discover how mobile app developers can rely on one IDE to create applications across platforms and approaches (web, native, and/or hybrid), saving time, money, and effort and introducing apps to market faster. You'll learn the trade-offs for gaining long …

  • IBM Worklight is a mobile application development platform that lets you extend your business to mobile devices. It is designed to provide an open, comprehensive platform to build, run and manage HTML5, hybrid and native mobile apps.

Most Popular Programming Stories

More for Developers

Latest Developer Headlines

RSS Feeds