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

  • Learn How A Global Entertainment Company Saw a 448% ROI Every business today uses software to manage systems, deliver products, and empower employees to do their jobs. But software inevitably breaks, and when it does, businesses lose money -- in the form of dissatisfied customers, missed SLAs or lost productivity. PagerDuty, an operations performance platform, solves this problem by helping operations engineers and developers more effectively manage and resolve incidents across a company's global operations. …

  • In the competitive marketplace that surrounds us today, customers shouldn't have to settle for legacy desktop or application delivery simply because they've relied on a certain vendor in the past. This white paper reviews how three customers decided to partner with VMware, and how they benefited from the latest VDI and app trends to improve the end-user experience, increase productivity, reliability and stability to deliver better SLAs - with lower cost and less time needed to manage end users.

Most Popular Programming Stories

More for Developers

RSS Feeds