Statisticians and Political Scientists

Statisticians and Political ScientistsAuthor(s): Harold F. GosnellSource: The American Political Science Review, Vol. 27, No. 3 (Jun., 1933), pp. 392-403Published by: American Political Science AssociationStable URL: http://www.jstor.org/stable/1947438 .

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STATISTICIANS AND POLITICAL SCIENTISTS

HAROLD F. GOSNELL

University of Chicago

In his classic book, Human Nature in Politics, published in 1908, Graham Wallas said: "We must aim at finding as many relevant and measurable facts about human nature as possible, and we must attempt to make all of them serviceable in political reasoning."' While the point of view which Wallas expressed at that time has by no means been universally accepted, and is today challenged by men like Charles A. Beard,2 certain steps have been taken toward its recognition.

Wallas was particularly impressed by the successful use of quantitative methods made by the economists, and well he might be. To mention a single case, the work of F. Y. Edgeworth, in the measurement of utility, the algebraical or diagrammatic determination of economic equilibriums, and the application of the theory of probability to sampling and in the measurement of economic value or index numbers, showed the trend of the times in economics. The twentieth century has marked an acceleration of this trend. Politi- cal scientists have not only lagged far behind the economists in the use of statistics, but they have shown important resistance in some sections to following in this general direction. What is the ex- planation of this situation?

It is obvious that units of measurement are harder to find in politics than in economics, where there are data in units of value such as price and wage data and also production data in physical units. What are the units of measurement in political science? George E. G. Catlin stoutly maintains that the vote constitutes a unit of measurement in politics which is analogous to the price unit in economics,3 but this view has met strenuous opposition.4 It is clear that in countries where there are dictatorships, as in Fascist Italy, in Russia, and in Turkey, the vote has not the same weight

1 Page 140. 2 Appearing under the title, "Political Science," Chap. Ix in W. Gee (ed.), Re-

search in the Social Sciences (New York, 1929). See also R. K. Gooch, "Government as an Exact Science," Southwestern Political and Social Science Quarterly, Vol. 9, pp. 252-263 (December, 1928).

3A Study of the Principles of Politics (New York, 1930). 4 W. Y. Elliott, in S. Rice (ed.), Methods in Social Science (Chicago, 1931), pp.

84-85. 392



STATISTICIANS AND POLITICAL SCIENTISTS 393

that it has in England, France, and the United States; and even in the so-called democratic countries, the weight of the vote varies with social and administrative conditions. The vote as a unit of political support has yet to be standardized. Another reason for the slow progress of the statistical method in political science as com- pared with economics is the fact that the traditional training of political scientists has been in history, philosophy, and law, and not in statistics and mathematics. Furthermore, the received body of political theory does not readily lend itself to the stating of problems in quantitative terms. Many of the so-called economic laws which have been verified by statistical investigations have been revised and restated in the process.

In addition, measurement studies have suggested empirical laws, like the law of cyclical fluctuations, which the economic theorists have endeavored to explain. Political theory has not yet reached this stage. G. E. G. Catlin, P. S. Florence,5 Stuart A. Rice,8 Herman C. Beyle,7 and others have started a re-formulation of political theory in terms which may permit the setting up of hypotheses for empirical investigation. Catlin has discussed a number of so-called political laws; Florence has developed the concepts of rule relations, work-sharing relations, and manning relations; and Rice has been concerned with "available evidence concerning those factors or 'forces' that give rise to political activity and that determine its form and direction." These are initial steps in the direction of a statistical politics, and they are very important.

While most political scientists have been continuing in the traditional ways of history and public law, their field has been invaded by economists, sociologists, psychologists, and educators equipped with statistical techniques who have seen interesting problems in the field of politics. It may be of interest here to review briefly how certain statistical techniques have been used in solving political problems of a non-administrative type. The importance of the studies which will be mentioned varies considerably, and so does the appropriateness of the techniques. In the space available, it is not possible to make an exhaustive review of the subject. The critics of quantitative methods in political science might employ some of the studies to be mentioned to argue their case for the use

6 The Statistical Method in Economics and Political Science (New York, 1929). 8 Quantitative Methods in Politics (New York, 1928). 7 The Identification of Attribute-Cluster-Blocs (Chicago, 1931).



394 THE AMERICAN POLITICAL SCIENCE REVIEW

of other methods. In this connection, it should be pointed out that no reputable statistician argues that the quantitative method must be used to the exclusion of other methods. Statistical studies depend upon qualitative descriptive analyses for fruitful hypotheses and interpretations.

An early step in any statistical investigation is that concerned with the question of units, terminology, scales, and questionnaires. It is obviously foolish to count data which are indefinite, inac- curate, and ambiguous, and expect the results to be definite. It is also ridiculous to use refined mathematical formulas on data which are full of errors that have been made in the original observations and records. For example, a number of studies of referendum votes in Chicago were made, using tabulation and correlation, before it was discovered that there was a large margin of error and fraud in the counting of these votes.9 It is likely that for some time the application of statistical method in politics will be confined largely to the testing of units and the standardization of terminology. This is by no means an easy task, as measurements in the social sciences are usually indirect and it is very difficult to indicate how closely the evidence which is counted is related to the quality which is being studied. As will be shown in some of the examples, the setting up of units or scales for some problems involves a thorough familiarity with the whole field of statistics.

The framers of the Constitution of the United States were confronted with problems of statistical terminology in laying the foundation for the federal census. The definition of "negro" raised many delicate questions, some of which are still confronting the federal authorities.10 Who were these "other persons?" How was free status to be established? How were the mixed bloods to be

8 In discussing this paper, Professor F. Stuart Chapin contended that measurement should be carefully distinguished from enumeration. Measurement involves the selection of an arbitrary scale, while enumeration is nothing more than counting. According to Graham Wallas, social scientists are not likely to discover a new physical unit like the ampere or wave length. In this paper, the word "measurement" is not used in the sense in which it is employed in the physical sciences. Measurement here means making the most exact, objective, clear, appropriate, and comparable observations possible. The whole question of units has been well discussed by G. A. Lundberg, in his Social Research (New York, 1929).

1 D. Maynard, "Fraud and Error in Chicago Referendum Returns," National Municipal Review, Vol. 19, p. 164 (1930).

10 On this point, see D. Young, "Statistical Studies of Race Relations," in S. A. IRice (ed.), Statistics in Social Studies (Philadelphia, 1930), Chap. v.




counted? As the scope of the federal census has expanded, there has been an ever-increasing number of problems of notation. Any political scientist who uses the federal census should consider the appropriateness of the census definitions for his purposes. For example, in trying to show the relationship between illiteracy as given by the census and voting responses, it should be remembered that the census enumerators do not give actual literacy tests, but merely ask a direct question which is not likely to be answered truthfully where literacy is generally regarded as a social necessity.

In connection with the analysis of the voting behavior of legislators and legislative groups, a number of units and scales have been developed. Legislative votes lend themselves to statistical analysis more readily than popular votes because they are not secret, and because they are much more varied in character. President Lowell was one of the first to recognize this, and he devised his ingenious definition of a party vote in a legislative body over thirty years ago.11 For more than twenty years, his work re- mained an unanswered challenge until Rice worked out his so- called indices of cohesion and of likeness between legislative groups.'2 Rice also attempted to define a legislative bloc in more generalized terms on the basis of the interrelation of the agree- ments between pairs of legislators."3 Herman Beyle has also worked on this problem, and he has devised a notation that he calls the "index of significant cohesion of pairs." While the logic of Beyle's method and the usefulness of his procedure is open to question, the actual steps that he takes in handling his data are definitely set forth, and his method can be checked by other statistical techniques. L. L. Thurstone has already suggested a different approach in an article in which he outlines the application of the method of multiple factor analysis to the discovery of blocs.'4 In contrast to Beyle's method, Thurstone's method utilizes all of the data and calls for the preparation of a four-fold table for every possible pair of measures and the calculation of a tetrachoric correlation coeffi-

"1 "The Influence of Party upon Legislation in England and America," Annual Report of American Historical Association, Vol. 1, pp. 431-542 (1901).

12 Farmers and Workers in American Politics (New York, 1924). '1 Quantitative Methods in Politics. 14 "Multiple Factor Analysis," Psychological Review, Vol. 38, pp. 406-427 (Sep-

tember, 1931); "A Multiple Factor Study of Vocational Interests," Personnel Journal, Vol. 10, pp. 198-205 (October, 1931). Tetrachoric r is discussed by T. L. Kelley, Statistical Method (New York, 1924), p. 253.




cient for each pair. The implication of Thurstone's work is that the definition of a legislative bloc involves elaborate mathematical logic.

The use of popular votes to study variations in political attitudes calls for the testing of the materials and the careful setting up of categories. What is the machinery for the determination of the number of eligible votes? What method will be used in defining a party vote? Edgeworth, in a study of popular votes in three British parliamentary elections, published in 1898, was confronted with the problem of what to do with non-contested constituencies, with double-member districts, and with minor party candidates.15 W. F. Ogburn, in his 1916 analysis of the political thought of social classes in Oregon as measured by referendum votes, faced the necessity of defining the social classes, urbanism, and the "radical" or "conservative" character of the measures voted upon.16 In work- ing on similar problems some years later, Rice devised his so-called index of progressivism and his ratio of nationality excess.17 A. N. Holcombe's treatment of congressional votes involved the definition of sectional and economic groupings.18 A number of other studies might be mentioned, but perhaps this enumeration has been sufficient to establish the point.

The vote is only a very rough index of political attitudes, since the choices are highly limited. A finer scale is necessary if the nature of political attitudes is to be examined more closely. Since the vote is secret, it is impossible to identify ballots and to relate directly a given kind of vote to economic and social factors. In studying such a subject as popular interest in voting, it is soon apparent that there are no available data on the number of eligible voters and on the characteristics of voters and non-voters. Field work by means of questionnaires and interviews is necessary in order to throw light on problems of this sort. W. T. Donaldson reports a study of the number and character of non-voters in two Ohio cities in 1913, based upon a very simple questionnaire.19 Some

16 "Miscellaneous Applications of the Calculus of Probabilities," Journal of the Royal Statistical Society, Vol. 61, pp. 534-544 (September, 1898).

16 F. Ogburn and Delvin Peterson, "Political Thought of Social Classes," Politi- cal Science Quarterly, Vol. 31, pp. 300-317 (June, 1916).

"7 Quantitative Methods in Politics, pp. 94, 198. 18 Political Parties of Today (New York, 1924). 19 Compulsory Voting and Absent Voting, with Bibliographies (Ohio Legislative

Reference Department Bulletin, No. 1, Columbus, (1914).




ten years later, a number of voting studies were started at the University of Chicago, using schedules which were more complete.20 The schedule in the second Chicago study and the one used by Ben Arneson in a study in a small Ohio city made improvements over the earlier schedules in objectivity and clarity.21 A more elaborate technique was employed by Gordon Allport in a study of the composition of political attitudes made in 1928. Various questions were ranked by competent persons as to the degree of radicalism which they indicated. The subjects were then ranked with the aid of this index, and at the same time certain other relevant information was obtained.22

The most highly developed technique for the measurement of attitudes is that devised by L. L. Thurstone.23 Using the analogy of psychophysical methods, he worked out procedures for assigning a scale value for each of a series of statements. One of his procedures uses as a scale value for a given statement the interpolated median judgment of a group of judges as to its position along an attitude continuum. The perfecting of a scale involves and requires con- siderable training in statistics. The Thurstone scales already standardized or in preparation which may be of interest to political scientists are those on the United States Constitution, law, Sunday observance, war, prohibition, communism, patriotism, public office, capital punishment, immigration, free trade, preparedness, the League of Nations, German war guilt, freedom of speech, and the Monroe Doctrine. Beyle has adapted this technique to the formation of a scale for measuring attitudes toward candidates.2' A modification of his method has been used to form a so-called

20 C. E. Merriam and H. F. Gosnell, Non-Voting: Causes and Methods of Control (Chicago, 1924); H. F. Gosnell, Getting Out the Vote (Chicago, 1927).

21 B. Arneson, "Non-Voting in a Typical Ohio Community," in this REVIEW, Vol. 19, pp. 816-825 (November, 1925).

22 "The Composition of Political Attitudes," American Journal of Sociology, Vol. 35, pp. 220-238 (September, 1929). The conclusion of this study is that political behavior is not specific, but is related to inclusive sets or attitudes in person- ality. The political character of men is, on the whole, bound up with many generic traits in their personalities.

23 L. L. Thurstone and E. J. Chave, The Measurement of Attitude, etc. (Uni- versity of Chicago Press, 1929). See G. B. Vetter, "The Study of Social and Politi- cal Opinions," Journal of Abnormal and Social Psychology, Vol. 25, pp. 26-39 (April, 1930), and G. and L. B. Murphy, Experimental Social Psychology (New York, 1931), for a review of the literature on this subject.

24 H. Beyle, "A Scale for the Measurement of Attitude Toward Candidates for Elective Governmental Office" in this REVIEW, Vol. 26, p. 527 (June, 1932).




hostility scale, representing the attitude of one country toward another as shown by selected newspaper editorials.25

It is apparent from the examples which have been cited that the selection of proper units for statistical studies in political science is a difficultt, but not impossible, task. Once the data are collected, the next problem is the selection of the proper statistical devices for the treatment of them. The use of averages, measures of dispersion, and skewness in political studies will be considered first. Edge- worth, in the study already referred to, was interested in whether the multifarious motives that sway voters at a contested election produce results dispersed about an average according to the nor- mal law of error. For this purpose he examined the relationship between the mean deviation, the quartile deviation, and a form of the standard deviation. In 1912, F. Stuart Chapin made a study of what he called "The Variability of the Popular Vote at Presidential Elections" by means of the standard deviation.26 Unfortunately, in this study proper units were not selected for the calculations, the little sigma values being computed directly from the raw figures of the party votes for each election. A rough check on this work by means of the coefficient of variation tended to show that claims made in this study were not well founded.

A study more nearly like that of Edgeworth has been reported by Rice, who was interested in the social density of attitudes toward LaFollette as measured by the percentages of votes cast for him in the counties of certain states.27 On the basis of the coefficients of variation, he concluded that the LaFollette strength was positively related to low relative variability among the percentages. Another use of averages has been made by W. S. Crowley in his study of the characteristics of leaders and non-leaders in three different situations.28 In order to determine whether a particular

25 Regarding the statistical analysis of newspaper and periodical material, see J. L. Woodward, Foreign News in American Newspapers (New York, 1930); Hornell Hart, "Changing Social Attitudes and Interests," in Recent Social Trends (New York, 1933); and S. Foster, American News of Europe, 1914-1917 (University of Chicago Ph.D. thesis, 1932).

28 American Journal of Sociology, Vol. 18, pp. 222-240 (September, 1912). 27 Quantitative Methods in Politics. See also R. and M. Fletcher, "The Frequency

Distribution of Voting in St. Louis," Social Forces, Vol. 8, pp. 427-429 (March, 1930).

28 "Three Distinctions in the Study of Leadership," Journal of Abnormal and Social Psychology, Vol. 33, No. 2 (July-September, 1928).




trait, as measured by a given test, was positively or negatively possessed by the leaders of one of his experimental groups, he calculated the standard error of the difference of the two means.

One of the most dramatic and widely discussed political problems involving the use of different averages has been the reap- portionment of Congress. The two leading contestants in this controversy have been W. F. Willcox, of Cornell University, who advocated the use of the method of major fractions, and E. V. Huntington, of Harvard University, who advocated the method of equal proportions.29 After the smoke of battle was cleared away following the barrage of calculations based on the 1930 census, it was discovered that as far as the particular figures were concerned, the results were the same.

While the economists have made many empirical studies of business cycles and trends, and have developed a body of theory to explain them, comparatively few statistical studies have been made of political cycles and trends. It is true that year-books and almanacs have printed data out of which such studies might have been made, and that some political scientists have referred to the swing of the electoral pendulum. But little has been done to analyze the amplitude and rhythm of political cycles. Sir Richard Martin discussed the swing of the pendulum in British politics in 1906. After an analysis of the election returns, he came to the conclusion that the swing of the pendulum in 1906 was a diversion of ten per cent of the votes of the victorious party to the other side.30 Simple time charts have been used in several studies to show the trend of party voting and of popular participation in elections in several countries.3"

In 1926, Rice reported a more ambitious attempt to analyze party turnover in New Jersey between 1877 and 1924, and to show the relationship between political and business cycles.32 In cal-

29 E. V. Huntington, "A New Method of Apportionment of Representatives," Publications of American Statistical Association, 1921, pp. 859 ff.; "Methods of Apportionment in Congress," in this REVIEW, Vol. 25, pp. 961-965 (November, 1931). The method of major fractions uses a form of the arithmetic mean and the method of equal proportions a form of the geometric mean.

30 Cited in Florence, op. cit., pp. 114-115. 31 A. Siegfried, Tableau Politique de la France de l'Ouest (Paris, 1913); A. N.

Holcombe, Political Parties of Today (New York, 1924); H. F. Gosnell, Why Europe Votes (Chicago, 1930).

32 Quantitative Methods in Politic8, pp. 280-293.




culating the political cycle, he chose the per cent that the aggregate vote for the Republican candidates for assemblyman was of the total aggregate vote for all candidates. After eliminating the secular trend for his so-called political cycle, he found that the coefficient of correlation between the business and political cycles was -.247. There are a number of questions which this study leaves unanswered. What evidence is there that the Republican votes for assemblyman in New Jersey are typical of Republican votes in the country at large? During what years was the Re- publican party in power? It is reasonable to suppose that when out of power it might benefit from adverse economic conditions. When is a party said to be in power? When it controls the state legisla- ture? When it controls the governorship? When it controls Con- gress? When it controls the President? What is the relationship between the votes for these various offices in New Jersey? These and other problems will have to be solved before refined mathematical techniques will be applicable to political cycles.

Clark Tibbitts, in an article on "Majority Votes and the Business Cycle," has pointed out that if business conditions and party popularity are to be studied together, the elections must have oc- curred during or immediately following periods of expansion or depression; for a remote issue is of little importance in swaying the electorate.33 However, Tibbitts does not seem to have answered satisfactorily the question of what is meant by a party in power. Another type of time series study was made by C. H. Titus, who was interested in the trend in popular participation in voting in California.34 Titus fitted straight lines to the votes cast per 1,000 of the population and to the votes per 1,000 of voting population. He fails to interpret his data in the light of ballot changes, shifts in the relative strength of the major parties, changes in the amount of money spent in elections, and other relevant factors. These time series studies show that significant results in this field depend upon the close cooperation between the political scientist and the statistician.

There are many other political times series which might be

33 American Journal of Sociology, Vol. 36, pp. 596-606 (January, 1931). ' "Voting in California Cities, 1900-1925," Southwestern Political Science

Quarterly, Vol. 8, No. 4 (March, 1928); "Rural Voting in California, 1900-1926," ibid., Vol. 9, No. 2 (September, 1928); "Voting in California, 1900-1926,"ibid., Vol. 10, No. 1 (June, 1929).




studied, such as the trend in referendum votes on particular issues,3" the rise and fall of minor party movements, the changing characteristics of representatives,36 etc. Such studies as these would require a thorough knowledge of the qualitative political factors involved, as well as the usual measurement techniques.

Since the perfection of correlation techniques some thirty-five years ago by Karl Pearson and others, there has been a tendency to define causation in terms of association. Economists and educators have made extensive use of correlation. In political science, these methods do not seem to have gained very general recognition. In 1919, Ogburn, together with Goltra, employed the method of partial correlation in order to discover how women voted in com- parison with men, in certain Oregon election precincts, on a number of referendum measures.37 Partial correlation is a powerful method for keeping constant factors other than the one regarding which measurements are desired. The votes of the men and women were not kept separate in Oregon, and it was therefore necessary to im- ply how the women voted from the way in which the precincts went in which there was a relatively high number of women voting. The partial coefficients enabled the investigators to keep constant a factor which they called a conservatism-radicalism factor.

Ten years later, Ogburn and Talbot applied the same technique to the analysis of factors in the presidential election of 1928.38 In this second study, five factors which appeared to have some influence upon the result of the election were analyzed, and the relative importance of each was determined by the regression equations. It happened that in this study the five factors selected, namely, foreign-born influence, rural influence, Democratic influence, Catholic influence, and wet influence, included a fairly large per- centage of the effective influences as shown by the coefficient of

35C. H. Wooddy and S. A. Stouffer, "Local Option and Public Opinion," American Journal of Sociology, Vol. 36, pp. 175-205 (September, 1930).

386 Rice, Quantitative Methods in Politics Chap. xxi. 3 W. F. Ogburn and Ines Goltra, "How Women Vote," Political Science Quar-

terly, Vol. 34, pp. 413-433, (September, 1919). 38 W. F. Ogburn and Nell Snow Talbot, "A Measurement of the Factors in the

Presidential Election of 1928," Social Forces, Vol. 8, pp. 175-183 (December, 1929). See also J. A. Neprash, The Brookhart Campaigns in Iowa, 1920-1926 (New York, Columbia University Press, 1932).

" C. H. Wooddy, The Case of Frank L. Smith (Chicago, 1931), Appendix V, "Statistical Studies of Illinois Elections."




multiple correlation. But this might not always be the case in analyzing elections by this method, as is shown by Wooddy and Stouffer's analysis of Illinois elections.39 On the basis of their partial coefficients calculated from data regarding election returns from 1918 to 1928, these investigators concluded that party regularity was the most important factor in Illinois elections. As is well known, the lines of party regularity were shattered in the Illinois election of November, 1930. However, one of my students found that the coefficient of correlation between the Republican vote for 1926 and the Republican vote for 1930 by counties was high, namely +.79.4? In other words, the losses which the Republican party suffered in the state were fairly constant as among the different counties. Where changes are so evenly distributed as in this case, the time series method is more appropriate.

The method of correlation is useful in studying other political problems. Dr. Madge McKinney has made a study of certain characteristics of citizenship by means of correlating combined ratings with test scores on a questionnaire.4' Thurstone has projected a series of research projects which involve intercorrelations between the scores on a number of his attitude scales. He hopes that this will throw some light upon patterns of atypical opinions. The pos- sibilities of the fruitful use of correlation seem to be limited by the absence of available data on some problems, the lack of familiarity with the technique among political scientists, the laboriousness of the process, and the deficiency of suggestive hypotheses.

There are many other statistical techniques which might be used in solving political problems, but for lack of space they will not be discussed here. Among these techniques should be mentioned map making,42 index numbers,43 forecasting44 and various applications of the theory of probability, particularly to sampling. The device of partial correlation suggests the use of another type of sampling,

40 Mr. Max White. 41 University of Chicago Ph.D. thesis, 1927. 42 For maps of presidential elections, see C. 0. Paullin, Atlas of the Historical

Geography of the United States (Washington and New York, 1932). Some use of maps is made in my Why Europe Votes (Chicago, 1930).

43 Lundberg, op. cit., Chaps. x-xi. 44 Claude E. Robinson, Straw Votes; A Study of Political Prediction (New York,

Columbia University Press, 1932). See also Robinson's preliminary analysis of the 1 932 returns of the Literary Digest and Hearst polls in the New York Times, October 16;? 1932, section 8.




namely, sampling to keep certain factors constant. In my study, Getting Out the Vote, an endeavor was made to measure the influence of a non-partisan canvass to get out the vote by matching the halves of selected precincts as to certain relevant factors. Thurstone measured the influence of a particular motion picture on the attitudes of high school pupils by having one of his attitude scales filled out before and after the showing of the picture.45 There are various other ways of establishing what might be called a control group.

In this brief summary, I have tried to outline some of the possible uses of statistics in the fields of political parties, public opinion, citizenship, legislative behavior, and political psychology. The statistical method is one of many methods that can be used to study political behavior. Very frequently, a quantitative study points the way for intensive qualitative studies of a particular sort. The interpretation of a statistical result always calls for logical inference and general familiarity with the materials. There are on hand a number of powerful statistical techniques developed by other disciplines which can be used by political scientists in connection with political research as soon as some rational hypotheses are developed, and as soon as some methods are devised for col- lecting more complete and reliable original data. If any so-called laws of political science are to be invented, it is likely that they will be expressed, not as invariant mechanical relationships, but as tendencies, trends, and average relationships.

46 L. L. Thurstone, "Influence of Motion Pictures on Children's Attitudes," Journal of Social Psychology, Vol. 2, pp. 291-305 (August, 1931).



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