In this issue:
Peter Bryant
College of Business
University of Colorado at Denver
Denver, CO 80217-3364
pbryant@castle.cudenver.edu
303-556-5833
As we go to press, it occurs to me that the season for meetings of many of our allied societies in IFCS is upon us. The Portuguese Society (CLAD) is meeting in December and the annual meeting of the German Classification Society is in March, for example. I urge all CSNA members to participate in any of these meetings they find appropriate. The links to the different styles and emphases represented by these societies is one of the most stimulating parts of CSNA activity for me and any support we in CSNA can show can only be helpful
Stanley L. Sclove
Department of Information and Decision Science
College of Business Administration
University of Illinois at Chicago
601 S. Morgan Street
Chicago, IL 60607-7124
slsclove@uic.edu
www.uic.edu/~slsclove
The Nominating Committee, consisting of Pascale Rousseau (chair), Glenn Milligan, and Stephen Hirtle, has submitted the following slate of nominees for CSNA offices:
For President:
F.R. McMorris
David Banks
Pierre Legendre
For Directors (two to be elected):
Bill Shannon
Francois-Joseph Lapointe
Ralph Stinebrickner
Doug Carroll
James Corter
Any member may nominate other candidates. Nominees will then be asked to provide statements to accompany the ballot, which will appear in the November CSNA Newsletter. The voting is by Hare method, ranking the individual candidates (not all combinations of them).
On the same ballot, there will be a motion to permit electronic elections (starting in 1998).
This year's ballots will be due by mail or e-mail at the Secretary/Treasurer's office by 15-December.
DATA ANALYSIS VIEWED FROM A LOGICAL STANDPOINT
J. P. Sutcliffe,
Department of Psychology
University of Sydney
Australia
jps@psych.usyd.edu.au
Operationally defined, "data analysis" is whatever individuals, identified by others and/or themselves as "data analysts", do in the way of developing and applying techniques and procedures to data. As with most operational definitions (see Bridgman, 1927), the operational definition above does not precisely specify the topic of interest or delimit its boundaries (see Benjamin, 1955): what is done, for example within the the North American tradition exemplified by Kempthorne (1952) and Torgerson (1958), (with its emphasis upon 'statistical inference') differs markedly - even after allowance for positions taken by such as Tukey (1977) and Rouanet et al. (1987) - from what is done in the European tradition (with its emphasis on "search for structure in data") exemplified by Benzecri (1973) and Cailliez and Pages (1976). See also Steyer et al. (1995), Barthelemy and Guenoche (1988), and Diday et al. (1994). About the only thing common to the American and European traditions of "data analysis" is the proliferation of techniques without obvious concern or justification for using one technique rather than another in any given empirical investigation; and it is unlikely that "data analysts" would wish to define their activities of "data analysis" in that way.
In a different tradition - critical enquiry in the manner of Anderson (1962), and O'Neil (1962), (see also Baker, 1986) - one can avoid those difficulties of operational definition by explicating the notion of data analysis within the logical framework of scientific method. Science progresses via conjecture and demonstration. The conjectures are the theories and/or hypotheses which guide enquiry, and the demonstrations are the activities - logical ones such as with proof, empirical ones such as with direct observation, and such logical/empirical ones (experiment, survey, etc.) within which "data analyses" may be made - involved in showing whether or not any guiding conjecture is true. This note considers "data analysis" from that logical standpoint.
A datum is a proposition which expresses something either known or assumed as fact and serves as a basis for reasoning or calculation. Thus data comprise a set of propositions. See Sutcliffe (1993). A datum is usually obtained by observation pertinent to predictions deriving from some conjecture under test. Contrary to a common misconception, data are neither numbers nor numerals nor other ciphers; and where numerals and/or ciphers are tabled (as is common practice), individually they are merely shorthands for the factual propositions (the items of data) into which they enter, such as where "45" may be a shorthand for the proposition "The age of particular person P, observed in year T under conditions C, was 45 years", "1" (or "M") may be a shorthand for the proposition "Person P is male" and "0" (or "F"), if used as an exclusive alternative in the same context, may be a shorthand for the proposition "Person P is female". In the common case where "data analyses" work arithmetically upon the zeroes and ones of an Objects x Properties matrix, it is incumbent upon the data analyst to make explicit the compound proposition denoted by any given (1,0)-element row, and to make manifest the logical operations on those compound propositions which are being carried by the data-analytic arithmetical operations on the corresponding zeroes and ones which denote them. See also Batchelder & Narens (1977).
Few if any data analysts analyse data so conceived in the (chemical) sense of decomposing data (the propositions stating facts) into components. Admittedly, with analysis of variance, factor analysis, discriminant functions, and more generally the regression model, specified numbers are expressed as weighted sums of other numbers, the latter being said to be (derived) "components" of the former. However, to say that the use of such methods is "analysis of data into components", on the analogy of "analysis of substances into chemical components", would then require that it be the numbers per se which constitute "the data". The numbers which are componentially analysed in the ways mentioned are such things as variances, covariances, and correlation coefficients, viz. quantities derived from data, but not themselves data. Even in the case of regression, a number "decomposed" is only a part of a datum, not the whole datum; e.g. in the proposition "P is 45 years old", "45" is the measure of the quantitative property "45 years of age" predicated of person P, and therefore that number "45" is not itself a proposition. Thus the word "analysis" in the phrase "data analysis", on the analogy of "chemical analysis" into components, is a misnomer. What one does with the data proper in such cases is to derive certain results such as that "the value of the total sum of squares is x", . "the value of the total sum of products is y" . , and so on, preliminary to yet further derivations: sum of squares implies variance; sum of products implies covariance; . and so on. Properly speaking, the phrase "data analysis" refers generally to the process of "drawing of inferences from data (factual propositions)". Just how that process relates to the drawing of the final conclusion(s) for the reporting of an enquiry remains to be spelled out in more detail as follows.
For this consideration of the process of "data analysis" it is helpful to begin at the end, that is, with its "conclusion". To close off an enquiry - whatever the "investigation", "analysis", "report", or suchlike - one states one's "conclusion(s)". Consider then some possibilities for the status of a "conclusion".
One possibility (very often realized) is that a "conclusion" is self-referentially rhetorical. That is, with the very use of the word "conclusion" (or any other conclusion-indicator such as "therefore") to preface what is then said, the user (speaker, writer) is seeking to convince someone (listener, reader) that s/he should believe (accept as true) what is being presented as "conclusion". There is obvious value in such rhetoric for the professional advancement of rhetoricians if part of their rhetorical program includes having other people believe that they are "scientists" and that they are making "scientific progress" with their "conclusions". Note, however, that one can not only correctly believe something to be true when it is true but alternatively one can mistakenly believe it to be false when it is true; and one can not only correctly believe something to be false when it is false but alternatively one can mistakenly believe it to be true when it is false. Thus, belief/disbelief being logically independent of truth/falsehood, rhetoric alone (urging belief) has no value for the progress of science. It is not sufficient to persuasively assert something as a "conclusion": more is required to warrant reception of an asserted "conclusion" as actual truth.
Another possibility (much less often realized) is that a "conclusion" is the final proposition of a valid argument. In the better cases the "conclusion" will also be true (in virtue of the chosen prior premisses of the argument themselves being true). The state of affairs referred to in the "conclusion" is independent of whether or not anyone "concludes" anything about it, and it is independent of whether or not anyone believes the "conclusion" stated about it to be true (or false). However, the state of affairs referred to in the "conclusion" provides cogent grounds for believing (or disbelieving) that the proposition put forward as a "conclusion" is true (false). What better grounds could there be for believing the proposition 'Pr. is true' than that Pr. is true, either as directly observed or as demonstrated by valid argument. For the progress of science, valid argument (as distinct from rhetoric) has value because - within the sociological context of scientific activity, with one scientist picking up where another leaves off - the next point of departure can then always be from an established truth rather than from an asserted "truth" which may be an actual falsehood.
Some logical notions need to be reviewed to make manifest when one has a conclusion in the logical, rather than in the otherwise rhetorical sense.
A simple proposition has a subject (the "object" of interest), a predicate (some "property" which the "object" may possess), and its copula (the asserting, usually via the verb "to be" that the "object" has the "property"). If it is the case that an object x has the property y predicated of it, then the simple proposition "x is y" is true; and if it is not the case that that object x has the property y predicated of it, then the simple proposition "x is y" is false. Not all statements or assertions are propositions. For example, neither the question "Does this article interest you?" nor the imperative "In any case, keep reading!" are propositions. Even where statements or assertions are indeed propositions, some thought may be needed to make clear their logical (propositional) form, that is, to see what is the subject, and what is the predicate, and what is the copula. To get on with this note, one must assume that in any particular venture such work would be done so that one would know what set of propositions were under consideration with respect to the guiding conjecture and its demonstration. A compound proposition is a conjunction (via &) of two or more simple propositions. Any such proposition is true if and only if each one of its component simple propositions is true. There are also conditional statements (ones which entail "if / then" structure); and there are compound conditional statements; and in each case there are statable conditions for their being either true or false.
The foregoing in principle enables one to set out a "theory" in the form of a compound of simple propositions and/or conditional statements and/or compound propositions and/or compound conditional statements. In such a propositional form, a "theory" (being as a whole a single though compound proposition) is either true or false, and it will be the goal of a particular enquiry to determine what is the case. (Some claim with respect to data analysis that the "models" which guide them in such analyses are neither true nor false; but if "models" are to have any scientific relevance, as distinct from being elements in rhetorical games one might otherwise play, they must be taken seriously and properly presented as theories to be tested.)
Theory conjoined with valid argument is essential for the statement of a logical conclusion. A valid argument is a sequence of propositions, the first batch of which are called the premisses of the argument, and the last of which is called the conclusion of the argument, such that the truth of the conclusion is entailed by the truth of the premisses. There are clearly specified grounds for logical implication. See Suppes (1957), for example, on the "rules of inference" for a logical system within which an argument is developed. Regardless of "hand-waving" rhetoric, no "conclusion" is a "logical conclusion" unless those inferential conditions are satisfied within the argument made. (There is in particular the matter of the distribution of terms. For example, for the argument to be valid it is necessary though not sufficient that any term in its conclusion be present in its premisses.)
On the way towards verification of the overall validity of an argument, it is useful for the checking of its composing sub- arguments to distinguish for selective investigation certain components of the "theory" - such as its definitions (given as needed to fix the essential concepts and to designate the universe of discourse), and its hypotheses (propositions whose truth status is as yet unknown). One can then sort the premisses of an argument into [i] the contingent parts of the overall theory (and within that the hypotheses and definitions); [ii] the empirical parts of the "overall theory" (propositions asserted in the light of relevant observations made, as with the data gathering of experiments, or surveys, or suchlike); and [iii] the convenient assumptions (propositions adopted tentatively as true for the sake of rendering the overall argument valid). In the case of category [iii], if any such assumption is actually false, even if the argument is valid the conclusion is not proven, and one should not be presenting that conclusion as true.
Considered generally then from a logical standpoint, "data analysis" is part of a process of argument from premisses - which include some conjecture to be demonstrated - to a conclusion - that the conjecture is true, or false as the case may be. More specifically, data analysis is properly just that part of an attempt to develop a (logical) argument from premisses to conclusion which brings those empirical propositions of category [ii] into their proper relationship with those contingent propositions of category [i] and those assumptions of category [iii] so that the validity of the overall argument can be tested as a preliminary to the determination of the truth status of the theory (and of its parts) under consideration. Within this conception, techniques and procedures of "data analysis" are simply ways of realizing some sub-stages of the overall argument.
It is incumbent upon data analysts to make manifest the logical form of their "arguments" in support of their "conclusions". Any such argument will be either valid (in the strict logical sense), or invalid. It can be readily determined from the scrutiny of almost any empirical report that the arguments of experimental/observational science are invalid (even where they could be properly completed and developed as valid). That means that their conclusions are not certainly true. Furthermore, in the discourse of science much argument is rhetorically invalid - amounting to "hand-waving" appeals to believe. The problem with an invalid argument is that it does not establish with certainty the truth of its conclusion, despite any rhetorical claim to the contrary that the conclusion put forward is true. What one needs instead from data analyses are valid arguments, not rhetoric.
One can claim that a "conclusion" is a "logical conclusion" if and only if the argument leading to it is valid. One can determine by argument whether or not a theory is true only if the "conclusion" of the argument is a "logical conclusion". One should not seek by argument to persuade others to believe the truth of a "conclusion" unless both some relevant tested theory is true, and the "conclusion" proposed is the logical conclusion of that valid argument which was used to demonstrate the truth of the relevant theory. Even if the seeking of "proof" were to be an unworkable counsel of perfection, it would remain that any line of argument which is as complete as possible, and for the most part valid in its sub-arguments, is to be favoured over any incomplete argument larded with fallacies.
What difference does it make to the understanding and prospective development of data analysis to see it from this logical point of view? The following notes make a start with the answering of that question.
At least two "philosophies" of data analysis are conventionally acknowledged: the "exploratory" (see for example Tukey, 1977); and the "confirmatory" (see for example Joreskog, 1969).
The primary motivation for carrying out "exploratory data analysis" was to avoid the strictures of statistical tests of significance. Eschewing consideration of the matter of chance inherent in the drawing, from a reference population of objects, that sample from which one subsequently obtains one's data, one was to consider just the data in hand, divining its "pattern" or "structure", and thence stating its "indications", (the latter being equivalent to stating one's "conclusions" from the "exploratory data analysis" made). There is, however, no guaranty that different "data analysts", when "exploring" independently one and the same corpus of data, will find in it one and the same "structure", or discern for it the same "indications", or draw from it the same "conclusions". Where there is such variation, "exploratory data analysis" is at most serving only an heuristic function for generating conjectures, albeit put forward in the guise of "conclusions." At that stage of enquiry, the truth status of any such "conclusion" does not differ at all from that of an hypothesis. More precisely, what is concluded is no more than a conjecture yet to be tested, rather than being an hypothesis already tested and shown to be true. Consequently, with the exception to follow, there is no justification for presenting any general "conclusion" from an "exploratory data analysis" as something to be believed as true. Using arguments presented above, it may be possible to justify a "conclusion" from some "exploratory data analysis", but only if some pertinent theory, previously implicit, is then made explicit within a valid argument. (To that end, a critical conceptual analysis of the notion "structure in data" may help to reveal theories implicitly entertained by exploratory data analysts. See Rozeboom, 1961.) Otherwise, in the absence of any explicit empirical theory, no general "conclusion" from an "exploratory data analysis" can be properly claimed to be true.
The primary motivation for "confirmatory data analysis" was to cut down (preferably to just one) the number of alternative "interpretations" one could put upon a data set. This was to be achieved by selecting and making explicit some hypotheses to be tested. One nominated a particular favoured hypothesis and sought by the confirming of it to establish the authority of that hypothesis over others for interpretation of the data. There are, however, three possible outcomes of the test of an hypothesis: the test may prove inconclusive; and otherwise a conclusive test will lead either to confirmation of the hypothesis or to its refutation. Any test should be neutral with respect to those three possible outcomes rather than be biased towards just one, viz. confirmation, (such as might flow from a rhetorician's desire to convince others of the truth of the hypothesis which s/he champions!) Thus, while "confirmatory data analysis" is consistent with the logical standpoint to the extent that it emphasises the making explicit of guiding hypotheses, there is need for unbiased testing of such hypotheses, and for a label more neutral than the adjective "confirmatory".
By considering data analysis from the logical point of view, one can both link the two aforementioned "philosophies", and come up with a merger which avoids the objections just directed at them. The nominal resolution is to drop the adjectives "confirmatory" and "exploratory", and to replace them with qualifiers in the respective phrases: "theory-implicit data analysis"; and "theory- explicit data analysis". At the same time, the methodological resolution is to see [a] that it is the question whether or not some guiding empirical theory is made explicit which primarily distinguishes "confirmatory" and "exploratory" data analyses; while [b] the questions, [b.1] whether or not one should address the matter of chance in the sampling of data, and [b.2] whether or not one should favour confirmation of some sponsored hypothesis over other hypotheses, are secondary. Question [b.1] is logically independent of question [a], and question [b.2] is interpretable only in the context of a prior affirmative answer to question [a].
In cases of "theory-implicit" data analysis, for lack of valid argument due to incompleteness of the theory, strictly speaking one cannot draw any final logical conclusion. In any such case, it is more appropriate to conceive of any so-called "conclusion" as as-yet-untested conjecture and thus needing further investigation incorporating "theory-explicit" data analysis. On the other hand, "theory-explicit" data analysis is not a panacea: if invalid arguments are used in association with "theory-explicit" data analysis, there too any final "conclusion" from the investigation is suspect. Provided, however, that valid argument is used throughout, disinterested enquiry incorporating "theory-explicit" data analysis can lead to true conclusions about the guiding theory tested. It is only in this latter case that one has objective grounds for urging anyone to believe one's "conclusions".
Some final notes from the logical point of view, concerning technical developments under the rubric of "data analytic techniques and procedures".
Within the operational tradition there is little or no reference to such theory as may be motivating the great proliferation of techniques and procedures during recent decades . That is, most often with respect to their development and application, one finds "theory-implicit" data analytic techniques and "theory-implicit" data analytic procedures. In the absence of awareness of the guiding function which empirical theory can serve with respect to data analysis, the failure to state at the outset any empirical theory pertinent to "data analysis" has led to the posing of questions such as (a) "where should this technique (or procedure) be applied?" and (b) "how may this technique (or procedure) be validated?" See for example, Bock (1994), Gordon (1996), and Lapointe (1996).
If one begins with an explicit empirical theory, say ET, one can then judge what techniques t and/or procedures p of data analysis may be needed to test ET. If such techniques and/or procedures t and p are already available, not fortuitously but having been specifically developed previously to help with the testing of some theory ET*, and if ET* is analogous to ET in relevant ways, then one may make use of t and/or p as required for the testing of ET. In any such case, relevant answers to the questions of (a) application and (b) validation are immediately obvious: (a) technique t (and/or procedure p) applies to data analysis in the context of testing ET because technique t (and/or procedure p) was specially devised to be used as part of the testing of theories of that sort; and (b) technique t (and/or procedure p) is valid to the extent that t (and/or p) fulfils its intended logical function in the process of testing ET. In this first "theory-explicit" case, the meanings and the conditions of relativity of the notions "application" and "validity" have been fixed. That is, with respect to the questions "In what context, X, is it appropriate to apply technique t (or procedure p)?" and "For what purpose, Y, is technique t (or procedure p) valid?", both X and Y have been specified.
On the other hand, outside of the "theory-explicit" case just considered, questions (a) and (b) are not immediately answerable because in this second "theory implicit" case neither the meanings nor the conditions of relativity of the notions "application" and "validity" have been specified. Obviously from the logical point of view, to avoid that difficulty, the formulation of any given data analytic technique or procedure must be prefaced explicitly by an empirical theory, as it is that which determines the context within which the technique or procedure may take its form, and have its place, and serve its proper function.
For science to progress, priority must be given to empirical theory, not only over experimentation, but also over the development for their own sake of techniques and procedures, and over the use of the latter for data analysis.
References
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& Robertson.
Baker, A. J. (1986) Australian realism: the systematic philosophy
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Barthelemy, J-P. et Guenoche, A. (1988) Les arbres et les
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Kempthorne, O. (1952) The design and analysis of experiments. New
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The 1998 annual meetings of the Classification Society of North America (CSNA) and the Psychometric Society (PS) will be held jointly at the University of Illinois in Urbana, Illinois from Wednesday June 17th until Sunday June 21st, 1998, at the Levis Faculty Center on the University of Illinois campus. The meeting is supported by the Department of Statistics and the Department of Psychology, University of Illinois.
Short courses are planed for Wednesday June 17th, with regular sessions beginning on the morning of Thursday June 18th. There will be a reception, business meetings of both societies, and a banquet during the meeting. CSNA and PS meetings are traditionally informal and very interdisciplinary. Abstracts of papers are distributed, but no formal proceedings are produced. Speakers are encouraged to discuss work in progress, of either applied or methodological nature.
The following contributed paper sessions are currently
planned:
Applications
Applied Statistical Methods
Bayesian Statistical Methods
Categorical Data Analysis
Classical Test Theory
Classification
Cluster Analysis
Correspondence and Homogeneity Analysis, and Optimal Scaling
Covariance Structure and Factor Analysis
Exploratory Data Analysis
Graphical Models
Item Response Theory
Linear Models
Longitudinal Data Analysis
Multidimensional Scaling
Multivariate Statistical Methods
Networks and Graph Theory
As traditional, the meeting will have presentations by the Presidents of the societies, and several invited lectures. There will be a special session for graduate student presentations. Current information about the meeting can be found at the WWW site http://www.conted.ceps.uiuc.edu/fmpro/psychometric_society.form.html
The program committee is Ulf Bockenholt, David Budescu, David Dubin, Stephen Hirtle, Jacqueline Meulman, with co-chairs Ivo Molenaar, Carolyn Anderson, and Stanley Wasserman. The committee is open to suggestions for topics, symposia, panel discussions, and other contributions. Please direct your suggestions to Stanley Wasserman, University of Illinois, 603 East Daniel Street, Champaign, IL 61820 USA; telephone 1-217-333-3325; fax 1-217- 244-5876; email pscsna98@s.psych.uiuc.edu. A formal announcement of the meeting will be issued late in 1997. Abstracts will be due in March, 1998.
* JULY 6-10, 1998: 14th Australian Statistical Congress, Jupiter's Casino, Gold Coast, Queensland, Australia. Programme Chair: K. Basford, Local Organization: W. Robb. Address: ASC14, School of Mathematical Sciences, Queensland University of Technology, GPO Box 2434, Brisbane QLD 4001, Australia. email: asc14@qut.edu.au, fax: +61 7 38642310. web: http://www.math.fsc.qut.edu.au/asc14.html
* JULY 21-24, 1998: 6th Conference of the International Federation of Classification Societies, Rome, Italy. Put it on your calendars - - - more information will be appearing later.
* SEPTEMBER 28-30, 1998: Ordinal and Symbolic Data Analysis, University of Massachusetts, Amherst, MA.
This conference continues a sequence of conferences which started with two conferences on Ordinal Data Analysis in March 1992 at the TH Darmstadt and in October 1993 at the University of Massachusetts (Amherst) and continued with the International Conference on Ordinal and Symbolic Data Analysis in June 1995 at the Ecole Nationale Superieure des Telecommunications (Paris), as well as the Ordinal and Symbolic Data Analysis Conference in March, 1997 at TH Darmstadt. The theme of the conferences is motivated by the fact that ordinal and symbolic data occur quite frequently, but theoretical tools for handling ordinal and symbolic data are not sufficiently developed. The physical layout of the facilities, as well as the design of the program, will encourage active discussions and frequent exchanges of information during the conference. E. Diday (Paris), M. F. Janowitz (Amherst), and R. Wille (Darmstadt) are the conference organizers. The conference will be supported in part by the University of Massachusetts. Despite this, attendance at the Conference will involve a nominal registration fee. Courses on Conceptual Data Analysis and on Conceptual Knowledge Processing will be offered immediately before the conference (the morning of September 28) at the University of Massachusetts.
The DEADLINE for applications and abstracts is July 1, 1998. If possible the abstract should be submitted in LaTex, and should not consist of more than a single page. A template for the abstracts is available on request.
Inquiries, applications and abstracts should be sent to:
Department of Mathematics and Statistics
University of Massachusetts
Lederle Graduate Research Tower
Box 34515
Amherst, MA 01003-4515, USA
or preferably by Email to:
OSDA98@math.umass.edu
Further information about the conference may be obtained from the Conference Web site:
Associated with the Conference there will be a special session on "Ordinal Structures in the Social and Behavioral Sciences". Information about this session may be obtained from its organizers, Professor Jean-Paul Doignon of the Universite Libre de Brussels (Email: doignon@ulb.ac.be) and Professor Jean-Claude Falmagne of the University of California at Irvine (Email: jcf@aris.ss.uci.edu)
Stephen Hirtle, hirtle+@pitt.edu, CSNA Webmaster.