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## Friedman-type statistics and consistent multiple comparisons for unbalanced designs with missing data (1988)

Venue: | J. Am. Stat. Assoc |

Citations: | 6 - 1 self |

### Citations

960 | Individual comparisons by ranking methods - Wilcoxon - 1945 |

839 | Testing Statistical Hypotheses - Lehmann, Romano - 2006 |

334 |
The use of ranks to avoid the assumption of normality implicit in the analysis of variance
- Friedman
- 1937
(Show Context)
Citation Context ...lysis, issappropriate (Wittkowski, in press).s, If a complete or balanced randomized block design issplanned, missing observations often occur through datasloss. Generalizations of the Friedman test (=-=Friedman 1937-=-)sto unbalanced designs were proposed by Benard and VansElteren (1953). Because the test statistic was not given insan easy-to-use form, earlier attention was restricted tos* Knut M. Wittkowski is Bio... |

295 | Use of ranks in one-criterion variance analysis - Kruskal, Wallis - 1952 |

5 | Generalizations of Chernoff-Savage Theorems on Asymptotic Normality of Nonparametric Test Statistics - Govindarajulu, Cam, et al. - 1965 |

5 | Marginal likelihoods based on Cox's regression and life model - D, Prentice - 1973 |

4 |
On the problem of incomplete rankings
- Prentice
- 1979
(Show Context)
Citation Context ... that all pairs of treatments are compa-srable in at least one block.sLet y = lim,, E(n1I2T. I Hn(0)) and D(W) = F:(x)(l - Fi(x))Ml+-2-rff(x) dx.syIV-y.. Then, straightforward computations (e.g., sees=-=Prentice 1979-=-) yield For fixed cell frequencies (Mi, = m) this reduces to thesresults of Rinaman [1983, p. 657, eq. (4.3)], where dFi(x)sshould be replaced by f f (x) dx. Note that 0 = 0 impliessD(W) = 0. The conv... |

4 |
Asymptotically efficient tests by the method of m rankings
- SEN
- 1968
(Show Context)
Citation Context ...symptotic relative efficiency results here. The expected adjusted scores vectors y is(i = 1, . . . ,sNevertheless, the asymptotic distribution of test statistics n) (with factor n1I2) are (see, e.g., =-=Sen 1968-=-)sunder alternatives needs to be investigated to prove con-ssistency of the test statistics; that is, that the power tendssto 1for fixed alternative. Consider a sequence of locationsparameter alternat... |

3 | A Generalization of the Method of m Rankings - Elteren - 1953 |

3 | On distribution-free rank tests for two-way layouts - Rinaman - 1983 |

3 |
The Analysis of Variance
- Scheffk
- 1959
(Show Context)
Citation Context ...nterest to analyze treatment pairs by means of multiplescomparisons. For special cases, Klotz (1980) and Skillingssand Mack (1981) attempted to generalize Scheffk-typesmultiple-comparison procedures (=-=Scheffk 1959-=-) to unbal-sanced designs with missing cells. Evaluating the noncen-strality these (as discussed in Secs.sand 6, can produce inconsistent ons@1988 American Statlstlcal AssociationsJournal of the Ameri... |

2 | A Rank-Test for Complete Block Designs - Haux, Schumacher, et al. - 1984 |

1 |
A Distribution-Free Test for Symmetry in Hierarchical Data
- Bhapkar, Gore
- 1973
(Show Context)
Citation Context ...TED SCORESsLet Rijk be the rank of Xijk within' block i. Where infor-smation on the underlying distribution is available (Sens1968) or Ho is defined with respect to certain aspects ofsthe data (e.g., =-=Bhapkar and Gore 1973-=-), the ranks r =s1, . . . , Mi+ can be transformed by score functions a;:sr -t ai(r). Because asymptotic results are calculated forsn -t m, the assumptions for the Chernoff-Savage theoremss(Govindaraj... |

1 | The Effects of Antihypertensive Therapy on the Quality of Life - Brown, Bulpitt, et al. - 1986 |

1 | Distribution-Free Tests for Main Effects in Multifactor Designs - J, Skillings - 1986 |

1 | The Theory of Rank Tests - Hijek, Sidik - 1967 |

1 |
Rank Analysis of Block Designs Having Different Cell Frequencies
- Rai
- 1987
(Show Context)
Citation Context ...sknown statistics [including the tests of Kruskal and Wallis (1952), Prentice (1979), and Rinaman (1983)l are proven to besspecial cases, whereas others (e.g., Klotz 1980; Groggel and Skillings 1986; =-=Rai 1987-=-; Skillings and Mack 1981) are shown tosbe less appropriate. Multiple comparisons are considered under both the global hypothesis and alternatives. Evaluating non-scentrality parameters under local sh... |

1 | Serum LH Levels and Preoptic Catecholamine Turnover Following Estradiol - Sandmann, Wittkowski, et al. - 1981 |