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By J. Edward Jackson

WILEY-INTERSCIENCE PAPERBACK SERIESThe Wiley-Interscience Paperback sequence contains chosen books which have been made extra obtainable to shoppers for you to elevate international allure and basic circulate. With those new unabridged softcover volumes, Wiley hopes to increase the lives of those works through making them to be had to destiny generations of statisticians, mathematicians, and scientists.From the studies of A User’s consultant to important Components"The publication is aptly and properly named–A User’s advisor. it's the form of booklet consumer at any point, beginner or expert practitioner, would need to have to hand for autotutorial, for refresher, or as a general-purpose consultant in the course of the maze of recent PCA."–Technometrics"I suggest A User’s consultant to valuable parts to an individual who's operating multivariate analyses, or who contemplates acting such analyses. those that write their very own software program will locate the publication important in designing higher courses. those that use off-the-shelf software program will locate it worthwhile in reading the results."–Mathematical Geology

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T . • v, t +2 0 -2 • 1 • ------. _---�------·---• +2 ------------- ------; ----------- -- •• • • or-----r%����-----------­ • -2 -4 . _________ �-------------------I I I 3 I I 5 I I 7 I I 9 I I II I I 13 I I 15 I I • • I ABC D FIGURE lA. Chemical example: Control charts ror oriainal variables and principal components; 9S% limita. Reproduced rrom Jackson ( 1980) with permission or the American Society ror Quality Control and Jackson ( 198S) with permission or Marcel Dekker. 2 Type I Erron When one uses two or more control charts simultaneously, some problems arise with the Type I error.

3), which is an indication that a particular observation vector cannot be adequately characterized by the subset of pc's one chose to use. This result can occur either because too few pc's were retained to produce a good model or because the observation is, truly, an outlier from the model. It is also possible in repetitive operations, such as quality control, that the underlying covariance 36 PCA WITH MORE THAN TWO VARIABLES structure and its associated vector space may change with time. This would lead to a general lack-of-fit by the originally defined pc's.

Scatter plots of combinations of the unretained pc's 3. Plots of retained vs. unretained pc's Related work on gamma plots was done by Wilk et al. ( 1962) and Wilk and Gnanadesikan (1964). "e given by Andrews ( 1979) in connection with robustness and by Daniel and Wood (1971), which, while designed for regression, have applications in PCA as well. 8 WHEN TO STOP? 1 Introdnction One of the greatest uses of PCA is its potential ability to adequately represent a p-variable data set ink< p dimensions.

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