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Two-dimensional goodness-of-fit testing in astronomy
Peacock, J. A.
AA(Royal Observatory, Edinburgh, Scotland)
Monthly Notices of the Royal Astronomical Society, vol. 202, Feb. 1983, p. 615-627. (MNRAS Homepage)
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NASA/STI Keywords:
Astronomy, Goodness Of Fit, Statistical Distributions, Monte Carlo Method, Power Spectra, Probability Distribution Functions, Quasars, Sampling, Significance, Virgo Galactic Cluster
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This paper deals with the techniques available to test for consistency between the empirical distribution of data points on a plane and a hypothetical density law. Two new statistical tests are developed. The first is a two-dimensional version of the Kolmogorov-Smirnov test, for which the distribution of the test statistic is investigated using a Monte Carlo method. This test is found in practice to be very nearly distribution-free, and empirical formulae for the confidence levels are given. Secondly, the method of power-spectrum analysis is extended to deal with cases in which the null hypothesis is not a uniform distribution. These methods are illustrated by application to the distribution of quasar candidates found on an objective-prism plate of the Virgo Cluster.

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