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For this example we create a small data set that has a Poisson distribution
Make/O/N=50 data1=30+poissonNoise(5)
To run bootstrap, in each iteration we draw (with replacement) 100 numbers and compute standard WaveStats on the drawn sample.
StatsResample/N=100 /ws=2/ITER=5 data1
The results for five iterations are shown in the table:
numPoints | 100 | 100 | 100 | 100 | 100 |
avg | 35.09 | 35.23 | 34.95 | 35.28 | 35.61 |
sdev | 2.19317 | 2.19667 | 2.20365 | 1.85363 | 2.14568 |
rms | 35.1578 | 35.2977 | 35.0187 | 35.3282 | 35.6739 |
adev | 1.83 | 1.8116 | 1.832 | 1.5144 | 1.6914 |
skew | -0.306796 | -0.171549 | 0.107583 | -0.276227 | -0.483667 |
kurt | -0.637302 | -0.595613 | -0.468839 | -0.173923 | -0.162058 |
sum | 3509 | 3523 | 3495 | 3528 | 3561 |
meanL1 | 34.6548 | 34.7941 | 34.5127 | 34.9122 | 35.1843 |
meanL2 | 35.5252 | 35.6659 | 35.3873 | 35.6478 | 36.0357 |
Increasing the number of samples does not change the results substantially:
StatsResample/N=10000 /ws=2/ITER=5 data1
The results for five iterations are shown in the table:
numPoints | 10000 | 10000 | 10000 | 10000 | 10000 |
avg | 35.2169 | 35.2089 | 35.2312 | 35.1799 | 35.2257 |
sdev | 2.04217 | 2.05121 | 2.06934 | 2.05897 | 2.04572 |
rms | 35.2761 | 35.2686 | 35.2919 | 35.2401 | 35.285 |
adev | 1.70327 | 1.71884 | 1.72827 | 1.71993 | 1.71226 |
skew | -0.212116 | -0.199756 | -0.192836 | -0.177744 | -0.215313 |
kurt | -0.424137 | -0.473013 | -0.439945 | -0.458874 | -0.450679 |
sum | 352169 | 352089 | 352312 | 351799 | 352257 |
meanL1 | 35.1769 | 35.1687 | 35.1906 | 35.1395 | 35.1856 |
meanL2 | 35.2569 | 35.2491 | 35.2718 | 35.2203 | 35.2658 |
Jacknife Example
We can use the Jacknife test to analyze the standard deviation of the same data. For this application our user function can be written in the form:
Function jackFunc(inWave) Wave inWave WaveStats/Q inWave return V_sdev End
To run the Jacknife test execute:
StatsResample/jckn=jackFunc data1
The results are displayed in the table:
N | 50 |
stdEstimate | 1.72 |
JKEstimate | 1.71928 |
JKTEstimate | 1.7551 |
sigmaJKEstimate | 0.165026 |
It is interesting to observe the differences between the standard deviation obtained by the bootstrap approach (above) to the oen obtained here.
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