Mid-American Review of Sociology

Sampson, S. 1969 Crisis in a Cloister. Ann Arbor: University Microfilms. Number IN RELATION TO SCIENCE AND SOCIAL 69-5775. NONSCIENCE: A CRITIQUE OF Shepard, R. and P. Arabie PEARSON AND FISHER 1979 "Additive clustering: representation of similarities as combi­ nations of discrete overlapping properties." Psychological Review 86:87-123. Snyder, D. and E. Kick Robert J. Wazienski 1979 "Structural position in the world system and economic growth, University ofKansas 1955-1970: a multiple network analysis of transnational inter­ actions." American Journal Sociology 84:1096-1126. Mid-American Review of Sociology, 1981, Vol. VI, No.1 :41-49 Steiber, S. 1980a "Quantitative models and methods for world-system analysis." The Sociological Quarterly 20:forthcoming. The objective set before us in this work is to explore the 1980b "International trade and domestic development: a cross­ direction which social science has taken in this century. We do national assessment of dependent relations in the world­ not intend to focus our attention on the nature and occurrence system." mimeo. of phenomena, for these empirical notations are important only Stolzenberg, R. 1979 "The measurement and decomposition of causal effects in if one wants them to be. Furthermore, they are not relevant to nonlinear and nonadditive models." Pp. 459-488 in K. Schess­ science. The goal here is to simply distinguish, using a few isolated ler (ed.), Sociological Methodology 1980. San Francisco: examples, between science and empiricism. Jossey-Bass. There seems to be remarkable confusion as to the distinc­ U.N.E.S.C.O tion between science and empiricism. We must note that this 1968 Statistical Yearbook 1966. Paris: United Nations Educational, confusion is not new. Scientific and Cultural Organization. White, H., S. Boorman, and R. Breiger 1976 "Social structure from multiple networks I." American Journal In ancient times there was no social science. What we call social of Sociology 81 :730-780. science was then called social philosophy or political philosophy or ethics. Aristotle's political and ethical philosophy, for ex­ ample, was the same as his social science. It was much latter, with the success of Newtonian science, that social thinkers felt _t1)~t it was .possible to cr~a~e. a J!lQd~r~ social ~si.en.ce. ~~i!iU to ,-. ~ the modern natural sciences. This modern or positivistic social science would have one basic characteristic, it was thought: it would be scientific (Stern, p. 1).

It was thought, and believed, that this "scientific" approach along with the statements derived thereof could introduce the capability of interpersonal agreement. The worth of this notion is sound, in that it is consistent with the function of science and reflects an adequate goal of the social sciences. However, along the path from social inquiry to social science, a reversal of the

40 A Critique of Pearson and Fisher Mid-American Review of Sociology Notice the bent to Galileo's perspective. It implies that pheno­ stated intention has occurred. It will suffice to say that the dis­ me?a (physical and social) has, or can have, an abstract represen­ cipline of sociology has advanced in a circular fashion, and that ration for studying it in the purest sense. It also indicates that modern empiricists are nowhere closer to the scientific approach modifications take place after abstraction. than they were three hundred years ago. Quite simply, they have Only w~th a conception of abstraction, can a modeling increased their efforts only to lose sight of their goal. In essence, proced~re (WIth laws and principles) be presented. It should be science has been put at bay for the sake of empiricism. emphasized that this modeling procedure, as an interpreted geo­ The task before us is to set down this scientific approach in m~try, must be a wholly and totally abstract representation. To the Galilean tradition, and to critically analyze the essential this extent, a modeling procedure indicates the order of pheno­ stance of two important authors in the social sciences; Karl mena and not the opposite. "... the phenomena to be investi­ Pearson and Sir Ronald Fisher. Although this task is fragmented gated is modeled and subsummed by the calculus ... such that a and isolates only a few examples, it provides an intellectual dynamic picture is generated. This formulation then guides the impetus for detailed analysis. whole o~ the experimental process..." (Willer, p. 3). The point of reference for this paper is the conception of . ThIS statem~nt, as a theoretical and methodological guide, exact science implicit in the work of Galileo Galilei's Dialog Con­ IS well gr?unded In.the work ofGalileo. As one example, " ... we cerning Two New Sciences. The work here cited is more than a are confirmed mainly by the consideration that experimental mere discourse of Mechanica (statics) and Movimenti Locali results are seen to agree with and exactly correspond with those (dynamics) but rather is a prescription for theory and methods properties w~ich have been ... demonstrated by us" (Galileo, in the scientific enterprise. . p. 160). That IS, we have demonstrated it first! Three issues are isolated in this paper, for they seem to mark By ~his we c~ s~~ that abs~raction is the necessary process (account for) much of the divergence of Pearson and Fisher from from which the scientific enterprIse proceeds. It is central to the exact science. They are abstraction, modeling, and rigidity. Each work of Galileo and it is absent (for the most part) in social of these concepts have been misused or ignored in the sociologi­ science. cal endeavor (theory and research) whUe they have been fun- We must also consider the most misunderstood term in damental to the exact sciences. social science today; that of rigidity (or rigor). When Galileo Galilee knew what abstraction meant. Furthermore, he ' state.s "I propose to demonstrate in a rigid manner," he means understood the difference between the abstract and the con-· precisely that he will define what is included in properties and crete. The distinction here is actually quite elementary if we .. p.roc;~clQres_alJ.q. ..what willbe ignored. In conjunction with abstrac­ ...consider the following: non and modeling this rigor is practiced in the exact sciences. The work of Galileo has set the premise for scientific achieve­ ... I .. . call to your attention the fact that these forces, resist ment, ye.t t~is direction has been misunderstood or ignored in every movements, figures, etc., may be considered either in the the apP~Ication of theory and methods in the social science. abstract, dissociated from matter, or in the concrete, associated Abstraction do~s. not dominate as the preliminary step in social with matter. Hence the properties which belong to figures that theory, as empirical observation has come to the fore. Modeling are merely geometrical and non-material must be modified procedures do not order anything, but rather are set to the cast when we fill these figures with matter..." (Galileo, P: 112). of empirical data. Rigor has been systematized to the point where uncertainty can be "rigorously" calculated. These attempts lead away from, and not toward, exact science. 43 42 A Critique ofPearson and Fisher Mid-American Review of Sociology discovery as the creation of the 1 f' . p. 76). So where does Pearson's c faw.o gravitation" (Pearson, We need only to turn to Karl Pearson to see how the aim of on US10n of abstracti . e answer to this questi .. h. straction come in? science is lost, to a degree, in regard to the science of society. Th on 15 ill IS CO . f aws or "resumes" These "b . f . nception 0 scientific He had provided a type of systematic empiricism that was not I · rie expressions' hi solely based upon observables but also based upon the prediction th an generalizations As such th ns are not mg more abstraction of law in th ey ~eed to be separated from the of events based on observables. The observables with which e exact SCIence P £ il d He states that "Th If. · earson a e to do so. Pearson is concerned, is human society. e aws 0 SCIence h ld b At the very beginning of his work, The Grammar ofScience, the creative imagination . "s ou e associated with saying that "(S) . dID man but contradicts himself by Pearson states that " ... a change has taken place in our apprecia­ cience en eavors to .d of the universe" (P prOVI e a mental 'resume' tion of the essential facts in the growth of human society," earson, p. 36) In h the "creative imagination" ith ' .. alessence e has associated (Pearson, P: 1) thus entrenching the need for scientific explora­ In The G WI. empmc generalizations. tion of the human entity. This, in itself, is a noble task (although rarnrnar of Science P our knowledge of the future b earson asserts the claim that not an original one) and is deserving of some commendation. J future will be like our e . IS ased on the past. "That the But, however clear the task may be, the "methods" lack severely. . xperlence of the . h tion under which we can di h. past IS t e sale condi- Consider the following statement (in a Weberian sense if you id pre ict w at 15 abou~ h choose) with respect to its honesty and intent. "The scientific gUl e our conduct" (Pearson 1957 to appen and so a distinct misunderstand" 'f h ,p. 3.6). ThIS statement shows man has above all things to strive at self-elimination in his judge­ mg 0 t e meanmg f sci £ C suppositions cannot p di d1 0 SCIence, or empiri- ments, to provide an argument which is as true for each indivi­ al. re ict regar e f h 11 :i:~:,~~~t;~~~j~~:·· gUIde. Furthermore it b ss 0 ow.we they may dual mind as for his own" (Pearson, P: 11). This statement is in ,ases tch e universe. reference to the role of science in society (citizenship) and taken ... ;';{~.<'.:,"~a-~;f.:~~~ regu ar) irregularity In thi h on an assumed (or 1 · 15 case t e fail . by itself (the "self elimination of judgements" concept) is in o f abstraction has led to th for lati ure to recogmze the use "science" where independ e ormudatlon. of a regularly inexact agreement with a scientific endeavor. But consider this "method" ence an equivalenc I d now in relation to how unscientific the perspective truly is..:;: .."...._,.~,.-'" .. ~;~~~';, We should turn back to GalU y are exc u ed, two essential points: namel b eo ~o see that Pearson missed "The classification of facts, the recognition of their sequence y a straction and m d 1· P and relative significance is the function of science" (Pearson, does not separate abstraction from ali 0 e mg. earson P: 11). The observant reader of Karl Pearson would realize that _~:',,";::~:;;!.'':~:-~1i:ilFIZ':' these generalizations are seen as "1 g~ne~. ~atlOns. To Pearson r"t.kC'Q11"-':7".klt:"'~ of accuracy in empirical I. hios W lC represent a degree these "facts" of which he writes so reverently are "d re ations IpS yet to I· or at best they are based on observables. Systematic empiricism ~,~::;.":,<,:,:,:,,;~~':" .: egree of accuracy" could I d i occur. n SCIence a The~ TssueISsue ISd further confusednotineatha us 1"0_..,any 1av•..T or premctlon.1·· thus oper·afes·undeLthe guh"'C of Sd-eLice..for Pearson. perlence does not sh at Pearson believed that ex- If the reader interprets Pearson to be thoroughly misled OW an exactness . lationshi t erefore, equivalence b t ill any re ationship, and (wrong) in his conception of science, it is just as easy to believe h e ween any rel ti hi . .It is clear that an und d. a Ions lp IS not possible. that he (Pearson) is thoroughly confused instead; for Pearson . erstan mg of th f b IS missing. Secondly hi " d 1. e purpose a a straction does display that he might know what science is. "The discovery , IS rna e ing" d . . of Law (scientific law) is the peculiar function of the ereanve cumulation of the "facts." A m d I. proce u:e IS a SImple ac- Its' predictive bili li . . 0 e IS not derived from "facts." imaginatio (Pearson, P: 32). This statement does not n" generalizations (an~t~he e: ~ ~~~ !evel of abstraction. Empirical Pearson from science in an inportant sense, but subsequent of uncertainty h. h P 0 a mes thereof) produce a "science" mentary does. The initial reaction is that Pearson has, after self. In this rew d 1C cannot prediict, def me or even justify it- an understanding of abstraction, as this misconception is on "Cause and ~a:-fec~~:r:~rboil~he~~plied reas?ns) his discourse supported: "The statement of this formula was not so much a lty 15 a moot pomt. 45 44 Mid-AmericanReview of Sociology A Critique ofPearson and Fisher By the time Sir Ronald Aylmer Fisher had completed The The implications of this are surely complex in mathematical empiricis~ beco~e Design of Experiments, systematic had" form. But this is where complex mathematical formulation is s~Ience. ~IS­ thoroughly confused with (and mislabeled) The muddled with the elements of science. The above statement does ~o~cerned tory ... of systematic empiricism in sociology IS ';Ith not involve a theoretic calculus based on an abstract model. It is the development of systematic methods of aSSOCIatIon, relation, based on observed error terms (deviation) or probablistic error and induction and was completed when Fisher provided a method terms resting on the. binomial expansion. It (itself) is precise, of association by significance tests" (Willer, p. 16). .. but only to the extent that it is a precise measure of non-deter­ To most empiricists, the procedures and practicality of mination. designing research has come to the foregr~und. The concern. is .Furthermo~:, Fisher's method assumes the interpretations of with setting up and evaluating research designs rather tha~ WIth classlc~ probabih~y theory (based on a-priori assumptions) while the logical process of going from "association to .relation to employing a rela~lve freque.nc! model (an a-posteriori approach). induction to produce an empirical generalization" (Wil!er, p. 61). The effects of rhis, contradlctlOn not withstanding, are misleading What has evolved is not the "rigid" process that Galileo speaks to the extent that the sum ofsquares principle cannot be attended of, but rather a "rigid" process whereby uncertainty is calculated to in any predictive sense. Yet Fisher's approach rests on it and is rigorously. "We may at once admit that any .inference from the commonly called "scientific." particular to the general must be attended WIth ~ome degree of . A. further comment must be made in light of the foregoing uncertainty, but this is not the same as to admit that such ~ d~cusslon. Although the analysis ofvariance technique is a test of inference cannot be absolutely rigorous" (Fisher, p. 4). ThIS dIf~erence in means, it is based upon the comparison ofvariances. statement prescribes nothing more than a rigorous calculation T~lS further aborts scientific modeling procedure by leaving cer­ of uncertainty. Furthermore, any induction at this point has no tam values "free to vary." promise (mathematical or theoretical) from which to proceed. , 7o.Fisher, testing a null hypothesis was simply a matter of In his calculation of uncertainty Fisher has adopted the distribution and randomness. His purpose was with the deter­ t~e normality assumption and in effect uses the equation for minatio~ of rand,o~y distributed differences and had very little normal curve along with measures of central tendency and dIS­ to do WIth associanon. In effect, a test of a random distribution persion. The resulting error terms are applied statistically to is a test of the. d~ta inc!usive of that distribution. It is not truly associations. a, test of ~ssocIatlOn. FIsher extends the application beyond a simple affrrmation of distribution and randomness to that of .~,~hemselves .. . estimates may be made, which contain the .. as~~c~atio~.. What he. has come up with, in reality, is a false. faith whole of the information available for finite samples. These in randomness. especially valuable and comprehensive estimates are called suffi­ cient statistics, and the great simplicity of problems, which fall Having decided that ·., our estimates of the error of the average under the head of theory of errors, is due to the fact that with difference must be based upon the discrepancies between the the normal distribution both the quantities requiring estimation, differences actually observed, we must next inquire what pre­ the mean, and the variance, posess sufficient estimates. It is for cautions are needed in the practical conduct of the experiment this reason that in so much experimental work we need only be to guarantee that such an estimate shall be a valid one .... concerned with the precision of the total, or mean, of the values Randomization properly carried out ... ensures that the esti­ observed, and with the estimation of this precision from the mates of error will take proper care of all [differencesJ, and sum of squares of the residual deviations (Fisher, p. 248). relieves the experimenter from the anxiety of considering and

46 47 Mid-American Review of Sociology A Critique of Pearson and Fisher

estimating the magnitude of the innumerable causes by which REFERENCES his data may be disturbed (see Fisher, p. 46-50). Carter, Lewis, N. Krishnan Namboodiri, and Hubert Blalock Carter, Naboodiri and Blalock state an interesting corrolary 1975 Applied Multivariate Analysis and Experimental Design. McGraw Hill. New York. to this. Fisher, Sir Ronald A. . 1935 The Design of Experiments. Oliver and Boyd. London. Sir Ronald Fisher ... was once asked: What would you do if, Galilei, Galileo drawing a Latin square at random for an experiment, you hap­ 1954 Dialogs Concerning Two New Sciences. Trans. Henry Crew paned to draw a Knut Vit square? Fisher remarked that he would and Alfonso de Salvia. Doves Publishing, Inc. New York. Pearson, Karl discard the selection and draw again..." (Carter et al., p. 13). 1937 The Grammar of Science. Dent. Ltd. London. Stern, Herold S. The commentary to this is that analysts should avoid random 1973 Social Nonscience: A Critique of Social Science. Stipes Pub­ arrangements which are clearly patterned. If this is so, then the lishing Co. Champaigne, concepts of randomization is valid only to the extent that it Toulman, Stephen reflects a-posteriori probability assumptions. Beyond this point, 1960 The Philosophy of Science. Harper and Row. New York. Willer, David and Judith Willer randomness is discarded. This is not science-it does not even 1973 Systematic Empiricism: Critique of a Pseudoscience. Prentice resemble scientific procedures. It surely is systematic, but such Hall. Englewood Cliffs. a badge is not "holy" enough for persons of this discipline to Willer, David wear. 1976 "What is Exact Theory?" Research paper presented to the On the basis of what has been written here it seems clear National Science Foundation. (even in so few examples) that Fisher and his method are not scientific. Fisher does not mention abstraction, and his "models" (experimental designs) are applied to mathematics as if they and ./~:i{;"£<~'_':~

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