Preface

The majority of ideas discussed here are for students who want to know the why of statistics, not only the how. The goal is to present the general linear model of statistical analysis in a concise, but complete outline. The general linear model is a powerful tool to assist scientific discovery, to foster objective knowledge, and to aid critical thinking. It is mathematically elegant, well integrated, and, to some people, beautiful.

        Underlying the narrative are dominant themes of variance, conceptualized as an information measure, and description of data analysis as consisting of formal methods for extraction of meaning from data matrices. The conceptualization of variance as an information measure stems from the author's lifelong involvement with the theory of logical relationships among variables. Pioneered by works of Bart, Cliff, Sato, Tatsuoka, some findings within this context have been introduced here as basic postulates of the general linear model of statistics.

        Throughout this text, the smallest possible examples are used to illustrate the statistical techniques that, in practice, would be applied to much larger data sets. Thus, the computational tedium that typically accompanies analysis of large data sets does not detract from learning the relevant principles involved. The importance of structural analysis and adequate interpretation of the information content is emphasized, as is the importance of integrating quantitative methodology with sound theoretical conceptualization. Special care has been taken to introduce relatively difficult material in a series of logically interlocking steps, complemented by concise description of computational algorithms.

        The brevity of the present text is due to striving for clarity of the presentation. Much more could have been said, but not without sacrificing the visibility of the guiding principles and the sharpness of contours of the structure of the narrative.

     Epistemological principles implicit to most of the statistical inquiry are discussed at several strategic points in the text. The point stressed is that statistics can be well conceptualized as a relatively new branch of epistemology. Accordingly, the statistical significance is not given the pivotal role it enjoys in many other texts on this subject. Instead, the accent is on the structural properties of statistical solutions and their visual representations.

        The conceptual differences of the text from the orthodoxy are subtle, but substantial. The traditional concepts of statistics such as that the key question of statistical analysis is whether whatever is analyzed is statistically significant are repeatedly challenged. The point stressed is that mere detection of nonrandom differences at the .05, .01, 001, etc. level of statistical significance is no longer a sole and sufficient goal of statistical analysis. The nonrandom components should be not only recognized, but also extracted, enhanced, their magnitudes ascertained and their locations given within the surrounding structures.

Let me propose an analogy that might make the above suppositions more clear. Remember the rather murky pictures of the surface of Venus in the early years of space explorations? Compare those with the computer-enhanced pictures of the Venus' surface obtained later. Transmission of information from Venus contains not only a ‘statistically significant' amount of information, but also noise. One might propose a null hypothesis that there are no stones on the surface of Venus, reject it at the .0001 level of significance, and still see very little surface detail. It was not testing of null hypotheses, but enhancement of information components by filtering out noise that lead to crystal clear transmission of images from that planet, shrouded in clouds.

        Another characteristic of this book is the avoidance of the 'sums of squares', 'mean square' terminology and associated computational techniques, typical of Fisher's conceptualization of statistics. Textbooks adapting Fisherian approach from the very beginning extract heavy penalties from students by forcing them to embrace a convoluted notational system and obtuse concepts and algorithms.

        This textbook departs significantly from standard introductory statistics texts on several other points, stressing the graphical rendering of data structures that make statistics 'visible' and intuitively plausible. The present text is not only a textbook, but also a polemic with the Fisherian tradition in statistics, an attempt to reaffirm the Pearson's legacy, and a programmatic statement of some key aspects of the modern, computer assisted statistical theory and practice.

 The intellectual ancestry of this book can be traced to many of my teachers, colleagues, and friends: Professors Olga Hampejzova and Milos Vojtechovsky at the Emperor Charles IV University, David J. Weiss, Marvin Roff, Cyril Hoyt, and William M. Bart at the University of Minnesota. Norman Cliff and William B. Michael at the University of Southern California. Gerald C. Helmstadter at the Arizona State University. Lin Chen Shan and Lin Sieh Hwa at the Taipei’s National University. Fred N. Kerlinger, at the University of Amsterdam.

 Early versions of the manuscript, were typed and re-typed by Jennifer Christ and Mindy Rich. Thank you, Jennifer and Mindy. Roxie Covey, Suzanne M. Wilkinson, Lenore Hoehl, Rita Archambault and Martin Hill edited this text for writing. However, most helpful in this respect was Professor James M. Webb of the Kent State University who helped to improve the clarity of presentation and continuity of the narrative. The most arduous task, however, of integration the many drafts into a manuscript, was endured by my wife Yung-Yung, pregnant at that time with our first daughter YiWen, caring for the family and later nursing the newborn child on the outskirts of a tropical jungle where most of the writing was done.

        This book was written for my students who, in turn, helped me to write it. During my teaching years…

 

Whenever I found myself growing grim about the mouth, whenever it was damp, drizzly November in my soul; whenever I found myself involuntarily pausing before coffin warehouses, I got together with my students.

 

Then, when there was the time to part, I paraphrased Dylan Thomas:

 

To think, then, is to enter into a perilous country, colder of welcome than the polar wastes, darker than a Scottish Sunday, where the hand of the unthinker is always raised against you, and where the parasites rule. To think is dangerous. Many potential scientists found it easier to writhe their way into the ranks of administrators or to droop into the slack ranks of those ruled by them. I beg you to devote your lives to science; I pledge you to adventure of discovery; I command you to experiment. Remember that the practice of statistics is vital to the progress of social sciences. Remember that the progress of social sciences is vital to bringing out a better society. And a better society than that we find ourselves in is worth fighting for. Forget what you like. But remember that.

 

Looking back at my 30 years of teaching, I still think that that journey was worth to travel.

 

David J. Krus

Professor Emeritus