A study of simple unbalanced factorial designs that use type ii and type iii sums of squares

J.D. Lewsey, W.P. Gardiner, G. Gettinby

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

Methods for analysing unbalanced factorial designs can be traced back to the work of Frank Yates in the 1930s . Yet, still today the question on how his methods of fitting constants (Type II) and weighted squares of means (Type III) behave when negligible or insignificant interactions exist, is still unanswered. In this paper, by means of a simulation study, Type II and Type III ANOVA results are examined for all unbalanced structures originating from a 2x3 balanced factorial design within homogeneous groups (design types) accounting for structure, number of observations lost and which cells contained the missing observations. The two level factor is further analysed to test the null hypothesis, for both Type II and Type III analyses, that the unbalanced structures within each design type provide comparable F values. These results are summarised and the conclusion shows that this work agrees with statements made by Yates Burdick and Herr and Shaw and Mitchell-Olds, but there are some results which require further investigation.
LanguageEnglish
Pages1315-1328
Number of pages13
JournalCommunications in Statistics - Simulation and Computation
Volume26
Issue number4
DOIs
Publication statusPublished - 1997

Fingerprint

Unbalanced Designs
Factorial Design
Sum of squares
Homogeneous Groups
Balanced Design
Missing Observations
Null hypothesis
Analysis of variance (ANOVA)
Simulation Study
Cell
Interaction
Design

Keywords

  • unbalanced hypotheses
  • negligible interactions
  • Type II and III SSs

Cite this

@article{9b96168bd675488b8fda262ddc6de926,
title = "A study of simple unbalanced factorial designs that use type ii and type iii sums of squares",
abstract = "Methods for analysing unbalanced factorial designs can be traced back to the work of Frank Yates in the 1930s . Yet, still today the question on how his methods of fitting constants (Type II) and weighted squares of means (Type III) behave when negligible or insignificant interactions exist, is still unanswered. In this paper, by means of a simulation study, Type II and Type III ANOVA results are examined for all unbalanced structures originating from a 2x3 balanced factorial design within homogeneous groups (design types) accounting for structure, number of observations lost and which cells contained the missing observations. The two level factor is further analysed to test the null hypothesis, for both Type II and Type III analyses, that the unbalanced structures within each design type provide comparable F values. These results are summarised and the conclusion shows that this work agrees with statements made by Yates Burdick and Herr and Shaw and Mitchell-Olds, but there are some results which require further investigation.",
keywords = "unbalanced hypotheses, negligible interactions, Type II and III SSs",
author = "J.D. Lewsey and W.P. Gardiner and G. Gettinby",
year = "1997",
doi = "10.1080/03610919708813442",
language = "English",
volume = "26",
pages = "1315--1328",
journal = "Communications in Statistics - Simulation and Computation",
issn = "0361-0918",
number = "4",

}

A study of simple unbalanced factorial designs that use type ii and type iii sums of squares. / Lewsey, J.D.; Gardiner, W.P.; Gettinby, G.

In: Communications in Statistics - Simulation and Computation, Vol. 26, No. 4, 1997, p. 1315-1328.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A study of simple unbalanced factorial designs that use type ii and type iii sums of squares

AU - Lewsey, J.D.

AU - Gardiner, W.P.

AU - Gettinby, G.

PY - 1997

Y1 - 1997

N2 - Methods for analysing unbalanced factorial designs can be traced back to the work of Frank Yates in the 1930s . Yet, still today the question on how his methods of fitting constants (Type II) and weighted squares of means (Type III) behave when negligible or insignificant interactions exist, is still unanswered. In this paper, by means of a simulation study, Type II and Type III ANOVA results are examined for all unbalanced structures originating from a 2x3 balanced factorial design within homogeneous groups (design types) accounting for structure, number of observations lost and which cells contained the missing observations. The two level factor is further analysed to test the null hypothesis, for both Type II and Type III analyses, that the unbalanced structures within each design type provide comparable F values. These results are summarised and the conclusion shows that this work agrees with statements made by Yates Burdick and Herr and Shaw and Mitchell-Olds, but there are some results which require further investigation.

AB - Methods for analysing unbalanced factorial designs can be traced back to the work of Frank Yates in the 1930s . Yet, still today the question on how his methods of fitting constants (Type II) and weighted squares of means (Type III) behave when negligible or insignificant interactions exist, is still unanswered. In this paper, by means of a simulation study, Type II and Type III ANOVA results are examined for all unbalanced structures originating from a 2x3 balanced factorial design within homogeneous groups (design types) accounting for structure, number of observations lost and which cells contained the missing observations. The two level factor is further analysed to test the null hypothesis, for both Type II and Type III analyses, that the unbalanced structures within each design type provide comparable F values. These results are summarised and the conclusion shows that this work agrees with statements made by Yates Burdick and Herr and Shaw and Mitchell-Olds, but there are some results which require further investigation.

KW - unbalanced hypotheses

KW - negligible interactions

KW - Type II and III SSs

UR - http://dx.doi.org/10.1080/03610919708813442

U2 - 10.1080/03610919708813442

DO - 10.1080/03610919708813442

M3 - Article

VL - 26

SP - 1315

EP - 1328

JO - Communications in Statistics - Simulation and Computation

T2 - Communications in Statistics - Simulation and Computation

JF - Communications in Statistics - Simulation and Computation

SN - 0361-0918

IS - 4

ER -