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Scheffy's Confidence Intervals in the Models of Analysis of Covariance
Author(s) -
Kuczyński M.,
Drwièa T.
Publication year - 1985
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.4710270605
Subject(s) - mathematics , estimator , covariance , confidence interval , block design , statistics , covariance matrix , scheffé's method , block (permutation group theory) , restricted randomization , linear model , combinatorics , analysis of variance , randomization , randomized controlled trial , medicine , surgery
Scheffe's confidence intervals for linear functions of some subvectors of a vector of parameters are presented. The considered subvectors are such that covariance matrices of their estimators are known non‐negative definite matrices multiplied by unknown positive constants. This property is characteristic of the least squares estimators of vectors of main and interaction effects in the analysis of covariance models of the following experimental designs: split‐block, split‐plot, completely randomized two‐factor design and randomized complete block design. The formulas for confidence intervals for linear functions of vectors of main or interaction effects in the designs mentioned above are given in the paper. The practical example is given as an illustration.