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### A.3.5 Statistics Window

Statistics Window

The Statistics Window shows statistics for the values in each of the table's columns. You can display it using the Column Statistics () button when the chosen table is selected in the Control Window's Table List.

The calculated values are displayed in a JTable widget with a row for each column in the main table, and a column for each of a number of statistical quantities calculated on some or all of the values in the data table column corresponding to that grid row.

You can interact with this JTable in the usual ways, for instance dragging columns sideways, changing their widths, and sorting the entries by clicking on the headings.

The following columns are shown by default:

Name
  The name of the column in the main table represented by this grid row.
Mean
  The mean value of the good cells. For boolean columns, this is the proportion of good cells which are True.
SD
  The population standard deviation of the good cells.
Minimum
  The minimum value. For numeric columns the meaning of this is quite obvious. For other columns, if an ordering can be reasonably defined on them, the 'smallest' value may be shown. For instance string values will show the entry which would be first alphabetically.
Maximum
  As minimum, but shows the largest values.
nGood
  The number of non-blank cells.

Several additional items of statistical information are also calculated, but the columns displaying these are hidden by default to avoid clutter. You can reveal these by using the Display menu:

Index
  The index of the column in the table, i.e. the order in which it is displayed.
$ID
  The unique identifier label for the column in the main table.
Sum
  The sum of all the values in the column. For boolean columns this is a count of the number of True values in the column.
Variance
  The population variance of the good cells.
Sample SD
  The sample standard deviation of the good cells.
Sample Variance
  The sample variance of the good cells.
Median Absolute Deviation
  The median of absolute deviations from the median: `median(abs(x-median(x))`. This is a robust measure of statistical dispersion.
Scaled Median Absolute Deviation
  The Median Absolute Deviation (see above) multiplied by 1.4826. This is supposed to be a consistent estimator for the standard deviation, on the assumption of a normal distribution.
Skew
  Gamma 1 measure of skewness of the value distribution.
Kurtosis
  Gamma 2 measure of peakedness of the value distribution.
Row of min
  The index of the row in the main table at which the minimum value occurred.
Row of max
  The index of the row in the main table at which the maximum value occurred.
nBad
  The number of blank cells; the sum of this value and the Good cells value will be the same for each column.
Cardinality
  If the column contains a small number of distinct values then that number, the column's cardinality will be shown here. Cardinality is the number of distinct values which appear in that column. If the number of values represented is large (currently >50) or a large proportion of the non-bad values (currently >75%) then no value is shown.

Some of these quantities are suitable only for array-valued columns, and calculate per-element array statistics that are arrays of the same length as the input values (the input arrays must all be the same length):

Array nGoods
  Per-element count of the number of non-blank values in the input arrays.
Array Sums
  Per-element sum of the values in the input arrays.
Array Means
  Per-element mean of the values in the input arrays.
Array SDs
  Per-element population standard deviation of the values in the input arrays.

In addition, some quantile values can calculated on demand (by selecting their values in the Display menu, as for the previous list). The available values are:

Q001:
  value below which 0.1% of rows fall
Q01:
  value below which 1% of rows fall (1st percentile)
Quartile1:
  value below which 25% of rows fall (first quartile)
Median:
  value below which 50% of rows fall (median)
Quartile3:
  value below which 75% of rows fall (third quartile)
Q99:
  value below which 99% of rows fall (99th percentile)
Q999:
  value below which 99.9% of rows fall

These are considerably more expensive to calculate than the other statistical quantities, and so they are not provided by default (the same applies to the MAD). If you attempt to calculate them for large tables, you may get a message saying that there is insufficient memory. In this case you can use an approximate quantile calculation method which is not memory limited: see the description below of the Approximate Quantile Calculation () option.

The quantities displayed in this window are not necessarily those for the entire table; they are those for a particular Row Subset. At the bottom of the window is the Subset For Calculations selector, which allows you to choose which subset you want the calculations to be done for. By clicking on this you can calculate the statistics for different subsets. When the window is first opened, or when it is invoked from a menu or the toolbar in the Control Window, the subset will correspond to the current row subset.

The toolbar contains the following extra buttons:

Save as Table
  Clicking this button will save the quantities displayed in this window to a table on disk. It can be saved in any of the tabular formats which TOPCAT understands.
Import as Table
  The table of statistical quantities displayed by this window (rows corresponding to input table columns and columns corresponding to statistical quantities) is itself a table. By clicking this button it can be loaded into TOPCAT as a new table and manipulated in all the usual ways. This has the same effect as saving the statistics to file (see previous button) and then reloading that file.
Recalculate
  Once statistics have been calculated for a given subset they are cached and not normally recalculated again. Use this button if you want to force a recalculation because the data may have changed.
Approximate Quantile Calculation
  If selected this button will cause the quantiles to be calculated using a method which is both approximate and slower than the default (exact) method, for which reason it's usually not preferred. However, the approximate method executes in constant memory, while the exact method can fail by running out of memory for very large row counts.

For a large table the calculations may take a little while. While they are being performed you can interact with the window as normal, but a progress bar is shown at the bottom of the window. If you initiate a new calculation (by pushing the Recalculate button or selecting a new subset) or close the window during a calculation, the superceded calculation will be stopped.

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TOPCAT - Tool for OPerations on Catalogues And Tables
Starlink User Note253
TOPCAT web page: http://www.starlink.ac.uk/topcat/
Author email: m.b.taylor@bristol.ac.uk
Mailing list: topcat-user@jiscmail.ac.uk