Stats (Statistical Summary)

Syntax:

    stats {<ranges>} 'filename' {matrix | using N{:M}} {name 'prefix'} {{no}output}

This command prepares a statistical summary of the data in one or two columns of a file. The using specifier is interpreted in the same way as for plot commands. See plot (p. ) for details on the index (p. ), every (p. ), and using (p. ) directives. Data points are filtered against both xrange and yrange before analysis. See set xrange (p. ). The summary is printed to the screen by default. Output can be redirected to a file by prior use of the command set print, or suppressed altogether using the nooutput option.

In addition to printed output, the program stores the individual statistics into three sets of variables. The first set of variables reports how the data is laid out in the file: The array of column headers is generated only if option set datafile columnheaders is in effect.

STATS_records	18#18	total number 15#15 of in-range data records
STATS_outofrange	19#19	number of records filtered out by range limits
STATS_invalid	19#19	number of invalid/incomplete/missing records
STATS_blank	19#19	number of blank lines in the file
STATS_blocks	19#19	number of indexable blocks of data in the file
STATS_columns	19#19	number of data columns in the first row of data
STATS_column_header	19#19	array of strings holding column headers found

The second set reports properties of the in-range data from a single column. This column is treated as y. If the y axis is autoscaled then no range limits are applied. Otherwise only values in the range [ymin:ymax] are considered.

If two columns are analysed jointly by a single stats command, the suffix "_x" or "_y" is appended to each variable name. I.e. STATS_min_x is the minimum value found in the first column, while STATS_min_y is the minimum value found in the second column. In this case points are filtered by testing against both xrange and yrange.

STATS_min		20#20	minimum value of in-range data points
STATS_max		21#21	maximum value of in-range data points
STATS_index_min		22#22	index i for which data[i] == STATS_min
STATS_index_max		23#23	index i for which data[i] == STATS_max
STATS_mean	24#24	25#25	mean value of the in-range data points
STATS_stddev	26#26	27#27	population standard deviation of the in-range data
STATS_ssd	28#28	29#29	sample standard deviation of the in-range data
STATS_lo_quartile			value of the lower (1st) quartile boundary
STATS_median			median value
STATS_up_quartile			value of the upper (3rd) quartile boundary
STATS_sum		30#30	sum
STATS_sumsq		31#31	sum of squares
STATS_skewness		32#32	skewness of the in-range data points
STATS_kurtosis		33#33	kurtosis of the in-range data points
STATS_adev		34#34	mean absolute deviation of the in-range data
STATS_mean_err		35#35	standard error of the mean value
STATS_stddev_err		36#36	standard error of the standard deviation
STATS_skewness_err		37#37	standard error of the skewness
STATS_kurtosis_err		38#38	standard error of the kurtosis

The third set of variables is only relevant to analysis of two data columns.

STATS_correlation		sample correlation coefficient between x and y values
STATS_slope		A corresponding to a linear fit y = Ax + B
STATS_slope_err		uncertainty of A
STATS_intercept		B corresponding to a linear fit y = Ax + B
STATS_intercept_err		uncertainty of B
STATS_sumxy		sum of x*y
STATS_pos_min_y		x coordinate of a point with minimum y value
STATS_pos_max_y		x coordinate of a point with maximum y value

Keyword matrix indicates that the input consists of a matrix (see matrix (p. )); the usual statistics are generated by considering all matrix elements. The matrix dimensions are saved in variables STATS_size_x and STATS_size_y.

STATS_size_x		number of matrix columns
STATS_size_y		number of matrix rows

The index reported in STATS_index_xxx corresponds to the value of pseudo-column 0 ($0) in plot commands. I.e. the first point has index 0, the last point has index N-1.

Data values are sorted to find the median and quartile boundaries. If the total number of points N is odd, then the median value is taken as the value of data point (N+1)/2. If N is even, then the median is reported as the mean value of points N/2 and (N+2)/2. Equivalent treatment is used for the quartile boundaries.

For an example of using the stats command to annotate a subsequent plot, see http://www.gnuplot.info/demo/stats.htmlstats.dem.

The stats command in this version of gnuplot can handle log-scaled data, but not the content of time/date fields (set xdata time or set ydata time). This restriction may be relaxed in a future version.