StatsResample

StatsResample /N=numPoints [ /ITER=n /JCKN=ufunc /K /Q /SQ=m /WS=m /Z ] srcWave

The StatsResample operation resamples srcWave by drawing (with replacement) numPoints values from srcWave and storing them in the output wave W_Resampled or M_Resampled if /MC is used. You can iterate the process and compute various statistics on the data samples.

Flags

/DSTJ=jkWave	Specify the destination wave for the Jack-Knife statistics. If you do not specify this flag, the operation saves this output in the wave W_JackKnifeStats in the current data folder.
	This flag was added in Igor Pro 10.00.
/DSTR=rWave	Specify the destination wave for the raw samples. If you do not specify this flag, the operation saves the output in the wave W_Resampled in the current data folder. The wave will have the same number of columns as the number of iterations. Note that various flags can, as a side effect, prohibit the creation of this wave.
	This flag was added in Igor Pro 10.00.
/DSTQ=qWave	Specify the destination wave for the results of StatsQuantilesTest applied to the resampled data. If you do not specify this flag, the operation saves the results in the wave M_StatsQuantilesSamples in the current data folder. The wave has the same number of columns as the number of iterations. Note that various flags can, as a side effect, prohibit the creation of this wave.
	This flag was added in Igor Pro 10.00.
/DSTW=wWave	Specify the destination wave for the results of WaveStats applied to the resampled data. If you do not specify this flag, the operation saves these results in the wave M_WaveStatsSamples in the current data folder. The wave has the same number of columns as the number of iterations.
	This flag was added in Igor Pro 10.00.
/FREE	Creates all user-specified destination waves as free waves.
	/FREE is allowed only in functions, and only if the destination waves are simple names or wave reference structure fields.
	See Free Waves for more discussion.
	The /FREE flag was added in Igor Pro 10.00.
/ITER=n	Repeats the resampling for n iterations, which is useful only when combined with /WS or /SQ.
	The /ITER flag is ignored by the Jack-Knife analysis (/JCKN).
/JCKN=ufunc	Performs Jack-Knife analysis.
	ufunc is a user function of the format:
	Function ufunc(inWave) wave inWave //... compute some statistic for inWave return someValue End
	The results are stored in the wave W_JackKnifeStats in the current data folder. Use
	Edit W_JackKnifeStats.ld
	to display the wave with dimension labels.
	In the Jack-Knife method the operation runs N iterations where N is the number of points in srcWave. In each iteration the opeation calls the user-defined function ufunc(inWave) passing it an internal wave which contains (N-1) samples from srcWave. The function computes some user-defined statistic, say "Z", and stores it in inWave. At the end of iterations the operation uses the Z values in inWave to compute various Jack-Knife estimates. The standard estimator is defined as:
	$\displaystyle Z=\operatorname{ufunc}({srcWave}) .$
	The Jack-Knife estimator is simply:
	$\displaystyle \hat{z}=\frac{1}{n} \sum_{i=1}^{n} z_{i} .$
	The Jack-Knife t-estimator is slightly less biased. It is given by:
	$\displaystyle t=n Z-(n-1) \hat{z},$
	The estimate of the standard error is given by:
	$\displaystyle \hat{\sigma}_{\hat{z}}=\sqrt{\frac{n-1}{n} \sum_{i=1}^{n}\left(z_{i}-\hat{z}\right)^{2}} .$
	The Jack-Knife analysis ignores the /N and /ITER flags. The number of points and the number of iterations are determined by the number of points in srcWave.
	This flag is incompatible with the flags /ITER /K /MC /SQ and /WS.
/K	Kills W_Resampled after passing it to WaveStats. When /ITER is used, W_Resampled is not saved.
/MC	Use this flag when you want to sample random (complete) rows from a multi-column 2D srcWave. The combination of /N=n with /MC results in the wave M_Resampled in the current data folder. M_Resampled will have n rows, the same number of columns and the same data type as srcWave.
/N=numPoints	Specifies the number of points sampled from srcWave.
	The /N flag is ignored by the Jack-Knife analysis (/JCKN).
/Q	No information printed in the history area.
/SQ=m	Uses StatsQuantiles to compute the data quartiles. The methods are:
	m =0: Tukey (default). m =1: Minitab. m =2: Moore and McCabe. m =3: Mendenhall and Sincich.
	See Details for information about how the results are stored.
	The default trim value is 25%.
/WS=m	Uses the WaveStats operation to calculate data statistics.
	m =0: Creates a new wave containing the samples (default). m =1: Creates the new wave and passes it to WaveStats/Q/M=1. m =2: Creates the new wave and passes it to WaveStats/Q/M=2.
	See Details for information about how the results are stored.
/Z	Ignores any errors.

Details

StatsResample can perform Bootstrap Analysis, permutations tests, and Monte-Carlo simulations. It draws the specified number of data points (with replacement) from srcWave and places them in a destination wave W_Resampled.

Specify /WS or /SQ to use the WaveStats or StatsQuantiles operations, respectively, to compute results directly from the data. StatsResample normally creates the wave W_Resampled and, optionally, the M_WaveStats and W_StatsQuantiles waves. Both options also create various V_ variables described below. If you use more than one iteration, StatsResample creates instead the waves M_WaveStatsSamples and M_StatsQuantilesSamples for the results.

M_WaveStatsSamples (with /WS) contains a column for each iteration. Each column is equivalent to the contents of M_WaveStats for that iteration. You can use the command

Edit M_WaveStatsSamples.ld

to display the results in a table using row labels, and, for example, to display a graph of the rms of the samples as a function of iteration number execute:

Display M_WaveStatsSamples[5][]

M_StatsQuantilesSamples (with /SQ) contains a column for each iteration. Each column consists of the contents of W_StatsQuantiles for the corresponding data. Here again you can execute the command

Edit M_StatsQuantilesSamples.ld

to display the wave in a table using row labels. To display a graph of the median as a function of iteration execute:

Display M_statsQuantilesSamples[2][]

Output Variables

StatsResample creates the following variables: V_Median, V_Q25, V_Q75, V_IQR, V_min, V_max, V_numNaNs, V_numINFs, V_avg, V_sdev, V_rms, V_adev, V_skew, V_kurt, and V_Sum.

These variables are valid only if you use either /SQ or /WS, but not both, and only if you do not use /ITER. Unused variables are set to NaN.

If you use /SQ the operation sets V_Median, V_Q25, V_Q75, V_IQR, V_min, and V_max.

If you use /WS the operation sets V_min, V_max, V_numNaNs, V_numINFs, V_avg, V_sdev, V_rms, V_adev, V_skew, V_kurt, and V_Sum.

See Also

Statistical Analysis, StatsSample, WaveStats, StatsQuantiles