WaveStats

WaveStats [flags] waveName

The WaveStats operation computes several values associated with the named wave.

Flags

/ALPH=val	Sets the significance level for the confidence interval of the mean (default val =0.05).
/C=method	Calculates statistics for complex waves only. Has no effect on real waves.
	You can use method in various combinations to process the real, imaginary, magnitude, and phase of the wave. The result is stored in the wave M_WaveStats (see Details for format).
	method =0: Default; the imaginary part of waveName is ignored. Use /W to also store statistics in M_WaveStats. method =1: Calculates statistics for real part of waveName and stores it in M_WaveStats. method =2: Calculates statistics for imaginary part of waveName and stores the result in M_WaveStats. method =4: Calculates statistics for magnitude of waveName, i.e., sqrt(real^2 +imag^2), and stores the result in M_WaveStats. method =8: Calculate statistics for phase of waveName using atan2(imag,real).
	If you use a single method the results are stored both in M_WaveStats and in the standard variables (e.g., V_avg, etc.). If you specify a method that is a combination of more than one binary field then the variables reflect the results for the lowest chosen field and all results are stored in the wave M_WaveStats.
	For example, if you use /C=12, the variables will be set for the statistics of the magnitude and M_WaveStats will contain columns corresponding to the magnitude and to the phase.
	In this mode V_numInfs will always be zero.
	note If you invoke this operation and M_WaveStats already exists in the current data folder, it will be either overwritten or initialized to NaN according to the /C flag.
/CCL	When computing per-column statistics using /PCST, /CCL tells Igor to copy the column dimension labels of the input to the corresponding columns of M_WaveStats. /CCL was added in Igor Pro 9.00.
/DEST=wStats	Specify a destination wave for WaveStats in place of the default M_WaveStats. Note that in order for the operation to create the destination wave, you must also specify the appropriate combination of /W and /C flags.
	This flag was added in Igor Pro 10.00.
/FREE	Creates the user-specified destination wave as a free wave. Note that this flag does not affect the default M_WaveStats or W_ZScores.
	/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.
/M=moment	Calculates statistical moments.
	moment =1: Calculates the lower moments: V_avg, V_npnts, V_numInfs, V_numNaNs. Use it if you do not need the higher moments. moment =2: Default; calculates both the lower moments and the higher order quantities: V_sdev, V_rms, V_adev, V_skew, v_kurt.
/P	Causes WaveStats to set the location output variables in terms of unscaled index values instead of the default scaled index values. The location output variables are:
	V_minRowLoc, V_maxRowLoc, V_minColLoc, V_maxColLoc V_minLayerLoc, V_maxLayerLoc, V_minChunkLoc, V_maxChunkLoc
	For 1D waves, V_minRowLoc and V_maxRowLoc are always unscaled.
	/P requires Igor Pro 8.03 or later.
/PCST	Computes the statistics on a per-column basis for a real valued wave of two or more dimensions. The results are saved in the wave M_WaveStats which has the same number of columns, layers and chunks as the input wave and where the rows, designated by dimension labels, contain the standard WaveStats statistics. All the V_ variables are set to NaN. Note that this flag is not compatible with the flags /C, /R, /RMD.
	The /PCST flag was added in Igor Pro 7.00.
/Q	Prevents results from being printed in history.
/R=(startX,endX )	Specifies an X range of the wave to evaluate.
/R=[startP,endP ]	Specifies a point range of the wave to evaluate.
	If you specify the range as /R=[startP ] then the end of the range is taken as the end of the wave. If /R is omitted, the entire wave is evaluated.
/RMD=[firstRow , lastRow ][firstColumn , lastColumn ][firstLayer , lastLayer ][firstChunk , lastChunk ]
	Designates a contiguous range of data in the source wave to which the operation is to be applied. This flag was added in Igor Pro 7.00.
	You can include all higher dimensions by leaving off the corresponding brackets. For example:
	/RMD=[firstRow,lastRow]
	includes all available columns, layers and chunks.
	You can use empty brackets to include all of a given dimension. For example:
	/RMD=[][firstColumn,lastColumn]
	means "all rows from firstColumn to lastColumn".
	You can use a * to specify the end of any dimension. For example:
	/RMD=[firstRow,*]
	means "from firstRow through the last row".
/W[=mode]	If the optional mode is not used, the operation stores results in the various V_ variables. For complex waves when /C is not specified, the statistics are computed for the real part only.
	mode=0: The operation stores the results in the V_ variables only and prints them to the history (subject to /Q). For complex waves, if /C is specified with a non-zero method, the operation creates the corresponding M_WaveStats wave. mode=1: The operation saves the results in both the V_ variables and in the wave M_WaveStats. mode=2: The operation stores the results only in M_WaveStats and does not print the V_ variables. When executed from a user function, the variables are created but are not updated by the operation.
/Z	No error reporting.
/ZSCR	Computes z scores
	$\displaystyle z_{i}=\frac{Y_{i}-\bar{Y}}{\sigma},$
	which are saved in W_ZScores.

Details

WaveStats uses a two-pass algorithm to produce more accurate results than obtained by computing the binomial expansions of the third and fourth order moments.

WaveStats returns the statistics in the automatically created variables:

V_npnts	Number of points in range excluding points whose value is NaN or INF.
V_numNans	Number of NaNs.
V_numINFs	Number of INFs.
V_avg	Average of data values.
V_sum	Sum of data values.
V_sdev	Standard deviation of data values,
	$\displaystyle \sigma=\sqrt{\frac{\sum\left(Y_{i}-V\_avg\right)^{2}}{V\_npnts-1}}$
	"Variance" is V_sdev2.
V_sem	Standard error of the mean $\displaystyle { sem }=\frac{\sigma}{\sqrt{V\_npnts}}$
V_rms	RMS of Y values $\displaystyle =\sqrt{\frac{1}{V\_npnts} \sum Y_{i}^{2}}$
V_adev	Average deviation $\displaystyle =\frac{1}{V\_npnts } \sum_{i=0}^{{V\_npts }-1}\left\|Y_{i}-\bar{Y}\right\|$
V_skew	Skewness $\displaystyle =\frac{1}{V\_npnts} \sum_{i=0}^{V\_npnts-1}\left(\frac{Y_{i}-\bar{Y}}{\sigma}\right)^{3}$
V_kurt	Kurtosis $\displaystyle =\left(\frac{1}{V\_npnts} \sum_{i=0}^{V\_npnts-1}\left(\frac{Y_{i}-\bar{Y}}{\sigma}\right)^{4}\right)-3$
V_minloc	X location of minimum data value.
V_min	Minimum data value.
V_maxloc	X location of maximum data value.
V_max	Maximum data value.
V_minRowLoc	Row containing minimum data value. See /P above for further information.
V_maxRowLoc	Row containing maximum data value. See /P above for further information.
V_minColLoc	Column containing minimum data value (2D or higher waves). See /P above for further information.
V_maxColLoc	Column containing maximum data value (2D or higher waves). See /P above for further information.
V_minLayerLoc	Layer containing minimum data value (3D or higher waves). See /P above for further information.
V_maxLayerLoc	Layer containing maximum data value (3D or higher waves). See /P above for further information.
V_minChunkLoc	Chunk containing minimum data value (4D waves only). See /P above for further information.
V_maxChunkLoc	Chunk containing maximum data value (4D waves only). See /P above for further information.
V_startRow	The unscaled index of the first row included in calculating statistics.
V_endRow	The unscaled index of the last row included in calculating statistics.
V_startCol	The unscaled index of the first column included in calculating statistics. Set only when /RMD is used.
V_endCol	The unscaled index of the last column included in calculating statistics. Set only when /RMD is used.
V_startLayer	The unscaled index of the first layer included in calculating statistics. Set only when /RMD is used.
V_endLayer	The unscaled index of the last layer included in calculating statistics. Set only when /RMD is used.
V_startChunk	The unscaled index of the first chunk included in calculating statistics. Set only when /RMD is used.
V_endChunk	The unscaled index of the last chunk included in calculating statistics. Set only when /RMD is used.

WaveStats prints the statistics in the history area unless /Q is specified. The various multidimensional min and max location variables will only print to the history area for waves having the appropriate dimensionality.

The format of the M_WaveStats wave is:

Row	Statistic
0	numPoints
1	numNaNs
2	numInfs
3	avg
4	sdev
5	rms
6	adev
7	skew
8	kurt
9	minLoc
10	min
11	maxLoc
12	max
13	minRowLoc
14	minColLoc
15	minLayerLoc
16	minChunkLoc
17	maxRowLoc
18	maxColLoc
19	maxLayerLoc
20	maxChunkLoc
21	startRow
22	endRow
23	sum
24	meanL1
25	meanL2
26	sem
27	startCol
28	endCol
29	startLayer
30	endLayer
31	startChunk
32	endChunk

meanL1 and meanL2 are the confidence intervals for the mean

$$\displaystyle { MeanL } 1={V\_avg}-t_{\alpha, v} \frac{V\_sdev}{\sqrt{V\_npnts}},$$

and

$$\displaystyle { MeanL2 }={V\_avg}+t_{\alpha, v} \frac{{V\_sdev}}{\sqrt{{V\_npnts}}}$$

where t_a,v is the critical value of the Student T distribution for alpha significance and degree of freedom v =V_npnts -1.

Use Edit M_WaveStats.ld to display the results in a table with dimension labels identifying each of the row statistics.

WaveStats is not entirely multidimensional aware. Even so, much of the information computed by WaveStats is useful. See Multidimensional Waves, particularly Analysis on Multidimensional Waves for details.

See the ImageStats operation for calculating wave statistics for regions in 2D matrix waves.

See Also

See Statistical Analysis for details on other statistics.

See the ImageStats operation for calculating wave statistics for regions in 2D matrix waves.

See the APMath operation if you require higher precision than provided by double-precision floating point.

WaveMax, WaveMin, WaveMinAndMax, mean, median, Variance