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Validity of the F ‐ratio Test for Replicated Latin Square Designs Under Relaxed Conditions
Author(s) -
Tardif S.
Publication year - 1992
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.4710340608
Subject(s) - mathematics , latin square , statistics , statistic , chi square test , row , test statistic , row and column spaces , square (algebra) , distribution (mathematics) , f test , exact test , combinatorics , statistical hypothesis testing , mathematical analysis , computer science , geometry , rumen , chemistry , food science , database , fermentation
In a replicated latin square design, the F ‐ratio test statistic enjoys a noncentral Fisher distribution under the assumption of i.i.d. normal errors. This paper shows that the latter distribution still holds if a certain correlation structure is introduced within the sets of errors associated with each latin square. The correlation structure is characterized by the fact that, put in form of matrices, these sets of errors have exchangeable rows and exchangeable columns.