Graphical Analysis of Multi-Response Data

by Tukey; John Wilder

• ISBN13: 9780849303845
• ISBN10: 0849303842
• Format: Hardcover
• Copyright: 1998-10-21
• Publisher: Chapman & Hall/

Summary

A comprehensive summary of new and existing approaches to analyzing multiresponse data, Graphical Analysis of Multiresponse Data emphasizes graphical procedures. These procedures are then used, in various ways, to analyze, summarize, and present data from a specific, well-known plant breeding trial.These procedures result in overlap plots, their corresponding semigraphical tables, scatter plot matrices, profiles across environments and attributes for individual genotypes and groups of genotypes, and principal components.The interpretation of these displays, as an aid to understanding, is illustrated and discussed. Techniques for choosing expressions for the observed quantities are also emphasized.Graphical Analysis of Multiresponse Data is arranged into three parts:o What can usefully be doneo Consequences for the exampleo Approaches and choices in more detailThat structure enables the reader to obtain an overview of what can be found, and to then delve into various aspects more deeply if desired. Statisticians, data analysts, biometricians, plant breeders, behavioral scientists, social scientists, and engineering scientists will find Graphical Analysis of Multiresponse Data offers invaluable assistance. Its details are also of interest to scientists in private firms, government institutions, and research organizations who are concerned with the analysis and interpretation of experimental multiresponse data.

Author Biography

Kaye E. Basford is a Reader in Biometry in the School of Land and Food at the University of Queensland, Brisbane, Australia John W. Tukey is Professor Emeritus at Princeton University, USA

Table of Contents

Preface	xiii
Acknowledgements	xvii
Part A
Introduction to Part A	1	(4)
The example	5	(6)
Styles of analysis	11	(36)
Preliminary considerations	11	(2)
Scatter Plot Matrices	13	(4)
Within environment analyses for single attributes	17	(5)
Overlap plots	22	(5)
Profiles across environments and B-confidence	27	(3)
Grouping the data	30	(5)
Smoothing the profiles	35	(4)
Profiles across attributes	39	(1)
Choice of expression	39	(4)
This account in a larger framework	43	(4)
Part B
Introduction to Part B	47	(4)
Overall behaviour: SPLOMs across attributes and across environments	51	(18)
Semigraphical comparison of genotypes for each attribute-environment pair	69	(32)
Profiles of individual genotypes and groups	101	(28)
SPLOMs for genotype groups	129	(8)
Re-attribution of the responses on the 43 genotypes	137	(18)
Our specific example	148	(4)
Styles of re-attribution	152	(3)
Semigraphical displays for the re-attributed data	155	(14)
Re-environmenting	169	(16)
Two remarks	181	(1)
Overview of position	181	(4)
Re-expression	185	(26)
Part C
Introduction to Part C	211	(2)
Global aspects of the data	213	(10)
Ordering of genotypes	213	(1)
Linear ordering of genotypes	214	(4)
Dispersed inheritance, etc	218	(1)
Characterizing and ordering of environments	219	(3)
Ordering of attributes	222	(1)
Data laundry	223	(8)
Seeking exotics	224	(2)
Winsorization of anomalies	226	(5)
Choices of expression	231	(2)
Comparative scaling	231	(1)
Comparative responses	231	(1)
Re-expression of individual attributes	232	(1)
Seeking exotic values	233	(26)
SPLOMs	233	(12)
Alternative displays	245	(9)
Correlations among environments	254	(5)
Local analyses and displays	259	(30)
Local analysis within environments	259	(1)
Adjustment of structured sets of s2 values	259	(3)
Choice of critical levels	262	(2)
Benjamini-Hochberg (FDR) procedure	264	(2)
Overlap plots	266	(9)
Dealing with ties in the BSD procedure	275	(3)
Profiles across environments and B-confidence	278	(7)
Some plausible developments for the BSD	285	(4)
Combined analyses	289	(12)
Analysis over environments	289	(8)
Analyses over attributes	297	(4)
Grouping and labelling genotypes	301	(2)
Grouping	301	(1)
Labelling	302	(1)
Idiolinkage, nearest and centroid	303	(4)
Nearest	303	(1)
Nearest algorithm	303	(1)
Centroid	304	(2)
Mean squared distance	306	(1)
Other blended forms; xpanded idiolinkage	307	(4)
Other blended forms	307	(1)
Xpanded linkage	307	(1)
Generalized xpansion	308	(1)
Techniques so far proposed	309	(2)
Robust forms of idiolinkage	311	(2)
Flexible Winsorization	311	(2)
Idiomax	313	(4)
Expansion	313	(2)
Plausible scope of exploration	315	(2)
Robust sphering	317	(6)
Robust orthogonalization	318	(1)
Simplification	319	(1)
Robust scaling	320	(1)
Comments	320	(1)
Relative importance?	320	(3)
A side issue and more careful sphering	323	(4)
Pattern of analysis	323	(1)
Choice of scaling	323	(2)
A possible exception	325	(1)
Postcomment	325	(2)
A suggestion about `G in or out'	327	(6)
Another suggestion	327	(6)
Detrivialization of one- and two-way tables: an introduction	333	(4)
The one-way case	333	(2)
The two-way case	335	(2)
Later attributes and subtables	337	(4)
The second attribute	337	(2)
The third attribute	339	(1)
Later attributes	339	(1)
Combination	340	(1)
Postcomment	340	(1)
Sphering the soybean data	341	(10)
Ordering of attributes	341	(1)
Robust orthogonalization	342	(5)
Robust scaling	347	(4)
Grouping the soybean genotypes	351	(12)
First-stage grouping	351	(3)
Second-stage grouping	354	(1)
Group responses	354	(3)
Alternative analyses	357	(1)
Partitioning variability within groups	357	(6)
Ordering the environments	363	(10)
Greedy close ordering of environments	363	(10)
One approach to plotting	373	(26)
Smoothing in general	374	(1)
Gropup 4 and attribute 1 as an example	375	(9)
Looking at the seven groups for attribute 1	384	(1)
Looking at the seven groups for all attributes	384	(15)
Smoothing short sequences (of perhaps 6 to 18 values)	399	(4)
3R 3pR E2	399	(3)
3+R E2	402	(1)
Presentations across attributes	403	(2)
Choice of expression: generalities	405	(12)
Matching re-expressions	406	(2)
Purposes of choice of expression	408	(1)
Rarity of conflict between these goals	409	(1)
Tools for diagnosis	410	(3)
Combining Q-diagnoses	413	(1)
Breaking down the example	413	(1)
Weighted regression	413	(4)
Removable inhomogeneity of variability	417	(16)
Replication within environments (e.g. 2x40)	418	(1)
Replication betwen environments (e.g. 8x40)	418	(1)
Inhomogeneity of interaction size (e.g. 8x40 or 8x18)	418	(1)
Variability between replications within environments	419	(10)
The special case of two versions	429
Interaction variability	428	(5)
Removable non-additivity	433	(8)
Extended fits	433	(1)
Choice of expression to promote additivity of response	434	(1)
General case of several versions	435	(6)
Linearity of response	441	(2)
Relative importance and combination	443	(8)
Bowstring plots	444	(7)
Interpretation and hybridization	451	(2)
Appendices	453	(122)
Appendix 1	453	(20)
Appendix 2	473	(8)
Appendix 3	481	(1)
Appendix 4	482	(4)
Appendix 5	486	(1)
Appendix 6	487	(9)
Appendix 7	496	(7)
Appendix 8	503	(1)
Appendix 9	504	(4)
Appendix 10	508	(4)
Appendix 11	512	(6)
Appendix 12	518	(6)
Appendix 13	524	(6)
Appendix 14	530	(6)
Appendix 15	536	(6)
Appendix 16	542	(6)
Appendix 17	548	(4)
Appendix 18	552	(1)
Appendix 19	553	(3)
Appendix 20	556	(8)
Appendix 21	564	(9)
Appendix 22	573	(2)
References	575	(4)
Author Index	579	(2)
Subject Index	581