Open AccessHypothesis testing for meagre data sets
Author(s) -
Lucy L. B.
Publication year - 2000
Publication title -
monthly notices of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.058
H-Index - 383
eISSN - 1365-2966
pISSN - 0035-8711
DOI - 10.1046/j.1365-8711.2000.03655.x
Subject(s) - statistics , statistic , goodness of fit , test statistic , pearson's chi squared test , poisson distribution , multinomial distribution , statistical hypothesis testing , confidence interval , physics , mathematics
Improved χ 2 statistics are defined for both Poisson and multinomial data sets. Numerical experiments with the Nousek–Shue test problem from X‐ray spectroscopy indicate that, in contrast to Pearson's statistic X 2 , these modified statistics remain approximately valid at the 2 σ level of significance even when the mean counts per bin is ≪1 provided that the total counts N ≳30. The simplest of the proposed statistics is formally equivalent to carrying out a goodness‐of‐fit test with Pearson's statistic but with modified confidence limits, and this procedure is recommended.