¹ Unless specifically noted in the text, “level of analysis” and “unit of analysis” are used interchangeably. This is a common practice in the international-relations literature. Less common and possibly more confusing is treating “system” and “aggregate” as synonyms. While the meaning of system is ambiguous, in the empirical studies examined in this paper the characteristics of the international system are built up by aggregating the characteristics of the components. Calculation of the number of deaths resulting from interstate war in the international system by adding the deaths of the individual states is a simple if not trivial example.

² Brody, Richard A., “Some Systematic Effects of the Spread of Nuclear Weapons Technology: A Study through Simulation of a Multinuclear Future,” Journal of Conflict Resolution, 7, no. 4 (December 1963), 663–753CrossRefGoogle Scholar; Cobb, Roger W. and Elder, Charles, International Community: A Regional and Global Study, (New York, 1971Google Scholar); and Rummel, R. J., “Indicators of Cross-national and International Patterns,” American Political Science Review, 63, no. 1 (March, 1969), 127–97.CrossRefGoogle Scholar

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⁵ J. David Singer, Stuart Bremer, and John Stuckey, “Capability Distribution, Uncertainty and Major Power War 1816–1965,” Peace, War and Numbers, ed. Bruce M. Russett (Beverley Hills, in press).

⁶ Singer, J. David and Small, Melvin, “Alliance, Aggregation and the Onset of War, 1815–1945,” Quantitative International Politics, ed. Singer, J. David (New York, 1968), 247–86Google Scholar; Singer, J. David and Wallace, Michael D., “Intergovernmental Organization and the Preservation of Peace, 1816–1965: Some Bivariate Relationships,” International Organization, 24, no. 3 (Summer, 1970), 520–47.CrossRefGoogle Scholar

⁷ Singer, J. David, “The Level of Analysis Problem in International Relations,” The International System: Theoretical Essays, ed. Knorr, Klaus and Verba, Sidney (Princeton, 1961), 77–92.Google Scholar

⁸ Ibid.

⁹ Ibid., 78.

¹⁰ Ibid., 77.

¹¹ Ibid., 84.

¹² James N. Rosenau and Wolfram Hanrieder think that there are logical problems. See Rosenau, , “Calculated Control as a Unifying Concept in the Study of International Politics and Foreign Policy,” The Scientific Study of Foreign Policy (New York, 1971Google Scholar, originally published in 1963); Hanrieder, , “Actor Objectives and International Systems,” Journal of Politics, 27, no. 1 (February 1965), 109–32CrossRefGoogle Scholar; “Compatibility and Consensus: A Proposal for the Conceptual Linkage of External and Internal Dimensions of Foreign Policy,” American Political Science Review, 61, no. 4 (December 1967), 971–83; “International and Comparative Politics: Toward a Synthesis?,” World Politics, 20, no. 3 (April 1968), 480–93. While Rosenau appears to have changed his earlier position, Hanrieder proposes concepts such as “penetrated system” as “cumulative proposition(s) that cover both analytical environments.” See his “Compatibility and Consensus,” 981.

¹³ “Level of Analysis Problem,” 82.

¹⁴ Robinson, W. S., “Ecological Correlations and the Behavior of Individuals,” American Sociological Review, 15 (1950), 351–7.CrossRefGoogle Scholar

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¹⁶ Choucri, Nazli, “The Nonalignment of Afro-Asian States: Policy, Perception and Behavior,” this Journal, 11, no. 1 (March, 1969), 1–17.Google Scholar

¹⁷ Hanrieder, “Compatability and Consensus,” 977.

¹⁸ Hanrieder, “International and Comparative Politics,” 491. He argues that the concepts must meet “the crucial test of isomorphism” (op. cit.). One is led to wonder how they should meet this test if they are not permitted to sit the examination. Ironically, Rosenau (“Calculated Control,” 199) confronting the same problem and also noting Singer's discussion states “One reason for the lack of conceptual links is that most students in the international field have not treated their subject as local politics writ large.”

¹⁹ Wallace, Michael D., “Power, Status and International War,” Journal of Peace Research, 8 (1971), 23–5.CrossRefGoogle Scholar

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²¹ If the identification problem is thought of in terms of a possible spurious relationship (“Identification Problem,” 27), it need only become a problem if covariation is found at the state level. Moving to the system level to avoid the identification problem may be avoiding a “problem” which is not a problem at all. In other words, analysis at the system level does not permit one to find a zero relationship at the state level. If the state level covariation is not zero, then the identification problem has to be confronted.

²² Coombs, Clyde, “Theory and Methods of Social Measurement,” Research Methods in the Behavioral Sciences, ed. Festinger, Leon and Katz, Daniel (New York, 1953), 480.Google Scholar

²³ Singer and Small, “Alliance Aggregation,” 286. More recently, Singer, referring to studies at the international system level of analysis, has stated “… until certain of the key ecological variables are identified and their own explanatory power ascertained, we will never know exactly how much control remained in the hands of the decision-makers and how much of the variance is accounted for by their environment.” See Singer, J. David, “From A Study of War to Peace Research: Some Criteria and Strategies,” Journal of Conflict Resolution, 14, no. 4 (December 1970), 536.CrossRefGoogle Scholar

²⁴ Singer, “The Level of Analysis Problem,” 91.

²⁵ Singer, J. David and Small, Melvin, “National Alliance Commitments and War Involvement, 1815–1945,” International Politics and Foreign Policy, ed. Rosenau, James N. (New York, 1969), 513–42.Google Scholar

²⁶ Singer and Small, “Alliance Aggregation.”

²⁷ “National Alliance Commitments,” 542.

²⁸ Ibid.

²⁹ The Pearson product-moment correlation coefficients and the Spearman rank-order correlation coefficients are not strictly comparable. In controlling for the effect of duration, I have followed the Singer and Small procedure of dividing the national values on each variable by the number of years a state was in the system. This procedure may not be the most appropriate. See Fernando Cortés and Przeworski, Adam, “Per Capita or Sin Capita: A Note of Caution,” a paper prepared for the Annual Meeting of the American Political Science Association, 1971.Google Scholar

³⁰ Duncan, Otis Dudley, Cuzzort, Ray P., and Duncan, Beverley, Statistical Geography (Glencoe, 1961), 166.Google Scholar As Somers, for one, has pointed out, the implicit assumption when interpreting a cross-sectional relationship longitudinally is “developmental equivalence.” See Somers, Robert, “Applications of an Expanded Survey Research Model to Comparative Institutional Studies,” Comparative Methods in Sociology: Essays on Trends and Applications, ed. Vallier, Ivan (Berkeley, 1971), 383–387Google Scholar and Moul, William B., “On Getting Nothing For Something: A Note On Causal Models of Political Development,” unpublished paper, Department of Political Science, University of British Columbia, May 1973.Google Scholar As it will become obvious below, the relationship between alliance involvement and war is not the same for all states.

³¹ Singer and Small, “Alliance Aggregation,” 251.

³² See Leik, Robert K. and Gove, Walter R., “The Conception and Measurement of Asymmetric Monotonic Relationships in Sociology,” American Journal of Sociology, 74, no. 6 (May 1969), 696–709.CrossRefGoogle Scholar

³³ In most cases the number of possible values on one variable is different from that on the other variable in the graph. Therefore, an exact mirror image is not possible.

³⁴ Singer and Small, “Alliance Aggregation.”

³⁵ Hilton, Gordon, “The 1914 Studies – a Re-assessment of the Evidence and Some Further Thoughts,” Peace Research Society (International) Papers, 13, (1970), 117–41.Google Scholar

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³⁷ “The 1914 Studies,” 121. Hilton does have a point with respect to temporal aggregations.

³⁸ Ibid., 138. Zinnes, Dina, “The Expression and Perception of Hostility in Prewar Crisis: 1914,” Quantitative International Politics, ed. Singer, J. David (New York, 1968), 138.Google Scholar

³⁹ Ibid., 102.

⁴⁰ Yule and Kendall, An Introduction to the Theory of Statistics.

⁴¹ Azar, Edward, “Analysis of International Events,” Peace Research Reviews, IV, no. 1, (November 1970), 90–1, 57–8.Google Scholar

⁴² Smoker, Paul, “Anarchism, Peace and Control: Some Ideas for Future Experiment,” Peace Research Reviews, 4, no. 4 (February 1972), 57.Google Scholar This paper was read to the Faculty Graduate Student Seminar, April 1971.

⁴³ Ole Holsti's reanalysis of the 1914 data, using daily aggregations, indicates that the results of the Stanford studies do not depend upon the width of the time slices. See Holsti, Ole R., Crisis, Escalation and War (Montreal, 1972CrossRefGoogle Scholar).

⁴⁴ Holsti, Ole R. and North, Robert C., “The History of Human Conflict,” The Nature of Human Conflict, ed. McNeil, Elton B. (Englewood Cliffs, 1965), 161.Google Scholar

⁴⁵ Gunnell, John G., Political Philosophy And Time (Middletown, Conn., 1968), 17–20.Google Scholar

⁴⁶ Lyman, S. and Scott, M.B., A Sociology of the Absurd (New York, 1971), 189–212.Google Scholar

⁴⁷ Scott, M. B., The Racing Game (Chicago, 1968), 78.Google Scholar Cited in ibid., 212. For further reading on social time see Pitirim Sorokin and Merton, Robert K., “Social Time: A Methodological and Functional Analysis,” American Journal of Sociology, 42, no. 5 (March 1937), 615–29Google Scholar; Moore, Wilbert E., Man, Time and Society (New York, 1963Google Scholar); Gurvitch, Georges, The Spectrum of Social Time (Dordrecht, Netherlands, 1964Google Scholar); Gurvitch, Georges, “Social Structure and the Multiplicity of Times,” Sociological Theory, Values and Sociocultural Change, ed. Teryakian, Edward A. (New York, 1963), 171–84Google Scholar; and The Voices of Time, ed. Fraser, J. T. (New York, 1966Google Scholar).

⁴⁸ Singer and Small, “Alliance Aggregation,” 256. Also see Tanter, “International Systems and Foreign Policy Approaches,” 22–4.

⁴⁹ Smoker has suggested this measure of psychological time. The literature on time in psychology is immense. See Doob, Leonard W., Patterning of Time (New Haven, 1971Google Scholar) for a convenient and extensive bibliography.

⁵⁰ Przeworski, Adam and Teune, Henry, Logic of Comparative Social Inquiry (New York, 1970), 29.Google Scholar

⁵¹ For a more complex and interesting time level of analysis problem see Smoker, Paul and Miall, Hugh, “The Arms Race 1952–1958: A Seven Nation Study” paper prepared for Peace Research Conference (Western Division) Vancouver, B.C., February 1972.Google Scholar

⁵² Duncan, Otis Dudley and Davis, Beverley, “An Alternative to Ecological Correlations,” American Sociological Review, 18 (1953), 665–66CrossRefGoogle Scholar; Goodman, Leo A., “Some Alternatives to Ecological Correlation,” American Journal of Sociology, 64 (1959), 610–25CrossRefGoogle Scholar; Shively, W. Phillips, “Ecological Inference: The Use of Aggregate Data to Study Individuals,” American Political Science Review, 63, no. 4 (December 1969), 1183–96.Google Scholar