GraphMu Multivariate Graphical Display for Macintosh Jean Thioulouse U.R.A. CNRS 243 "Biométrie, Génétique et Biologie des populations" Université Lyon 1 - 69622 Villeurbanne Cedex - France Fax : 72 44 84 66 - Telex : 330722 F e-mail : jean@biomac.univ-lyon1.fr - THIOULOU@FRCISM51.BITNET 3 June 1991 GRAPHMU MULTIVARIATE GRAPHICAL DISPLAY PROGRAM FOR THE MACINTOSH Jean THIOULOUSE Laboratoire de Biométrie, Génétique et Biologie des populations U.R.A. CNRS 243 - Université Lyon 1 69622 Villeurbanne Cedex - France Fax : 72 44 84 66 - Telex : 330722 F e-mail : jean@biomac.univ-lyon1.fr - THIOULOU@FRCISM51.BITNET This document is the GraphMu user manual. A detailed introduction describes the basic principles. The various commands of each menu are then reviewed with a description of each of the dialog boxes. At the end of the manual several examples of graph construction are given. GraphMu can be used independently of any multivariate data analysis method. The MacMul program facilitates the carrying out of basic analyses (principal component analysis (PCA), correspondence analysis (CA) and multiple correspondence analysis (MCA)) and supplies files which are directly compatible with GraphMu. ADECO (Analysis of Ecological Data) is a complete system based on HyperCard and Microsoft QuickBasic, with developed analysis methods, and also provides files which are compatible with GraphMu. MacMul and GraphMu are available from the author. ADECO is available from: D. Chessel Laboratoire d'Ecologie des Eaux Douces Université Lyon 1 69622 Villeurbanne Cedex. I should like to mention here the importance of the work of Y. Auda in the field of graphical display in data analysis and in particular his thesis, which is the origin of the development of GraphMu (Y. Auda, 1983. Rôle des méthodes graphiques en analyse des données: application au dépouillement des enquetes écologiques. 3rd cycle thesis, Lyon 1 University, 127 p.). Publication of results obtained with this software in scientific reviews is submitted to citation of one of the following papers: Thioulouse J. (1989). Statistical analysis and graphical display of multivariate data on the Macintosh. Computer Applications in the Biosciences, 5, 4, 287-292. Thioulouse J. (1990). MacMul and GraphMu : two Macintosh programs for the display and analysis of multivariate data. Computers and Geosciences, 16, 8, 1235-1240. Contents 1 - Introduction ...................…

46 GraphMu - Multivariate graphical display on Macintosh Laboratoire de Biométrie, Génétique et Biologie des Populations - U.R.A. CNRS 243 GraphMu - Multivariate graphical display on Macintosh 47 5 - EXAMPLES OF USE In the MacMul user manual, various examples were used to perform different analyses. Here we will use the same examples to show in detail how to obtain certain figures with GraphMu. We will not consider the examples concerning the drawing of ellipses and Gauss curves, which have already been explained in the MacMul manual. All the figures were produced on a Macintosh SE/30, system 6.0.3 with Multifinder, 4Mbyte memory, 40 Mbyte hard disk and Radius TPD A3 black and white screen (882 by 1152 pixels). The programs used were GraphMu version 4.06, MacMul version 2.14, Microsoft Word 4, SuperPaint 1.0 and MacDraw II. In all cases, a Macintosh Plus with 1 Mbyte memory and a 20 Mbyte hard disk would be sufficient. Digitization is however easier with a larger screen (e.g., Apple's 12 inch screen). Factor planes The most used graphic (for want of being the most relevant) in data analysis is the factorial diagram, or "factor plane". In GraphMu terminology it is a "Character map" graphic. Figures 6.7 and 6.8 of the MacMul user manual gives the F1 x F2 factor plane of the rows and columns of the PCA of the data set used by Doledec et Chessel: Doledec, S. et Chessel, D., (1987). Rythmes saisonniers et composantes stationnelles en milieu aquatique. I - Description d'un plan d'observation complet par projection de variables. Acta Œcologica, Œcologia Generalis, 8, 403-426. Reading this article and the paper by Thioulouse and Chessel: Thioulouse J. et Chessel D. (1987). Les analyses multitableaux en écologie factorielle. I: De la typologie d'état à la typologie de fonctionnement par l'analyse triadique. Acta Œcologica, Œcologia Generalis, 8, 463-480. will help in understanding the examples considered here. We will examine how these graphics are obtained from the files created by MacMul. The factor coordinates of the rows and columns are arranged in the "cn1.CPLI" (row coordinates) and "cn1.CPCO" (column coordinates) files. The number of columns of these files is equal to the number of factors saved in the analysis, here 4. The number of rows of the "cn1.CPLI" file is equal to the number of rows of the data table (i.e. 24) and the number of rows of the "cn1.CPCO" file is equal to the number of columns of the data table (i.e. 10). The first stage in drawing the F1 x F2 factor plane of the rows consists in selecting the "Character map" command of GraphMu "Graphics" menu (figure 3.1). This gives access to the first dialog window (figure 3.4). Just click the "File XY" button Laboratoire de Biométrie, Génétique et Biologie des Populations - U.R.A. CNRS 243 48 GraphMu -…