Create a Code Snippet by Logging In or Creating an Account

Averaging Histogram

Tue, 11/24/2009 - 12:44 pm

This function takes as an input irregularly spaced data (at time points in timewave) and creates evenly spaced data (with x-values at the center of each bin). The data in each bin are averaged, and the standard error of the mean is given, too. It should work with bins that have one or two points in them.

Note that the standard deviation calculated should be used with caution. In reporting the standard error of the mean, the function implicitly assumes that the variation of the data across the bin is small compared to the statistical errors in the data. In the example code below the function, this condition is not met, and the error is really a combination of a deterministic spread and statistical error.

Note that the function requires v6.1 only because it uses the new /FREE flag. If you use an earlier version, just omit the flag. You may then want to add a KillWaves statement to delete those temporary waves.

Function HistAvgSd(datawave,timewave,dt,tmin)       // average all points in interval dt; computes sd, too

    Wave datawave,timewave                      // datawave = data taken at unevenly spaced times

    Variable dt,tmin                    // dt = bin size, tmin = start time of binned data

    Variable n = numpnts(datawave)              // number of points in datawave

    Variable tmax = timewave[numpnts(timewave)-1], k=ceil((tmax-tmin)/dt)   // number of bins

    String wd_string = NameOfWave(datawave)+ "_avg", ws_string = NameOfWave(datawave) + "_sd"

    Make /o/n=(k) $wd_string=NaN,$ws_string=NaN             //  avg & sd waves

    Make /o/n=(k+1) /FREE indexwave                 // left-bin positions (temp wave)

    Wave wd = $wd_string, ws = $ws_string

    SetScale/P x tmin+dt/2,dt,"", wd, ws                    // x-scaling for average, sd waves

    SetScale/P x tmin,dt,"", indexwave                  // x-scaling for index wave

    Duplicate /o /FREE datawave datawave1                  // sorted waves (temporary)

    Duplicate /o /FREE timewave timewave1   

    Sort timewave1 timewave1,datawave1                  // sort according to times

    indexwave = BinarySearch(timewave1,x)+1                // index vals for left edges of bins

    indexwave[k] = n                            // to get all the points in last bin

    wd = mean(datawave1,indexwave[p],indexwave[p+1]-1)

    wd = (indexwave[p+1]== indexwave[p]) ? NaN : wd             // if no data in bin set to NaN

    ws = sqrt(Variance(datawave1,indexwave[p],indexwave[p+1]-1)/(indexwave[p+1]-indexwave[p]))

End

Here is some code to test the function:

•make /o/n=20 dtwave,datwave

•dtwave = enoise(1)+1

•Integrate dtwave/D=twave                     // irregularly spaced time points

•datwave = p + gnoise(1)

•display datwave vs twave

•HistAvgSd(datwave,twave,5,0)

•append datwave_avg

•ModifyGraph mode=3,marker(datwave)=8,marker(datwave_avg)=19;DelayUpdate

•ModifyGraph rgb(datwave_avg)=(1,4,52428);DelayUpdate

•ErrorBars datwave_avg Y,wave=(datwave_sd,datwave_sd)

•ModifyGraph grid(bottom)=2

Forum

Support

Gallery

Averaging Histogram

Igor Pro 9

Igor XOP Toolkit

Igor NIDAQ Tools MX