The arrays Sn and R consist of p rows and p columns. The size of all of the arrays is determined by the number of variables, p.The subscript n on the array Sn is a mnemonic device used to remind you that n is employed as a divisor for the elements s k The descriptive statistics computed from n measurements on p variables can also be organized into arrays.ġ0 Chapter 1 Aspects of Multivariate Analysis The sample mean array is denoted by i, the sample variance and covariance array by the capital letter Sn, and the sample correlation array by R. The sum of squares of the deviations from the mean and the sum of crossproduct deviations are often of interest themselves. The values of s k and r k should be quoted both with and without these observations. Suspect observations must be accounted for by correcting obvious recording mistakes and by taking actions consistent with the identified causes. They provide cogent numerical summaries of association when the data do not exhibit obvious nonlinear patterns of association and when wild observations are not present. In spite of these shortcomings, covariance and correlation coefficients are routinely calculated and analyzed. On the other hand, these quantities can be very sensitive to "wild" observations ("outliers") and may indicate association when, in fact, little exists. Their values are less informative for other kinds of association. Covariance and correlation provide measures of linear association, or association along a line. Nonlinear associations can exist that are not revealed by these descriptive statistics. The quantities sik and r k do not, in general, convey all there is to know about the association between two variables.
, n, provided that the conable are changed to Yjk = cxjk + d, j stants a and c have the same sign. The value of r k remains unchanged if the measurements of the ith variable are changed to Yji = axj + b, j = 1, 2.
Pearson Prentice HaHn 0 implies a tendency for one value of the pair to be large when the other value is large and also for both values to be small together. No part of this book may be reproduced, in any form or by any means, without permission in writing from the publisher. Upper Saddle River, NJ 07458Īll rights reserved. Pearson Prentice Hall Pearson Education, Inc. ::Over Designer: Bruce Kenselaar 1\rt Studio: Laserswords >enior Managing Editor: Lindd Mihatov Behrens ~anufacturing Buyer: Maura Zaldivar Associate Director of Operations: Alexis Heydt-Long Aarketing Manager: Wayne Parkins >darketing Assistant: Jennifer de Leeuwerk &Iitorial Assistant/Print Supplements Editor: Joanne Wendelken \rt Director: Jayne Conte Director of Creative Service: Paul Belfanti. \xecutive Acquisitions Editor: Petra Recter Vice President and Editorial Director, Mathematics: Christine Haag roject Manager: Michael Bell Production Editor: Debbie Ryan. Statistical Analysis '":IP Data Available brary of Congress Cataloging-in- Publication Data Applied Multivariate Statistical AnalysisĪpplied Multivariate Statistical Analysis RICHARD A.
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