TIP: Statistics

WEBINAR: On-demand webcast

How to Boost Database Development Productivity on Linux, Docker, and Kubernetes with Microsoft SQL Server 2017 REGISTER >


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.



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



  • 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

  • As all sorts of data becomes available for storage, analysis and retrieval - so called 'Big Data' - there are potentially huge benefits, but equally huge challenges...
  • The agile organization needs knowledge to act on, quickly and effectively. Though many organizations are clamouring for "Big Data", not nearly as many know what to do with it...
  • Cloud-based integration solutions can be confusing. Adding to the confusion are the multiple ways IT departments can deliver such integration...

Most Popular Programming Stories

More for Developers

RSS Feeds

Thanks for your registration, follow us on our social networks to keep up-to-date