Stats (Statistical Summary)

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 for details on the index, every, and using directives. Data points are filtered against both xrange and yrange before analysis. See set xrange. 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:

STATS_records N total number of in-range data records
STATS_outofrange number of records filtered out by range limits
STATS_invalid number of invalid/incomplete/missing records
STATS_blank number of blank lines in the file
STATS_blocks number of indexable blocks of data in the file
STATS_columns number of data columns in the first row of data

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 min(y) minimum value of in-range data points
STATS_max max(y) maximum value of in-range data points
STATS_index_min i | yi = min(y) index i for which data[i] == STATS_min
STATS_index_max i | yi = max(y) index i for which data[i] == STATS_max
STATS_mean 11#11 = 12#1213#13y mean value of the in-range data points
STATS_stddev σy = 14#14 population standard deviation of the in-range data
STATS_ssd sy = 15#15 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 13#13y sum
STATS_sumsq 13#13y2 sum of squares
STATS_skewness 16#1613#13(y-11#11)3 skewness of the in-range data points
STATS_kurtosis 17#1713#13(y-11#11)4 kurtosis of the in-range data points
STATS_adev 12#1213#13| y-11#11| mean absolute deviation of the in-range data
STATS_mean_err σy/18#18 standard error of the mean value
STATS_stddev_err σy/19#19 standard error of the standard deviation
STATS_skewness_err 20#20 standard error of the skewness
STATS_kurtosis_err 21#21 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

When matrix is specified, all matrix entries are included in the analysis. The matrix dimensions are saved in the variables STATS_size_x and STATS_size_y.

It may be convenient to track the statistics from more than one file or data column in parallel. The name option causes the default prefix "STATS" to be replaced by a user-specified string. For example, the mean value of column 2 data from two different files could be compared by

stats "file1.dat" using 2 name "A"
stats "file2.dat" using 2 name "B"
if (A_mean < B_mean) {...}
The keyword columnheader or function columnheader(N) can be used to generate the prefix from the contents of the first row of a data file:
do for [COL=5:8] { stats 'datafile' using COL name columnheader }

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 stats.dem.

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

Copyright 1986 - 1993, 1998, 2004 Thomas Williams, Colin Kelley
Distributed under the gnuplot license (rights to distribute modified versions are withheld).