Premium
Normal Approximations of Exact Tests in Configural Frequency Analysis
Author(s) -
Bergman L. R.,
von Eye A.
Publication year - 1987
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710290714
Subject(s) - mathematics , independence (probability theory) , limit (mathematics) , statistics , laplace's method , laplace transform , statistical hypothesis testing , central limit theorem , calculus (dental) , mathematical analysis , medicine , dentistry
The most common tests for types and antitypes in configural frequency analysis are normal approximations of exact tests. In the paper such statistics under the complete independence model and under the fixed margins model are discussed. It turns out that these test statistics are not acceptable when the number of simultaneously performed tests is large or when the expected frequencies are small. In these cases, the use of exact tests is advocated and some existing computer programs for such tests are indicated. A normal approximation based on the strong version of the De Moivre‐Laplace limit theorem is also discussed. Empirical examples are given from longitudinal data describing psychological development of boys.