**dataTaker Logger Performs Mathematical Calculations**

**Covariance** is a method of measuring how strongly variables are related to each other. Covariance is commonly used calculation used in a wide number of areas from microclimate flux and carbon sequestration, aquiculture, stock market predictions, to measurement of the southern oscillation index. In our latest Tech Article, CAS DataLoggers shows you how to calculate covariance using a dataTaker DT80 intelligent data logger.

**When Do Variables Covary?**

- If the result of the covariance calculation is
**zero**, then the two variables are not related to one another.

- When the result is
**positive**, then the two variables have moved in the same direction. The larger the result, the more strongly related the two variables are. - If the result is
**negative**, then the two variables have a negative relationship with one another, i.e. they have moved in opposite directions.

**Covariance Formula:**

Traditionally we need the average value of each variable before we can calculate the variation of each individual sample from the average reading. However, this would be computationally intensive and tedious to implement, so for our purposes we’ll use this simplified version of the covariance formula:

*CoVar *(*A*, *B *) = *Ave *( *A *· *B *) – *Ave *(*A*) · *Ave *( *B *)

Since the average of a series of numbers is the sum of the sample divided by the number of samples taken, this is far easier to implement from a computational standpoint.

Instead of storing each sample for later processing, we only need to keep running sums of variables A, B and A*B, and keep a count of the number of samples taken.

Users can implement a simple **dataTaker** program to do this. Below is an example which is compatible with the **DT80 Series data loggers**:

**Example Program:**

** BEGIN** “COVAR”

‘============================================

‘ Schedule A (Read Variables)

‘ – Runs every 1 second

“

‘============================================

__RA1S__** LOGOFFA**

1V (=1CV, W) ‘Read the A and assign to 1CV

2V (=2CV, W) ‘Read the B and assign to 2CV

3CV (W) =3CV+1CV ‘3CV = Sum of A

4CV (W) = 4CV+2CV ‘4CV = Sum of B

5CV (W) =5CV+ (1CV*2CV) ‘5CV = Sum A*B

6CV (W) =6CV+1 ‘Number of samples

‘=============================================

‘ Schedule B (Reporting Schedule)

‘ – Reports the Covariance

‘=============================================

** RB** (“B: ”

**, ALARMS :**OV: 10KB

**, DATA:**OV: 1MB) 10S

**LOGONB**

‘Calculate Covar (A,B) and save

7CV (“Covariance”) = (5CV/6CV) – ( (3CV/6CV) * (4CV/6CV) )

‘Reset the variables and start again

1..7CV (W) = 0

__END__