Standard Deviation code

[Alex Chambers]

Hello,

Can anyone help me with the code for calculating a standard deviation for an array of type double? I'm no good with maths at all!

inputarray(0-20) = Double type values to calculate S.D on (eg: 2.0120)
outputarray(0-20) = Would be the values for 1 S.D of inputarray

Many thanks for any help you can provide,
Alex

[Paul Dixon]

Alex,
look here:

http://en.wikipedia.org/wiki/Standard_deviation#Definition_and_calculation

It gives very simple steps for finding standard deviation of a set of numbers.

Paul.

[Alex Chambers]

Thanks Paul - I think I've got it now.

Alex

[Andre Smit]

This sub was posted to the forums previously. Apologies but I was unable to find the original author. It calcs stats of data stored in double array a.

sub pResults(a() as double)
 local i,j,n as long
 local s,ave,adev,sdev,var,skew,curt,p as double
 
 n=ubound(a())+1
 s = 0#
 FOR j = 0 TO n-1
  s = s + a(j)
 NEXT j
 ' calculate mean
 ave = s / n
 adev = 0#
 var = 0#
 skew = 0#
 curt = 0#
 FOR j = 0 TO n-1
  s = a(j) - ave
  adev = adev + ABS(s)
  p = s * s
  var = var + p
  p = p * s
  skew = skew + p
  p = p * s
  skew = skew + p
  curt = curt + p
 NEXT j
 adev = adev / n
 var = var / (n - 1)
 sdev = SQR(var)
 IF var <> 0# THEN
  skew = skew / (n * sdev ^ 3)
  curt = curt / (n * var ^ 2) - 3#
 ELSE
  stdout " No skew or kurtosis when zero variance."
 END IF
 ' print results
 stdout
 stdout " Samples n ........: " + str$(n)
 stdout " Average ..........: " + str$(ave)
 stdout " Average  Deviation: " + str$(adev)
 stdout " Standard Deviation: " + str$(sdev)
 stdout " Variance .........: " + str$(var)
 stdout " Skewness .........: " + str$(skew)
 stdout " Kurtosis .........: " + str$(curt)
 stdout
END sub

[Alex Chambers]

Thanks also Andre.

I had already figured the solution out from the Wikipedia link. Here's my code for 1 S.D - I've tested it thoroughly and it works a charm

====================================================

REGISTER sm AS EXT
REGISTER aa AS EXT
REGISTER mn AS EXT
REGISTER stdv AS EXT

REGISTER idx AS LONG
REGISTER i1 AS LONG

FOR idx = datastart TO dataend

' First calculate moving average up to this point (20 periods)

sm = 0
FOR i1 = idx - 19 TO idx
sm = sm + inputarray(i1)
NEXT i1
mn = sm / 20

' Now calculate 1 S.D for last 20 periods

sm = 0
FOR i1 = idx - 19 TO idx
aa = mn - inputarray(i1)
sm = sm + (aa * aa)
NEXT i1
sm = sm / 20

outputarray(idx) = SQR(sm) ' This is 1 S.D


NEXT idx

[Paul Purvis]

I had purchased a book a while back(many years ago) in statistics that was really a nice find.
I believe it was called either "Statistics for the Beginner" or "Simple Statistics".
I will try to find it in the next couple of days, but it was the best and easiest book on the subject of statistics i had ever read.
If i remember, the book was paperback, with large pages, black background on the cover with some bright colorful characters used to spell out the book's title.
it was cheap too.

paul

[Emil Menzel]

Probably the most useful and intelligible single book I have encountered for computing or writing programs in statistics is:

James L. Bruning & B.L. Kintz, Computational handbook of statistics, 3rd ed., 1987. Scott, Foresman Company

An extended appendix lists the BASIC source code for every statistic that is discussed, and a companion diskette can (or could, in days of yore) be ordered from the second author. The programs are written in GWBasic and in my experience they are 100% compatible with PBDOS & easily translatable into other varieties of PB.

[Roger Rines]

Here is what I use here:

'  ----------------------------------------------
'  "STDDEV"
'  Function returns the standard deviation calculation for a
'  single dimension data series.  The calculation used is
'  determined as follows:
'
'  Population Method:
'     Assign Zero To the Sample variable Or ignore it
'        eg.  Sample = 0
'  Sample Method:
'     Any value other than Zero will invoke this method
'        eg.  Sample = 1
'
FUNCTION StdDev( x() AS DOUBLE, OPTIONAL BYVAL Sample AS LONG) AS DOUBLE
   LOCAL Itm AS LONG, Count_Start AS LONG, Count_End AS LONG, Item_Count AS LONG
   Local Sum, SumSqr, MeanVal As Double

   LOCAL x_Ptr AS DOUBLE PTR
   LOCAL Sum_Ptr AS DOUBLE PTR
   LOCAL MeanVal_Ptr AS DOUBLE PTR
   LOCAL SumSqr_Ptr AS DOUBLE PTR

   '  Array Boundary Values
   Count_Start = LBOUND(x)
   Count_End = UBOUND(x)

   '  Be sure there is something to Count
   IF Count_Start < Count_End THEN

     '  Calcuate the number of array elements
      Item_Count = Count_End - Count_Start

      '  Obtain address locations
      x_Ptr = VarPtr(x(Count_Start))
      Sum_Ptr = VarPtr(Sum)
      SumSqr_Ptr = VarPtr(SumSqr)
      MeanVal_Ptr = VarPtr(MeanVal)

      For Itm = 0 To Item_Count
         @Sum_Ptr = @Sum_Ptr + @x_Ptr[Itm]
      Next Itm

      '  Determine Mean of the data series
      @MeanVal_Ptr = @Sum_Ptr / (Item_Count + 1)

      '  Sum the Squared values of the data - Mean
      For Itm = 0 To Item_Count
         @SumSqr_Ptr = @SumSqr_Ptr + (@x_Ptr[Itm] - @MeanVal_Ptr)^2
      Next Itm

      '  Select the Calculation method
      If Sample = 0 Then
         '  Population Calculation
         Function = Sqr( @SumSqr_Ptr / (Item_Count + 1))
      Else
         '  Sample Calculation
         Function = Sqr( @SumSqr_Ptr / (Item_Count ))
      End If
   ELSE
      '  When No values or just 1 element is
      '  in the array, the variance must be Zero
      FUNCTION = 0
   END IF
END FUNCTION   '  StdDev

'  ----------------------------------------------