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Galton's Problem in Cross-National Research

Published online by Cambridge University Press:  18 July 2011

Marc Howard Ross  and
Elizabeth Homer
Elizabeth Homer
Affiliation:
Bryn Mawr College
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Extract

Galton's problem raises questions about the nature of explanation in cross-national research using aggregate data. When political units such as states interact, to what extent can correlations between two traits or behaviors, such as socioeconomic development and political stability, be explained in terms of functional relationships within political systems, and to what extent are they the result of diffusion or borrowing among them? This article explores the logic of Galton's problem and then evaluates several empirical solutions to it, using data drawn from three different types of crossnational samples. The solutions juxtapose explanations based on internal (functional) relationships and external (diffusion) patterns, and suggest that previous research which has ignored diffusion may have led to incomplete or incorrect conclusions.

Type
Research Article
Information
World Politics , Volume 29 , Issue 1 , October 1976 , pp. 1 - 28
Copyright
Copyright © Trustees of Princeton University 1976

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References

1 For a discussion of Galton’s problem in cross-cultural analysis see Naroll, Raoul, “Galton's Problem,” in Naroll, and Cohen, Ronald, eds., A Handbook of Method in Cultural Anthropology (New York: Columbia University Press 1973), 974–89Google Scholar; and Naroll, Raoul, Michik, Gary L., and Naroll, Frada, “Hologeistic Theory Testing,” in Jorgensen, Joseph G., ed., Comparative Studies by Harold E. Driver and Essays in his Honor (New Haven: HRAF Press 1974), 121–48Google Scholar, which give a good overview of the problem. For a detailed discussion of some of the methodological issues involved, see Schaefer, James M., ed., Studies in Cultural Diffusion: Galton's Problem (New Haven: HRAF Press 1974)Google Scholar.

2 Tylor, Edward E., “On a Method for Investigating the Development of Institutions Applied to the Laws of Marriage and Descent,” Journal of the Royal Anthropological Institute, XVIII (1889), 245–72Google Scholar; reprinted in Moore, Franky, ed., Readings in Cross- Cultural Methodology (New Haven: HRAF Press 1963), 1–25Google Scholar.

3 Tylor (fn. 2), 272.

4 One exception may be found in Hobhouse, L. T., Wheeler, G. C., and Ginsberg, M., The Material Culture and Social Institutions of the Simpler Peoples (London: Chapman and Hall 1930)Google Scholar.

5 For example, Murdock, George P., Social Structure (New York: Macmillan 1949)Google Scholar; Whiting, John W. M. and Child, Irvin L., Child Training and Personality (New Haven: Yale University Press 1953)Google Scholar; and Otterbein, Keith, The Evolution of War: A Cross-Cultural Study (New Haven: HRAF Press 1970)Google Scholar. For an overview of substantive findings using the cross-cultural method, see Naroll, Raoul, “What Have We Learned from Cross-Cultural Surveys?” American Anthropologist, Vol. 72 (December 1970), 1227–88CrossRefGoogle Scholar.

6 Naroll (fn. 1), 974–75.

7 Naroll, , “Some Thoughts on Comparative Method in Cultural Anthropology,” in Blalock, Hubert M. Jr., and Blalock, Ann B., eds., Methodology in Social Research (New York: McGraw-Hill 1968), 259Google Scholar; and Naroll (fn. 1), 976.

8 For example, see Lipset, Seymour Martin, “Some Social Requisites of Democracy: Economic Development and Political Legitimacy,” American Political Science Review, Vol. 53 (March 1959), 69–105CrossRefGoogle Scholar.

9 In addition to the works of Naroll cited above, see his “Two Solutions to Galton's Problem,” Philosophy of Science, XXVIII (January 1961), 16–39Google Scholar; and “A Fifth Solution to Galton's Problem,” American Anthropologist, Vol. 66 (1964), 863–67CrossRefGoogle Scholar; Naroll, and D'Andrade, Roy G., “Two Further Solutions to Galton's Problem,” American Anthropologist, Vol. 65 (1963), 1053–67CrossRefGoogle Scholar; Murdock, George P., “World Ethnographic Sample,” American Anthropologist, Vol. 59 (August 1957), 664–87CrossRefGoogle Scholar; Strauss, David J. and Orans, Martin, “Galton's Problem: A Critical Appraisal,” Current Anthropology, XVI (December 1975), 573–94CrossRefGoogle Scholar; Simonton, Dean Keith, “Galton's Problem, Autocorrelation and Diffusion Coefficients,” Behavior Science Research, X (1975), 239–48CrossRefGoogle Scholar; Rolf Wirsing, “Measuring Diffusion: The Geary Method and the Dacey Method,” in Schaefer (fn. 1), 197–219; and Fredrick L. Pryor, “Toward a More Simple and General Solution to Galton's Problem: The Diffusion Possibility Method,” American Ethnologist (forthcoming). The number of proposed solutions to Galton's problem is proliferating rapidly. Keeping an accurate count of them is increasingly difficult as it is not clear which solutions ought to be considered independent inventions and which represent duplication from a common original, due to high levels of interaction within the academic community!

10 Vermeulen, C. J. J. and de Ruijter, A., “Dominant Epistemological Presuppositions in the Use of the Cross-Cultural Survey Method,” Current Anthropology, XVI (March 1975), 34Google Scholar.

11 Ibid., 35.

12 Naroll, , “Reply to Vermeulen and de Ruijter,” Current Anthropology, XVI (March 1975). 42Google Scholar.

13 Not all proposed solutions employ the strategy of removing diffusion effects as an initial step. Naroll's cluster test, Naroll (fn. 9, “Two Solutions . . .”), Naroll and D’Andrade's matched-pair method (fn. 9), and Driver and Chaney's test derived from the matched-pair method, all estimate the relative importance of both diffusion and function. See Harold E. Driver and Richard P. Chaney, “Cross-Cultural Sampling and Galton's Problem,” in Naroll and Cohen (fn. 1), 990–1003. Interestingly, under the influence of Kroeber, cross-cultural research in anthropology for many years consisted mainly of mapping patterns of diffusion and borrowing between cultures of a single region. Chaney, Richard P., “Comparative Analysis and Retroductive Reasoning or Conclusions in Search of a Premise,” American Anthropologist, Vol. 75 (October 1973), 1359–60CrossRefGoogle Scholar.

14 Przeworski, Adam and Teune, Henry, The Logic of Comparative Social Inquiry (New York: John Wiley 1970)Google Scholar.

15 Vermeulen and de Ruijter (fn. 10), 49.

16 Gillespie also sees two general types of solutions to Galton's problem in comparative political analysis: one entails incorporating into the analysis additional variables that measure the relative impact of diffusion and function; a second involves the selection of cases in such a way as to approximate independence. John V. Gillespie, “Galton's Problem, and Parameter Estimation in Comparative Political Analysis,” paper presented to the Annual Meeting of the Midwest Political Science Association, April 29-May 2, 1973, p. 17. Charles D. Elder, in a personal communication, has suggested labeling the two solutions a “sampling” solution and an “additional variables” solution.

17 Although some cross-cultural researchers have paid equal attention to functional and diffusion explanations in their empirical solutions to Galton's problem (see fn. 13), Driver is the only one who has incorporated additional variables measuring diffusion into his analysis. In one study, he uses a sample of 277 ethnic units from North America to reconsider the relationship between residence rules and kin avoidance that Tylor originally investigated. He finds diffusion (what he calls geographical-historical factors) to be relatively more important than psycho-functional ones in explaining his correlations. What is of importance here is the use of variables measuring both diffusion and function in the same study, and his use of partial correlation in assessing the relative impact of each type of variable. Harold E. Driver, “Geographical-Historical Versus Psycho-Functional Explanations of Kin Avoidances,” Current Anthropology, vii (April 1966), 131–60.

18 Charles D. Elder, in a personal communication, has pointed out that the grouping of diverse phenomena under the common heading “diffusion” may mask independent processes.

19 Naroll (fn. 1), 974; Richard E. Hildreth and Raoul Naroll, “Galton's Problem in Cross-National Studies” (mimeo), 1971.

20 Przeworski and Teune (fn. 14), 51–53, cite Naroll's articles and say that the problem is relevant to comparative political research, but offer no solutions to it. John V. Gillespie writes, “In macro-cross-national research, we must separate the variables that are the product of historical interaction of political systems from those that might be hypothesized as the internal conditions producing a given system attribute.” See “An Introduction to Macro-Cross-National Research,” in Gillespie, John V. and Nesvold, Betty A., eds., Macro-Quantitative Analysis: Conflict Development and Democratization (Beverly Hills: Sage Publications 1971), 24Google Scholar; Grimshaw, Allan D., “Comparative Sociology: In What Ways Different from other Sociologies?” in Armer, Michael and Grimshaw, Allan D., eds., Comparative Social Research: Methodological Problems and Strategies (New York: John Wiley Interscience 1973), 7Google Scholar. After quickly describing the problem, Joseph W. Elder offers no empirical solutions, only the view that, “The problems of unit comparability and unit independence promise to remain with crosscultural research for many years.” See “Problems of Cross-Cultural Methodology: Instrumentation and Interviewing in India,” ibid.; John V. Gillespie (fn. 16). Stein Rokkan suggests that comparative research can resolve Galton's problem insofar as comparativists “build the communication-diffusion-innovation variables directly into their models and to focus their comparative analyses on units developed through the merger of smaller societies of the type studied by anthropologists.” See “Cross-Cultural, Cross-Societal and Cross-National Research,” in Rokkan, , ed., Main Trends of Research in the Social and Human Sciences (Paris: Mouton/UNESCO 1970), 668Google Scholar. Although we agree with this assessment of what the components of a solution might be in cross-national research, we question Rokkan's assertion that this is found in the work of comparativists such as Lipset, Almond, Deutsch, Huntington, or Holt and Turner. These scholars have pointed out the potential importance of historical diffusion and communications processes, but they have hardly provided systematic solutions to treating the relative importance of internal and external determinants of national behavior. Arend Lijphart points out that Galton's problem involves the question of the independence of cases in comparative research and suggests that this indicates that researchers should use the comparative method that involves a smaller number of cases rather than statistical studies. They can then pay more attention to details that are likely to be overlooked in aggregate analysis. See Lijphart, , “The Comparable-Cases Strategy in Comparative Research,” Comparative Political Studies, VIII (July 1975), 171–72Google Scholar. Finally, William B. Moul presents data drawn from Banks and Textor which show high correlations between former colonial affiliation and a number of measures of modernization and political development as a way of illustrating the importance of diffusion in cross-national data. He stresses the lack of consideration of diffusion as a basis for explanation in most cross-national research on political development. See “On Getting Something for Nothing: A Note on Causal Models of Political Development,” Comparative Political Studies, VII (July 1974), 150–55Google Scholar.

21 Most cross-national research only employs intra-national data which are then correlated across nations, despite the professed theoretical interest in international relations for interactive processes which Rokkan (fn. 20) cites. For a sampling of typical crossnational research, see Gillespie and Nesvold (fn. 20); Rummel, Rudolph J., “The Dimensionality of Nations Project,” in Merritt, Richard and Rokkan, Stein, eds., Comparing Nations: The Use of Quantitative Data in Cross-National Research (New Haven: Yale University Press 1966)Google Scholar; Taylor, Charles Lewis, Hudson, Michael C., and others, eds., The World Handbook of Political and Social Indicators (2d ed., New Haven: Yale University Press 1972)Google Scholar; Morrison, Donald G. and Stevenson, Hugh M., “Integration and Instability: Patterns of African Political Development,” American Political Science Review, Vol. 66 (September 1972), 902–27CrossRefGoogle Scholar. One fascinating study relies almost exclusively on either interactive data or data based on scores for pairs of nations, rather than the score of a single country: Cobb, Roger W. and Elder, Charles D., International Community: A Regional and Global Approach (New York: Holt, Rinehart & Winston 1970)Google Scholar.

22 Putnam, Robert D., “Toward Explaining Military Intervention in Latin American Politics,” World Politics, XX (October 1967), 83–110CrossRefGoogle Scholar.

23 Midlarsky, Manus, “Mathematical Models of Instability and a Theory of Diffusion,” International Studies Quarterly, XVI (November 1970), 60–84CrossRefGoogle Scholar.

24 Li, Richard P. Y. and Thompson, William R., “The ‘Coup Contagion’ Hypothesis,” Journal of Conflict Resolution, XIX (March 1975), 63–88CrossRefGoogle Scholar.

25 Collier, David and Messick, Richard E., “Prerequisites Versus Diffusion: Testing Alternative Explanations of Social Security Adoption,” American Political Science Review, Vol. 69 (December 1975), 1299–1315CrossRefGoogle Scholar.

26 Walker, Jack L., “The Diffusion of Innovations Among the American States,” American Political Science Review, Vol. 63 (September 1969), 880–99CrossRefGoogle Scholar.

27 Gray, Virginia, “Innovation in the States: A Diffusion Study,” American Political Science Review, Vol. 67 (December 1973), 1174–85CrossRefGoogle Scholar; see also Walker, Jack L., “Comment: Problems in Research of the Diffusion of Policy Innovations,” American Political Science Review, Vol. 67 (December 1974), 1186–91CrossRefGoogle Scholar; Gray, , “Rejoinder to ‘Comment’ by Jack L. Walker,” American Political Science Review, Vol. 67 (December 1973), 1192–93CrossRefGoogle Scholar.

28 Gray (fn. 27), 1182.

29 Resolving Galton's problem does not necessarily make explanation of any set of findings easy. “Galton's problem is just one of the many competing hypotheses that must be eliminated in successful cross-cultural research.” Loftin, Colin, “Galton's Problem as Spatial Autocorrelation: Comments on Ember's Empirical Test,” Ethnology, XI (October 1972), 432Google Scholar.

30 Morrison, Donald G., Mitchell, Robert C., Paden, John N., and Stevenson, Hugh M., Blac\ Africa: A Comparative Handbook (New York: Free Press 1972)Google Scholar.

31 Ivo K. Feierabend and Rosalind L. Feierabend, “Aggressive Behaviors Within Polities, 1948–1962: A Cross-National Study,” in Gillespie and Nesvold (fn. 20), 141–66.

32 Przeworski and Teune (fn. 14), 34–39.

33 Rogers, Everett M., Diffusion of Innovations (New York: Free Press 1962)Google ScholarPubMed; Rogers, Everett M. and Shoemaker, F. Floyd, Communication of Innovations (New York: Free Press 1971)Google Scholar; Driver, Harold E., Indians of North America (Chicago: University of Chicago Press 1961)Google Scholar; Harold E. Driver and Richard P. Chaney, “Cross-Cultural Sampling and Galton's Problem,” in Jorgensen (fn. 1), 109–21; Brams, Steven J., “Transaction Flows in the International System,” American Political Science Review, Vol. 60 (December 1966), 880–98CrossRefGoogle Scholar.

34 In Naroll's linked pair test, “The societies in a cross-cultural sample are aligned geographically. . . . With respect to each trait being studied, each tribe is correlated with its neighbor. . . . Thus we are getting a measure of similarity between neighbors. . . . This measure can be compared with similarly generated coefficients of correlation between substantive traits.” If the correlation between neighbors’ scores is significant, these effects of diffusion can be removed through the use of partial correlations “in which the influence of diffusion as measured by the linked pair method is the control factor.” Naroll (fn. 1), 984–86. The partial correlation solution Naroll proposes initially (p. 986), is statistically useless, as is pointed out in Loftin, Colin, “Partial Correlation as an Adjustment Procedure for Galton's Problem,” Behavior Science Research, X (1975), 131–41CrossRefGoogle Scholar; see also Strauss and Orans (fn. 9), 578. Rolf Wirsing has shown how partial correlations can be used in conjunction with the linked pair test: “Second-order Partials as a Means to Control for Diffusion,” Behavior Science Research, X (1975), 143–59Google Scholar. His formula for computing the second-order partials is incorrect, lanhowever, as Wirsing neglects to square the r terms under the radical signs in the denominator (p. 151). Rather than aligning countries geographically, we have paired countries in our sample with other countries on the basis of several different criteria (see text). Hildreth and Naroll (fn. 19, p. 30), suggest that the linked pair method is not an adequate test of the relative importance of diffusion and functional association. Their comment is appropriate for a sample, but not when the entire population is included in the study, as is the case here and in much cross-national research. One unresolved problem is that if the results do show significant effects of diffusion, the actual number of independent cases will be lower than the actual sample size and the probabilities of finding a significant correlation by chance will be higher than they should be. See Naroll, Michik, and Naroll (fn. 1), 128–29.

35 In the African sample, the pairings were made on the basis of the language spoken by the colonial power immediately prior to independence. This variable was intended to indicate the general political and cultural patterns of mutual attention that developed within the continent. Liberia and Ethiopia were not paired with any other nations because of their lack of a colonial experience. Somalia was dropped because of the uniqueness of its colonial history. Therefore, the sample size is reduced to 29 for the analyses involving this variable.

36 The statistically significant negative correlations between the nature of a country's legal system and that of the country with which it is paired are curious. They might be understood in terms of several alternative hypotheses: (1) in creating a legal system, states are careful to do things differently from their neighbors, possibly because they do not want to repeat the defects in neighboring systems; (2) the correlation reflects the impact of an unspecified third variable, which, when controlled for, reduces the correlation to zero.

37 When the colonial language alone (French or English) is correlated with each of the substantive variables, seven of the relationships are significant; thus, while colonial traditions may have had some influence in Africa, they are not as important as simple neighboring or as neighboring plus language commonality.

38 Most research has assumed that diffusion increases the size of a correlation. See Edwin E. Erikson, “Galton's Worst: A Note on Ember's Reflection,” in Schaefer (fn. 1), 63–83. A situation where diffusion lowers a correlation is less obvious intuitively. The easiest way to think about this case is to realize that two variables may diffuse somewhat independently of each other, or that only one variable may diffuse, so that changes in one will not be highly related to changes in the other. When the effect of these changes is removed through partial correlation, the relationship between the two variables may increase. The common assumption that diffusion will only raise a correlation is limited to those situations where two traits diffuse together. When the patterns of diffusion are different, the effect on the substantive correlation is not predictable. This is the case in the correlation in Table 2 between communal conflict and defense spending. The zero-order correlation is .40; the second-order partial, removing the effects of diffusion, is .73. Only one of the substantive variables, defense spending, shows high diffusion (.63); the diffusion score for communal conflict is only .16. T h e two diffusion measures are unrelated (.15). The other two correlations needed in computing the partials are between communal violence and the diffusion measure for defense spending (—.24), and between defense spending and the diffusion measure for communal violence (.18). There is some evidence that in cases where the correlation between the two diffusion measures is very high, the partial correlation procedure may be biased in favor of the diffusion explanation because it removes variance attribute to the diffusion of each variable individually as well as that which is due to their association in the neighboring country, Wirsing (fn. 34), 156. Some of the latter variance, however, may be due to functional association. To avoid this, Loftin (fn. 29), 133–35, proposes analyzing the correlation between residuals, as does Elder (personal communication). Loftin also points out that diffusion may lead to underestimation off the standard error because samples appear more homogeneous than the population from which they are drawn (fn. 29), 429.

39 Colin Loftin and Sally K. Ward, “An Evaluation of Wirsing's Adjustment Procedure for the Effects of Galton's Problem,” Behavior Science Research (forthcoming).

40 Ibid.

41 Ibid.

42 In the presence of multicollinearity, or high correlation among the independent variables, the variances (or standard errors) of the estimated coefficients will be relatively high. Though the estimates are unbiased, they are imprecise, so that the hypothesis that the estimated coefficients do not differ from zero often cannot be rejected. Large standard errors and nonsignificant relationships may be due to other causes as well as to multicollinearity. When multicollinearity is present, one available strategy is to combine highly correlated variables in a single index and estimate their joint effects. In short, without additional information there is little that can be done about the problem. Kmenta, Jan, Elements of Econometrics (New York: Macmillan 1971), 390Google Scholar. Rockwell discusses various criteria that have been proposed to indicate the presence of multicollinearity and suggests using the Haitovsky test of the singularity of the matrix. When a matrix is significantly nonsingular, multicollinearity can be rejected as a problem. Rockwell, Richard C., “Assessment of Multicollinearity: The Haitovsky Test of the Determinant,” Sociological Methods and Research, III (February 1975). 308–20CrossRefGoogle Scholar.

43 Vermeulen and de Ruijter (fn. 10) are right in suggesting that most cross-cultural studies have tended to treat diffusion in this manner, but we wish to stress that explanations that include diffusion processes may be just as nomothetic as functional explanations.

44 Cobb and Elder report a similar finding when they show that various forms of interaction between European states, such as mail flows, student exchange, and trade are virtually unrelated to the development of positive attitudes toward states for whom the interaction levels are high (fn. 21), 96–99.

45 Feierabend and Feierabend (fn. 31), 154.

46 The list of the 84 nations used in the study and the instability scores for each is provided in Feierabend and Feierabend (fn. 31), 146. The data for the measures of socioeconomic development are from Russett, Bruce M. and others, World Handbooks of Political and Social Indicators (New Haven: Yale University Press 1964)Google Scholar.

47 When no neighbor in the sample spoke the same language, pairing was made on the basis of second-language speakers.

48 The Feierabends report their findings using dichotomized data and chi square tests (fn. 31), 154. We have treated the data as at least ordinal in nature and present Pearson correlations. Only in the case of persons per physician does the significance of the results differ. When we use Spearman rank-order correlations, there are no differences at all with their results at the zero-order (Table 5).

49 Murdock (fn. 9).

50 Przeworski and Teune (fn. 14), 34–39.

51 Vermeulen and de Ruijter advocate a strategy of “stratified random sampling in which the different strata represent different levels of the independent variable under study” (fn. 10), 37. This strategy has some common elements with the “most different systems” design.

52 Naroll is cautious and does not rule out the possibility of diffusion between even the two most remote cultures in his samples, but there does seem to be more face validity to this design in cross-cultural than in cross-national research as a way of ruling out diffusion effects.

53 Russett, Bruce M., “Delineating International Regions,” in Singer, J. David, ed., Quantitative International Politics (New York: Free Press 1968), 317–52Google Scholar.

54 We first aimed at getting a core country in each of Russett's regions. In order to try to maximize regional differences and minimize diffusion effects, it was replaced, however, if it was also in another of Russett's regions. In addition, we wanted states for which there would be n o missing data. In adding an African country, we selected what seemed to be the most representative one for which the Feierabends’ instability score existed. The countries included in the final sample are: El Salvador, South Korea, Thailand, Colombia, Lebanon, Turkey, Norway, Argentina, and Ghana.

55 Table 5 presents the Spearman rank-order correlations for both the Feierabends’ and the “most different systems” samples. Because the smaller sample severely violated the assumptions of normality, the Pearson r should not be used. The correlation coefficients are actually not very different, however. Only the relationships between instability and telephones per capita and GNP per capita are statistically significant for the “most different systems” sample when the Pearson r is used.

56 The effect of geographical proximity in the international system is not quite clear. See, for example, the discussion in Cobb and Elder (fn. 21), 26–28, 88–90; Mohr (fn. 20).

57 Rolf Wirsing (fn. 9) presents techniques that are variations on methods used by geographers. Pryor (fn. 9) calculates a diffusion possibility matrix in which each unit (culture, nation) receives a score based on the degree to which it shares traits likely to promote diffusion, such as closeness or common language, with each other unit in the sample. H e then offers a variety of tests that calculate the degree to which the diffusion possibility scores are related to the actual distribution of the substantive traits under study. Michael Weinstein has suggested to us that each country in the sample might receive a diffusion score for each variable based on the scores for all other countries in the sample, weighted by their similarity in terms of cultural traits, their proximity, or any other plausible ways in which the trait at hand might have diffused.

58 Our discussion is relevant primarily for cross-sectional data. When time-series data are available, techniques such as those used by Midlarsky (fn. 23) or Gray (fn. 27) should be particularly useful in identifying, if not explaining, how diffusion works.

59 Naroll makes this point in his first article on Galton's problem (fn. 9, “Two Solutions . . . “) , 30–31. Vermeulen and de Ruijter argue, however, that Naroll and others are guilty of categorizing ecological and geographical clustering of traits as diffusion (fn. 10), 34. This problem might be handled empirically by including variables that measure these traits in the analysis. Unless the correlations among the independent variables are extremely high, the researcher can then test the alternative hypotheses. Erikson offers the suggestion that certain types of variables are more likely than others to diffuse and to create higher and lower risks of incurring Galton's problem (fn. 38), 78–81. For a further discussion of differential diffusion rates across substantive areas, see Stanley Witkowski, “Galton's Opportunity: The Hologeistic Study of Historical Processes,” in Schaefer (fn. 1), 84–112. The independence of different processes of diffusion is seen in the correlation matrix of the diffusion measures in the African sample, where the variation in both the magnitude and, in a few cases, the direction of the diffusion is large.

60 Several authors have suggested techniques which try to correct for diffusion through the estimation of an adjusted sample size which is lower than the actual N. See Strauss and Orans (fn. 9), and Simonton (fn. 9).

61 Not all anthropologists consider Galton's problem important. For example, see Vermeulen and de Ruijter's quote (fn. 51). Melvin Ember also suggests that random sampling is all that is needed, even if some of the units in the sample happen to be in close contact with each other. See “An Empirical Test of Galton's Problem,” Ethnology, X (January 1971), 98–106Google Scholar. Loftin's (fn. 29) and Erikson's (fn. 38) responses to Ember show the weakness of this position.

62 Several anthropologists have suggested that the most important problem is the nature of the units under study in cross-cultural research and the degree to which they can be compared. Known as Flower's problem, this question is beyond the scope of this paper. See Frankel, Barbara, “Reply Comment on Vermeulen and de Ruijter,” Current Anthropology, XVI (March 1975), 39Google Scholar; Barnes, J. A., “Comment on Strauss and Orans,” Current Anthropology, XVI (December 1975), 585Google Scholar.