Gives conditions under which a sum of squares of jointly normal random variables can be decomposed into independent chi-squared components. Named for William G. Cochran, it underlies the distribution theory behind analysis of variance.
Facts
StatementCochran's theorem justifies results about the probability distributions of statistics used in the analysis of variance, showing that certain quadratic forms built from normal samples are independently chi-squared distributed. 1 Classification
Statement FormCharacterization Theorem 1 Connections
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Proved By
Source Cochran's Theorem (Wikipedia)
Sources
1. Cochran's Theorem (Wikipedia)
Wikimedia FoundationIntroduction
In statistics, Cochran's theorem, devised by William G. Cochran, is a theorem used to justify results relating to the probability distributions of statistics that are used in the analysis of variance.
Proved By: William Gemmell Cochran, Lead sentence, attribution
devised by William G. Cochran
In Group: Mathematical Statistics and Estimation, Lead section
In statistics, Cochran's theorem, devised by William G. Cochran
View the Source 2. MacTutor History of Mathematics, University of St Andrews: William Gemmell Cochran - MacTutor History of Mathematics
MacTutor History of Mathematics, University of St AndrewsBiographyQuote, Biography
The other 1934 paper The distribution of quadratic forms in a normal system, with applications to the analysis of covariance contains what today is known as "Cochran's Theorem".
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