## NAME

kolmov -- Kolmogorov-Smirnov test for goodness of fit.

## USAGE

`kolmov infile datcolnam reffile refcolnam comptype`

## DESCRIPTION

The Kolmogorov-Smirnov test measures how closely the statistical behavior of a sample (or a population) is approximated---either by a distribution function or by another sample. Appropriate questions one may have in mind when performing the test are "Are the differences between the observed data and my theoretical model normally distributed with zero mean?" or "Is the statistical clumping of quasars (sample 1--thought by some to be nearby objects) closer to the clumping of distant galaxies (sample 2--far away objects) or to the clumping of globular clusters (sample 3--nearby objects)?"

This task accepts data in either STSDAS tables or in ASCII list files. The name of the column containing the data should follow the file name in brackets e.g., file.tab[col]. The test may be performed against a second data sample (this is typical) or against a theoretical distribution, which may be specified in two ways: there are three distribution functions that can be calculated by the task, or the user may provide a model distribution in the second data file.

The results of the tests are the maximum discrepancies between the sample distribution and the reference distribution. The discrepancies which are computed are the 2 one-sided cases, and the two-sided case. To each discrepancy is added the probability that the 2 distributions match (note that discrepancy and probability evolve in opposite directions).

The two-sided test works best with at least 40 items in the sample. When comparing 2 samples, the probability of a match is always underestimated. When comparing with an internally generated distribution, it is assumed (both inherently by the method and by the software) that the sample data is also a distribution.

## PARAMETERS

- infile [string]
- The test sample data file. Following the file name is the column name in brackets. If a list file is used, the column number in the list file should be given in place of the name.

- reffile [string]
- The sample data are compared against either another test sample or a theoretical distribution. Following the file name is the column name in brackets. If a list file is used, the column number should be given in place of the name.

- (comptype = sample) [string, allowed values: sample | uniform |
- exponential | powerlaw | pareto | distribution]

Form of comparison to be performed. When "sample" is selected, the two input samples are analyzed simply as two lists of discrete data. A single sample may be compared to a theoretical distribution either by choosing one of the available functional forms ("uniform", "exponential", or "powerlaw"; "pareto" is the same as "powerlaw") or by specifying "distribution". When one of the internal functions is used, the second input file (`reffile`) is ignored. If the user has a special model, the data for the model are entered in a file that is specified as`reffile`, with`comptype="distribution"`.

- (fmin = 0.) [real]
- Minimum value of the test sample. (See the description of
`fmax`, below, for details of how this parameter works in conjunction with`fmax`).

- (fmax = 0.) [real]
- When the user selects a
`comptype`that is one of the internally generated theoretical distributions ("uniform", "exponential", "powerlaw", "pareto"), the user may specify the limits of the function using the`fmin`and`fmax`parameters. If`fmin`and`fmax`are the same, the distribution function boundaries default to the minimum and maximum values of the test sample. If comptype="sample" or comptype="distribution", then`fmin`and`fmax`are ignored.

- (power = 1.) [real, min=0.]
- When the user selects comptype="powerlaw" or comptype="pareto" (which is the same thing), the power law index (exponent) must be specified with this parameter.

## EXAMPLES

1. Compare the third and fifth columns in the ASCII file `qso.txt`.

st> kolmov qso.txt[3] qso.txt[5] sample

## SEE ALSO

Type "help statistics option=sys" for a higher-level description of
the `statistics` package.