Measures of Association for Cross Classifications. II: Further Discussion and References

  • Leo A. Goodman
  • William H. Kruskal
Part of the Springer Series in Statistics book series (SSS)


Our earlier discussion of measures of association for cross classifications [66] is extended in two ways. First, a number of supplementary remarks to [66] are made, including the presentation of some new measures. Second, historical and bibliographical material beyond that in [66] is critically surveyed; this includes discussion of early work in America by Doolittle and Peirce, early work in Europe by Körösy, Benini, Lipps, Deuchler and Gini, more recent work based on Shannon-Wiener information, association measures based on latent structure, and relevant material in the literatures of meteorology, ecology, sociology, and anthropology. New expressions are given for some of the earlier measures of association.


Latent Structure Weather Forecast AMERICAN Statistical Association Association Measure American Anthropologist 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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  1. [1]
    Andreoli, Giulio, “Sulla definizione di certi indici, relativi a caratteri di omogamia, in problemi statistici,” Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche (Classe della Società Reale di Napoli), Ser. 4, 4 (1934), 36–41.MATHGoogle Scholar
  2. [2]
    Andreoli, Giulio, “Teoria generale di certi indici nei fenomeni statistici (omagamia, endogamia, diffusione, etc.),” Rendiconto dell’Accademia delle Scienze Fisiche e Matematiche (Classe della Società Reale di Napoli), Ser. 4, 5 (1935), 108–24.Google Scholar
  3. [3]
    Bachi, Roberto, “Gli indici della attrazione matrimoniale,” Giornale degli Economisti e Rivista di Statistica, 69 (1929), 894–938.Google Scholar
  4. [4]
    Benini, Rodolfo, Principii di Demografia, Firenzi, G. Barbèra, 1901. No. 29 of Manuali Barbèra di Scienze Giuridiche Sociali e Politiche.Google Scholar
  5. [5]
    Benini, Rodolfo, “Grupi chiusi e gruppi aperti in alcuni fatti colletivi di combinazioni,” Bulletin de l’Institut International de Statistique, 23 (1928), 362–83.Google Scholar
  6. [6]
    Berkson, Joseph, “Cost utility as a measure of the efficiency of a test,” Journal of the American Statistical Association, 42 (1947), 246–55.MATHCrossRefGoogle Scholar
  7. [7]
    Berkson, Joseph, “The statistical study of association between smoking and lung cancer,” Proceedings of the Staff Meetings of the Mayo Clinic, 30 (1955), 319–48.Google Scholar
  8. [8]
    Bijvoet, H. C., and Bleeker, W., “The value of weather forecasts,” Weather, 6 (1951), 36–9.Google Scholar
  9. [9]
    Bilham, E. G., “A problem in economics,” Nature, 109 (1922), 341–2.CrossRefGoogle Scholar
  10. [10]
    Bleeker, W., “The verification of weather forecasts,” Mededeelingen en Verhandelingen, Ser. B, Deel 1, No. 2 (1946); Koninklijk Nederlandsch Meteorologisch Instituut, No. 125.Google Scholar
  11. [11]
    Boas, Franz, “The measurement of differences between variable quantities,” Journal of the American Statistical Association, 18 (1922–23), 425–45.CrossRefGoogle Scholar
  12. [12]
    Bogue, Donald J., The Structure of the Metropolitan Community. University of Michigan, Ann Arbor, 1949.Google Scholar
  13. [12a]
    Bonferroni, C. E., “Nuovi indici di connessione fra variabili statistiche,” Pubblicazioni dell’Istituto di Statistica, Università Commerciale “Luigi Bocconi,” Milan. Vol. I (1942) of Studi Sulla Correlazione e Sulla Connessione, 57–100.Google Scholar
  14. [13]
    Bonferroni, Carlo Emilio, “Indici unilaterali e bilaterali di connessione,” 49–60 in: Mazzoni, Pacifico, and Lasorsa, Giovanni (ed.), Studi in Memoria di Rodolfo Benini, Facoltà di Economia e Commercio, Università degli Studi di Bari, Bari, 1956.Google Scholar
  15. [14]
    Brambilla, Francesco, La Variabilità Statistica a Due Dimensioni. La Teoria Statistica della Correlazione e delta Connessione. Università Commerciale “Luigi Bocconi,” Istituto di Statistica, Casa Editrice Ambrosiana, Milan, 1949. This volume is part 2 of Brambilla’s Manuale di Statistica.Google Scholar
  16. [15]
    Bresciani, Costantino, “Sui metodi per la misura delle correlazioni,” Giornale degli Economisti, 38 (1909), 401–14, 491–522.Google Scholar
  17. [16]
    Brier, Glenn W., “Verification of forecasts in terms of probability,” Monthly Weather Review, 78 (1950), 1–3.CrossRefGoogle Scholar
  18. [17]
    Brier, Glenn W., and Allen, Roger A., “Verification of weather forecasts,” 841–8 in: Malone, Thomas F. (ed.), Compendium of Meteorology, American Meteorological Society, Boston, 1951.Google Scholar
  19. [18]
    Brier, G. W., “The effect of errors in estimating probabilities on the usefulness of probability forecasts,” Bulletin of the American Meteorological Society, 38 (1957), 76–8.Google Scholar
  20. [19]
    Cartwright, Desmond S., “A rapid non-parametric estimate of multi-judge reliability,” Psychometrika, 21 (1956), 17–29.MATHCrossRefGoogle Scholar
  21. [20]
    Chrétien, C. Douglas, “The quantitative method for determining linguistic relationships. Interpretation of results and tests of significance,” University of California Publications in Linguistics, 1 (1943–8), 11–19. Published in 1943.Google Scholar
  22. [21]
    Chrétien, C. Douglas, “Culture element distributions: XXV. Reliability of statistical procedures and results,” University of California Publications in Anthropological Records, 8 (1942–5), 469–90. Published in 1945.Google Scholar
  23. [22]
    Chrétien, C. Douglas, “Word distributions in Southeastern Papua,” Language, 32 (1956), 88–108.CrossRefGoogle Scholar
  24. [23]
    Clayton, H. H., “On verification of weather forecasts,” Bulletin of the American Meteorological Society, 25 (1944), 368.Google Scholar
  25. [24]
    Clements, Forrest E., Schenck, Sara M., and Brown, T. K., “A new objective method for showing special relationships,” American Anthropologist, 28 (1926), 585–604.CrossRefGoogle Scholar
  26. [25]
    Clements, Forrest E., “Quantitative method in ethnography,” American Anthropologist, 30 (1928), 295–310.CrossRefGoogle Scholar
  27. [26]
    Clements, Forrest, “Plains Indian tribal correlations with sun dance data,” American Anthropologist, 33 (1931), 216–27.CrossRefGoogle Scholar
  28. [27]
    Clements, Forrest E., “Use of cluster analysis with anthropological data,” American Anthropologist, 56 (1954), 180–99.CrossRefGoogle Scholar
  29. [28]
    Cole, La Mont C, “The measurement of interspecific association,” Ecology, 30 (1949), 411–24.CrossRefGoogle Scholar
  30. [29]
    Cramer, Harald, “Remarks on correlation,” Skandinavisk Aktuarietidskrift, 7 (1924), 220–40.Google Scholar
  31. [30]
    Czekanowski, Jan, “Objective Kriterien in der Ethnologie,” Mitteilungen der Anthropologischen Gesellschaft in Wien, 42 (1912), Sitzungsberichte (1911–12) Section, 17–21.Google Scholar
  32. [31]
    de Meo, G., “Su di alcuni indici atti a misurare l’attrazione matrimoniale in classificazioni dicotome,” Rendiconto dell’Accademia dette Scienze Fisiche e Matematiche (Classe della Società Reale di Napoli), Ser. 4, 4 (1934), 62–77.MATHGoogle Scholar
  33. [32]
    Deuchler, Gustav, “Über die Methoden der Korrelationsrechnung in der Pädagogik und Psychologie,” Zeitschrift fÜr Pädagogische Psychologie und Experimentelle Pädagogik, 15 (1914), 114–31, 145–59, and 229–42.Google Scholar
  34. [33]
    Deuchler, Gustav, “Über die Bestimmung von Rangkorrelationen aus Zeugnisnoten,” Zeitschrift fÜr Angewandte Psychologie, 12 (1916–17), 395–439.Google Scholar
  35. [34]
    Deuchler, Gustav, “Über die Bestimmung einseitiger Abhängigkeit in pädagogischpsychologischen Tatbeständen mit alternativer Variabilität,” Zeitschrift fÜr Pädagogische Psychologie und Experimentelle Pädagogik, 16 (1915), 550–66.Google Scholar
  36. [35]
    Doolittle, M. H., “The verification of predictions” (abstract), Bulletin of the Philosophical Society of Washington, 7 (1885), 122–7. A summary of this article appears in The American Meteorological Journal, 2 (1885–6), 327–9.Google Scholar
  37. [36]
    Doolittle, M. H., “Association ratios” (abstract), Bulletin of the Philosophical Society of Washington, 10 (1888), 83–7 and 94–6.Google Scholar
  38. [37]
    Dornbusch, Sanford M., and Schmid, Calvin F., A Primer of Social Statistics, McGraw-Hill, New York, 1955.Google Scholar
  39. [38]
    Driver, H. E., and Kroeber, A. L., “Quantitative expression of cultural relationships,” University of California Publications in American Archaeology and Ethnology, 31 (1931–3), 211–56.Google Scholar
  40. [39]
    Driver, Harold E., “Culture element distributions: X. Northwest California,” University of California Publications in Anthropological Records, 1(6) (1939), 297–433.Google Scholar
  41. [40]
    Driver, Harold E., “Statistics in anthropology,” American Anthropologist, 55 (1953), 42–59.CrossRefGoogle Scholar
  42. [41]
    Duncan, Otis Dudley, Ohlin, Lloyd E., Reiss, Albert J., Jr., and Stanton, Howard R., “Formal devices for making selection decisions,” The American Journal of Sociology, 58 (1953), 573–84.CrossRefGoogle Scholar
  43. [42]
    Duncan, Otis Dudley, and Duncan, Beverly, “A methodological analysis of segregation indexes,” American Sociological Review, 20 (1955), 210–7.CrossRefGoogle Scholar
  44. [43]
    Eyraud, Henri, “Les principes de la mesure des corrélations,” Annales de l’Université de Lyon, Ser. A (3), 1 (1936), 30–47.Google Scholar
  45. [44]
    Faleschini, Luigi, “Indici di connessioni,” Contribua del Laboratorio di Statistica, Ser. 6, Università Cattolica del Sacro Cuore [Milan], Publicazioni, Nuova Serie, 21 (1948), 112–51.Google Scholar
  46. [45]
    Féron, Robert, “Mérites comparés des divers indices de corrélation,” Journal de la Société Statistique de Paris, 88 (1947), 328–50. Discussion on pp. 350–2.Google Scholar
  47. [46]
    Féron, Robert, “Information, Régression, Corrélation,” Publications de l’Institut de Statistique de l’Université de Paris, 5(3–4) (1956), 113–215.MATHGoogle Scholar
  48. [47]
    Finley, Jno. P., “Tornado predictions,” The American Meteorological Journal, 1 (1884), 85–8.Google Scholar
  49. [48]
    Florence, P. Sargant, Investment, Location, and Size of Plant. Cambridge University Press, Cambridge, 1948.Google Scholar
  50. [49]
    Forbes, S. A., “On the local distribution of certain Illinois fishes: an essay in statistical ecology,” Bulletin of the Illinois State Laboratory of Natural History, 7 (1904–9), 273–303, plus 32 plates.Google Scholar
  51. [50]
    Fréchet, Maurice, “A general method of constructing correlation indices,” Proceedings of the Mathematical and Physical Society of Egypt, 3 (2) (1946), 13–20. (Additional note 3 (4) (1948), 73–4.)MathSciNetMATHGoogle Scholar
  52. [51]
    Fréchet, Maurice, “Anciens et nouveaux indices de corrélation. Leur application au calcul des retards économiques,” Econometrica, 15 (1947), 1–30. (Errata pp. 374–5.)MathSciNetCrossRefGoogle Scholar
  53. [52]
    Fréchet, Maurice, “Sur les tableaux de corrélation dont les marges sont données,” Annales de l’Université de Lyon, Sec. A (3), 14 (1951), 53–77.Google Scholar
  54. [53]
    Fréchet, Maurice, “Sur les tableaux de corrélation dont les marges sont données,” Comptes Rendus Hebdomadaires des Scéances de l’Académie des Sciences, Paris, 242 (1956), 2426–8.MATHGoogle Scholar
  55. [54]
    Galvani, L., “A propos de la communication de M. Thionet: L’école moderne de statisticiens italiens,” Journal de la Société de Statistique de Paris, 88 (1947), 196–203.Google Scholar
  56. [55]
    Gilbert, G. K., “Finley’s tornado predictions,” The American Meteorological Journal, 1 (1884), 166–72.Google Scholar
  57. [56]
    Gini, Corrado, “Di una misura della dissomiglianza tra due gruppi di quantità e delle sue applicazioni allo studio delle relazioni statistiche,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, Series 8, 74 (2) (1914–5), 185–213.Google Scholar
  58. [57]
    Gini, Corrado, “Indice di omofilia e di rassomiglianza e loro relazioni col coefficiente di correlazione e con gli indici di attrazione,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, Series 8, 74 (2), (1914–5), 583–610.Google Scholar
  59. [58]
    Gini, Corrado, “Nuovi contributi alla teoria delle relazioni statistiche,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, Series 8, 74 (2), (1914–5), 1903–42.Google Scholar
  60. [59]
    Gini, Corrado, “Sul criterio di concordanza tra due caratteri,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti, Series 8, 75 (2), (1915–6), 309–31.Google Scholar
  61. [60]
    Gini, Corrado, “Indici di concordanza,” Atti del Reale Istituto Veneto di Scienze, Lettere ed Arti. Series 8, 75 (2), (1915–6), 1419–61.Google Scholar
  62. [61]
    Gini, Corrado, “The contributions of Italy to modern statistical methods,” Journal of the Royal Statistical Society, 89 (1926), 703–24.CrossRefGoogle Scholar
  63. [61a]
    Gini, Corrado, “Die Messung der Ungleichheit zweier Verteilungen, angewendet auf die Untersuchung von qualitativen Rassenmerkmalen,” Archiv fÜr Mathematische Wirtschafts- und Sozialforschung, 3 (1937), 167–84, plus two appendixes by Vittorio Castellano.Google Scholar
  64. [62]
    Gini, Corrado, Metodologia Statistical la Misura dei Fenomeni Collettivi, Vol. III, Part 2a, Chap. 55, 245–321, Enciclopedia delle Matematiche Elementari, edited by Luigi Berzolari, Ulrico Hoepli, Milan, 1948.Google Scholar
  65. [63]
    Gini, Corrado, Corso di Statistica, a cura di S. Gatti e Benedetti, nuova edizione aggiornata, Università degli Studi di Roma, Facoltà di Scienze Statistiche, Demografiche ed Attuariali, Libreria Eredi Virgilio Veschi, Rome, 1954–5.Google Scholar
  66. [63a]
    Glass, D. V. (ed.), Social Mobility in Britain, Routledge and Kegan Paul, London, 1954.Google Scholar
  67. [64]
    Goodall, D. W., “Quantitative aspects of plant distribution,” Biological Reviews of the Cambridge Philosophical Society, 27 (1952), 194–245.CrossRefGoogle Scholar
  68. [65]
    Goodman, Leo A., “On urbanization indices,” Social Forces, 31 (1953), 360–2.CrossRefGoogle Scholar
  69. [66]
    Goodman, Leo A., and Kruskal, William H., “Measures of association for cross classifications,” Journal of the American Statistical Association, 49 (1954), 723–64.Google Scholar
  70. [67]
    Greenberg, Joseph H., “The measurement of linguistic diversity,” Language, 32 (1956), 109–15CrossRefGoogle Scholar
  71. [68]
    Gringorten, Irving, I., “The verification and scoring of weather forecasts,” Journal of the American Statistical Association, 46 (1951), 279–96.CrossRefGoogle Scholar
  72. [69]
    Gringorten, Irving I., Lund, Iver A., and Miller, Martin A., “A program to test skill in terminal forecasting,” Air Force Surveys in Geophysics, No. 80, Geophysics Research and Development Command, June, 1955.Google Scholar
  73. [70]
    Gringorten, Irving I., “Methods of objective weather forecasting,” pp. 57–92 in: Landsberg, H. E. (ed.), Advances in Geophysics, Vol. 2, Academic Press, New York, 1955.Google Scholar
  74. [71]
    Gringorten, Irving I., “Tests of significance in a verification program,” Journal of Meteorology, 12 (1955), 179–95.CrossRefGoogle Scholar
  75. [71a]
    Gringorten, Irving I., “On the comparison of one or more sets of probability forecasts,” Journal of Meteorology, 15 (1958), 283–7.CrossRefGoogle Scholar
  76. [72]
    Gringorten, Irving I., Lund, Iver A., and Miller, Martin A., “The construction and use of forecast registers,” Geophysical Research Papers, No. 53, Geophysics Research Directorate, Air Force Cambridge Research Center, Air Research and Development Command, June, 1956.Google Scholar
  77. [73]
    Guilford, J. P., Fundamental Statistics in Psychology and Education, McGraw-Hill, New York, First edition, 1942, second edition, 1950.Google Scholar
  78. [73a]
    Halphen, Etienne, “L’analyse intrinsèque des distributions de probabilité,” Publications de l’Institut de Statistique de l’Université de Paris, 6 (2) (1957), 79–159.MathSciNetMATHGoogle Scholar
  79. [74]
    Harris, J. Arthur, and Treloar, Alan E., “On a limitation in the applicability of the contingency coefficient,” Journal of the American Statistical Association, 22 (1927), 460–72.CrossRefGoogle Scholar
  80. [75]
    Harris, J. Arthur, Treloar, Alan E., and Wilder, Marian, “On the theory of contingency II. Professor Pearson’s note on our paper on contingency,” Journal of the American Statistical Association, 25 (1930), 323–7.MATHCrossRefGoogle Scholar
  81. [76]
    Harris, J. Arthur, and Tu, Chi, “A second category of limitation in the applicability of the contingency coefficient,” Journal of the American Statistical Association, 24 (1929), 367–75.MATHCrossRefGoogle Scholar
  82. [77]
    Hazen, H. Allen, “Verification of tornado predictions,” American Journal of Science, Ser. 3, 34 (1887), 127–31.Google Scholar
  83. [78]
    Höffding, Wassilij, “Massstabinvariante Korrelationstheorie,” Schriften des Mathematischen Instituts und des Instituts fÜr Angewandte Mathematik der Universität Berlin, 5 (3) (1940), 181–233.Google Scholar
  84. [79]
    Höffding, Wassilij, “Massstabinvariante Korrelations masse fÜr diskontinuienliche Verteilungen,” Archiv fÜr Mathematische Wirtschafts- und Sozialforschung, 7 (1941), 49–70.Google Scholar
  85. [80]
    Höffding, Wassilij, “Stochastische Abhängigkeit und funktionaler Zusammenhang,” Skandinavisk Aktuarietidskrift, 25 (1942), 200–27.MATHGoogle Scholar
  86. [81]
    Holloway, J. Leith, Jr., and Woodbury, Max A., “Application of information theory and discriminant function analysis to weather forecasting and forecast verification,” Technical Report No. 1, Meteorological Statistics Project, Institute for Cooperative Research, University of Pennsylvania, Feb., 1955.Google Scholar
  87. [82]
    Hoover, Edgar M., Jr., “The measurement of industrial localization,” Review of Economic Statistics, 18 (1936), 162–71.CrossRefGoogle Scholar
  88. [83]
    Hoover, Edgar M., Jr., “Interstate redistribution of population, 1850–1940,” Journal of Economic History, 1 (1941), 199–205.Google Scholar
  89. [84]
    Irwin, J. O., “Correlation methods in psychology,” British Journal of Psychology, General Section, 25 (1934–5), 86–91.CrossRefGoogle Scholar
  90. [84a]
    Johnson, H. M., “Maximal selectivity, correctivity and correlation obtainable in a 2X2 contingency table,” American Journal of Psychology, 58 (1945), 65–8.CrossRefGoogle Scholar
  91. [85]
    Jordan, Charles, “Les coefficients d’intensité relative de Körösy,” Revue de la Société Hongroise de Statistique (Magyar Statisztikai Társaság, Revue), 5 (1927), 332–45.Google Scholar
  92. [86]
    Jordan, Charles, “Critique de la corrélation au point de vue des probabilités,” Actes du Colloque Consacré à la Théorie des Probabilités, No. 740 of Actualités Scientifiques et Industrielles, Hermann, Paris, 1938.Google Scholar
  93. [87]
    Jordan Károly, “A Korreláció számitása (Sur le calcul de la corrélation) I,” Magyar Statisztikai Szemle Kiadványai (Központi Statisztikai Hivatal), (1941) 1 Szám. Hungarian with French summary.Google Scholar
  94. [87a]
    Katz, Elihu, and Lazarsfeld, Paul E., Personal Influence, The Free Press, Glencoe, Illinois, 1955.Google Scholar
  95. [88]
    Kendall, Patricia, Conflict and Mood, The Free Press, Glencoe, Illinois, 1954.Google Scholar
  96. [89]
    Klein, Herman J., “Ergebnisse rationeller PrÜfungen von Wetterprognosen und deren Bedeutung fÜr die Praxis,” Wochenschrift fÜr Astronomie, Meteorologie und Geographie, NF 28 (1885), 9–14, 20–2, 25–8, 35–7, 41–4, and 57–61.Google Scholar
  97. [90]
    Kluckhohn, Clyde, “On certain recent applications of association coefficients to ethnological data,” American Anthropologist, 41 (1939), 345–77.CrossRefGoogle Scholar
  98. [91]
    Köppen, Wladimir, “Die Aufeinanderfolge der unperiodischen Witterungserscheinungen nach den Grundsätzen der Wahrscheinlichkeitsrechnung,” Repertorium fÜr Meteorologie, Akademiia Nauk, Petrograd, 2 (1870–1), 189–238.Google Scholar
  99. [92]
    [Köppen, W.?], “Eine rationelle Methode zur PrÜfung der Wetterprognosen,” Meteorologische Zeitschrift, 1 (1884), 397–404.Google Scholar
  100. [93]
    Körösi, Joseph, “Kritik der Vaccinations-Statistik und neue Beiträge zur Frage des Impfschutzes,” Transactions of the Ninth International Medical Congress, Washington, D. C, 1887, Vol. 1, 238–418.Google Scholar
  101. [94]
    Kroeber, A. L., and Chrétien, C. D., “Quantitative classification of Indo-European language,” Language 13 (1937), 83–103.CrossRefGoogle Scholar
  102. [95]
    Kruskal, William H., “Historical note on the Wilcoxon unpaired two-sample test,” Journal of the American Statistical Association, 52 (1957), 356–60.MATHCrossRefGoogle Scholar
  103. [96]
    Kruskal, William H., “Ordinal measures of association,” Journal of the American Statistical Association 53 (1958), pp. 814–61.MathSciNetMATHCrossRefGoogle Scholar
  104. [97]
    Lakshmanamurti, M., “Coefficient of association between two attributes in statistics,” Proceedings of the Indian Academy of Sciences, Ser. A, 22 (1945), 123–33.MathSciNetMATHGoogle Scholar
  105. [98]
    Leight, Walter G., “The use of probability statements in extended forecasting,” Monthly Weather Review, 81 (1953), 349–56.CrossRefGoogle Scholar
  106. [99]
    Linfoot, E. H., “An informational measure of association,” Information and Control, 1 (1957), 85–9.MathSciNetMATHCrossRefGoogle Scholar
  107. [100]
    Lipps, Gottl. Friedr., “Die Bestimmung der Abhängigkeit zwischen den Merkmalen eines Gegenstandes,” Berichte Über die Vorhandlungen der Königlich Sächsischen Gesellschaft der Wissenschaften zu Leipzig, Mathematisch-Physische Klasse, 57 (1905), 1–32.Google Scholar
  108. [101]
    Lipps, G. F., Die Psychischen Massmethoden, F. Vieweg und Sohn, Braunschweig, 1906. Vol. 10 of the monograph series, Die Wissenschaft.Google Scholar
  109. [102]
    Loevinger, Jane, “A systematic approach to the construction and evaluation of tests of ability,” Psychological Monographs, 61 (4), (1947).Google Scholar
  110. [103]
    Loevinger, Jane, “The technic of homogeneous tests compared with some aspects of ‘scale analysis’ and factor analysis,” Psychological Bulletin, 45 (1948), 507–29.CrossRefGoogle Scholar
  111. [104]
    Long, John A., “Improved overlapping methods for determining the validities of test items,” Journal of Experimental Education, 2 (1934), 264–8.Google Scholar
  112. [105]
    Lorey, W., “Neue Abhängigkeitsmasse fÜr zufällige Grossen,” Deutsches Statistisches Zentralblatt, 25 (1933), 153–4.Google Scholar
  113. [106]
    Mainland, Donald, “The risk of fallacious conclusions from autopsy data on the incidence of diseases with applications to heart disease,” American Heart Journal, 45 (1953), 644–54.CrossRefGoogle Scholar
  114. [107]
    McGill, William J., “Multivariate information transmission,” Psychometrika, 19 (1954), 97–116.MATHCrossRefGoogle Scholar
  115. [108]
    Meyer, Hugo, Anleitung zur Bearbeitung Meteorologischer Beobachtungen fÜr die Klimatologie, Julius Springer, Berlin, 1891.Google Scholar
  116. [109]
    Muller, Robert Hans, “Verification of short-range weather forecasts (a survey of the literature),” Bulletin of the American Meteorological Society, 25 (1944), 18–27, 47–53, and 88–95.Google Scholar
  117. [110]
    Niceforo, Alfredo, La Misura delta Vita, Fratelli, Bocca, Torino, 1919.Google Scholar
  118. [111]
    Niceforo, Alfredo, La Méthode Statistique et ses Applications aux Sciences Naturelles aux Sciences Sociales et à l’Art, Marcel Giard, Paris, 1925. Translation by R. Jacquemin, with some changes, of Niceforo’s Il Metodo Statistico (1923).MATHGoogle Scholar
  119. [112]
    Pearson, Karl, “On a coefficient of class heterogeneity or divergence,” Biometrika, 5 (1906), 198–203.Google Scholar
  120. [113]
    Pearson, Karl, “On the theory of contingency. I. Note on Professor J. Arthur Harris’ paper on the limitation in the applicability of the contingency coefficient,” Journal of the American Statistical Association, 25 (1930), 320–3.MATHCrossRefGoogle Scholar
  121. [114]
    [Pearson, Karl?], “Remarks on Professor Steffensen’s measure of contingency. Editorial,” Biometrika, 26 (1934), 255–60.Google Scholar
  122. [115]
    Peirce, C. S., “The numerical measure of the success of predictions” (letter to the editor), Science, 4 (1884), 453–4.CrossRefGoogle Scholar
  123. [116]
    Pietra, G., “The theory of statistical relations with special reference to cyclical series,” Metron, 4 (3–4), (1924–5), 383–557.Google Scholar
  124. [117]
    Pollaczek-Geiringer, H., “Bemerkungen zur Korrelations-theorie,” Verhandlungen des Internationalen Mathematiker-Congress, Zurich (1932), 2, 229–30.Google Scholar
  125. [118]
    Pollaczsk-Geiringer, H., “Korrelationmessung auf Grund der Summenfunktion,” Zeitschrift fÜr Angewandte Mathematik und Mechanik, 13 (1933), 121–4.CrossRefGoogle Scholar
  126. [119]
    Quetelet, M. A., Letters addressed to H.R.H. the Grand Duke of Saxe Coburg and Gotha on the Theory of Probabilities as Applied to the Moral and Political Sciences (translated from the French by Olinthus Gregory Downs), Charles and Edwin Layton, London, 1849.Google Scholar
  127. [120]
    Reuning, H., “Evaluation of square contingency tables. A simple method of condensation for small samples,” Bulletin, National Institute for Personnel Research, (South African Council for Scientific and Industrial Research, Johannesburg), 4 (1952), 160–7.Google Scholar
  128. [121]
    Saile, Tivadar Antal, Influence de Joseph de Körösy Sur l’évolution de la Statistique, Kiadja a Magyar Tudományos Akadémia, Budapest, 1927. Hungarian with French summary.Google Scholar
  129. [122]
    Salvemini, Tommaso, “Su alcuni indici usati per la misura delle relazioni statistiche,” Statistica, 7 (1947), 200–18.Google Scholar
  130. [123]
    Salvemini, T., “Nuovi procedimenti di calcolo degli indici di dissomigliaza e di connessione,” Statistica, 9 (1949), 3–27.MathSciNetGoogle Scholar
  131. [124]
    Salvemini, Tommaso, “Su alcuni aspetti della dissomiglianza e della concordanza con applicazione alle distribuzioni degli sposi secondo l’età,” Bulletin de l’Institut International de Statistique, 34 (2), (1954), 283–300.MATHGoogle Scholar
  132. [125]
    Salvemini, Tommaso, “Fondamenti razionali, schemi teorici e moderni aspetti delle relazioni tra due o più variabili,” Atti della XV Riunione Scientificà, Societa Italiana di Statistica, 1955.Google Scholar
  133. [126]
    Savorgnan, Franco, “La misura dell’endogamia e dell’omogamia,” in Proceedings of the International Congress for Studies on Population (Rome, 7th–10th September 1931–IX), Vol. X, 9–37. Published by the Comitato Italiano per lo Studio dei Problemi della Popolazione, through the Istituto Poligrafico dello Stato, Rome, 1934.Google Scholar
  134. [126a]
    Smith, H. Fairfield, “On comparing contingency tables,” The Philippine Statistician, 6 (1957), 71–81.Google Scholar
  135. [127]
    Steffensen, J. F., “Deux problèmes du calcul des probabilités,” Annales de l’Institut Henri Poincaré, 3 (1932–3), 319–44. Plus one non-numbered page of errata.MathSciNetGoogle Scholar
  136. [128]
    Steffensen, J. F., “On certain measures of dependence between statistical variables,” Biometrika, 26 (1934), 250–5.Google Scholar
  137. [129]
    Steffensen, J. F., “On the ω test of dependence between statistical variables,” Skandinavisk Aktuarietidskrift, 24 (1941), 13–33.MathSciNetMATHGoogle Scholar
  138. [130]
    Striefler, Heinrich, “Zur Methode der Rangkorrelation nach Tönnies,” Deutsches Statistisches Zentralblatt, 23 (1931), 128–35 and 160–7.Google Scholar
  139. [131]
    “Student” [W. S. Gösset], “An experimental determination of the probable error of Dr Spearman’s correlation coefficients,” Biometrika, 13 (1920–1), 263–82. Reprinted in: Pearson, E. S., and Wishart, John (ed.), “Student’s” Collected Papers, Biometrika Office, University College, London, 1942. Pp. 70–89.Google Scholar
  140. [132]
    Thionet, Pierre, “L’école moderne de statisticiens italiens,” Journal de la Société de Statistique de Paris, 86 (1945), 245–55, and 87 (1946), 16–34.MathSciNetGoogle Scholar
  141. [133]
    Thionet, Pierre, “Résponse de l’auteur de la communication du 21 novembre 1945,” Journal de la Société de Statistique de Paris, 88 (1947), 203–8.Google Scholar
  142. [134]
    Thirring, Gustave, obituary of Joseph de Körösy, Bulletin de l’Institut International de Statistique, 16 (1907–8), 150–4.Google Scholar
  143. [135]
    Thompson, J. C., “On the operational deficiencies in categorical weather forecasts,” Bulletin of the American Meteorological Society, 33 (1952), 223–6.Google Scholar
  144. [136]
    Thompson, J. C., and Brier, G. W., “The economic utility of weather forecasts,” Monthly Weather Review, 83 (1955), 249–54.CrossRefGoogle Scholar
  145. [137]
    Tönnies, Ferdinand, “Eine neue Methode der Vergleichung Statistischer Reihen (im Anschluss an Mitteilungen Über kriminalstatistische Forschungen),” Jahrbuch fÜr Gesetzgebung, Verwaltung und Volkswirtschaft im Deutschen Reich, 33 (1909), 699–720.Google Scholar
  146. [138]
    Tönnies, Ferdinand, “Korrelation der Parteien in Statistik der Kieler Reichstagswahlen,” JahrbÜcher fÜr Nationalökonomie und Statistik, 122 (1924), 663–72.Google Scholar
  147. [139]
    Tylor, Edward B., “On a method of investigating the development of institutions; applied to laws of marriage and descent,” Journal of the Anthropological Institute of Great Britain and Ireland, 18 (1888–9), 245–69. Discussion, 270–2.CrossRefGoogle Scholar
  148. [140]
    van der Bijl, Willem; “Statistische Bemerkungen zu H. MÜller-Annen : ‘Versuche von Langfristvorhersagen mit einer Kontingenzmethode’ (Ann. Met. 6, S. 257) nebst weiteren Betrachtungen Über den prognostischen Wert von Kontingenztabellen,” Annalen der Meteorologie, 7 (1955–6), 289–302.Google Scholar
  149. [141]
    Wahl, Eberhard W., “Das statistisch Entropieverhältnis, ein Hilfsmittel zur Lösung von Vorhersageproblemen,” Meteorologische Rundschau, 8 (1955), 51–4.Google Scholar
  150. [142]
    Wallis, W. Allen, and Roberts, Harry V., Statistics, A New Approach, The Free Press, Glencoe, Illinois, 1956.Google Scholar
  151. [143]
    Wallis, Wilson D., “Probability and the diffusion of culture traits,” American Anthropologist, 30 (1928), 94–106.CrossRefGoogle Scholar
  152. [144]
    Weida, Frank M., “On various conceptions of correlation,” Annals of Mathematics, 29 (1928), 276–312.MathSciNetMATHCrossRefGoogle Scholar
  153. [145]
    Williams, Josephine J., “Another commentary on so-called segregation indices,” American Sociological Review, 13 (1948), 298–303.CrossRefGoogle Scholar
  154. [146]
    Wilson, Edwin B., “Morbidity and the association of morbid conditions,” The Journal of Preventive Medicine, 4 (1930), 27–38.Google Scholar
  155. [147]
    Wirth, Wilhelm, Spezielle Psychophysische Massmethoden, Urban and Schwarzenberg, Berlin and Vienna, 1920. Part of Abderhalden, Emil (ed.), Handbuch der Biologischen Arbeitsmethoden; Lieferung 4, Abt. 6, Methoden der Experimentellen Psychologie, A. Heft 1.Google Scholar
  156. [148]
    Wood, Karl D., “Rapid correlation by an empirical method,” Journal of Educational Psychology, 19 (1928), 243–51.CrossRefGoogle Scholar
  157. [149]
    Yule, G. Udny, “On the association of attributes in statistics: with illustrations from the material from the Childhood Society, &c,” Philosophical Transactions of the Royal Society of London, Ser. A, 194 (1900), 257–319.MATHCrossRefGoogle Scholar
  158. [150]
    Yule, G. Udny, “On the methods of measuring association between two attributes,” Journal of the Royal Statistical Society, 75 (1912), 579–642. Discussion 643–52.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag New York 1979

Authors and Affiliations

  • Leo A. Goodman
    • 1
  • William H. Kruskal
    • 1
  1. 1.University of ChicagoUSA

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