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Quantitative Approaches to International Relations Case Study of Research Design in the International Political Economy Case Study of Research Design in International Environmental Policy Case Study of Research Design in International Security Studies Why Quantitative Analysis? Allows inferences about reality using the law of probability. How? Through large aggregate of cases your able to draw relationships between elements and check if the relationship is by chance or purposeful. Linear Correlation- r Multiple Regression- R Squared P-Value Analysis of Variance- ANOVA The Correlation Coefficient: Definition Bruce Ratner, Ph.D. The correlation coefficient, denoted by r, is a measure of the strength of the straight-line or linear relationship between two variables. The correlation coefficient takes on values ranging between +1 and -1. The following points are the accepted guidelines for interpreting the correlation coefficient: 0 indicates no linear relationship. +1 indicates a perfect positive linear relationship: as one variable increases in its values, the other variable also increases in its values via an exact linear rule. -1 indicates a perfect negative linear relationship: as one variable increases in its values, the other variable decreases in its values via an exact linear rule. Values between 0 and 0.3 (0 and -0.3) indicate a weak positive (negative) linear relationship via a shaky linear rule. Values between 0.3 and 0.7 (0.3 and -0.7) indicate a moderate positive (negative) linear relationship via a fuzzy-firm linear rule. Values between 0.7 and 1.0 (-0.7 and -1.0) indicate a strong positive (negative) linear relationship via a firm linear rule. The value of r squared is typically taken as “the percent of variation in one variable explained by the other variable,” or “the percent of variation shared between the two variables.” Linearity Assumption. The correlation coefficient requires that the underlying relationship between the two variables under consideration is linear. If the relationship is known to be linear, or the observed pattern between the two variables appears to be linear, then the correlation coefficient provides a reliable measure of the strength of the linear relationship. If the relationship is known to be nonlinear, or the observed pattern appears to be nonlinear, then the correlation coefficient is not useful, or at least questionable. A p-value is a statistical value that details how much evidence there is to reject the most common explanation for the data set. It can be considered to be the probability of obtaining a result at least as extreme as the one observed, given that the null hypothesis is true. Theory should determine the research design, not vice versa. The Hypothesis and the operationalization of variables should drive the methodology The Ability not just to describe association among phenomena but to calculate the probabilities that such associations are the product of chance The ability to gain a better understanding of the sources of human behavior in international affairs Errors of Specification: 3 Types of Errors 1. Too much effort calculating correlations with little or no attention to theory 2. Theory itself often is weak and difficult to test because it is too imprecise or too shallow 3. Empirical researchers often impose a statistical model on the theory instead of crafting a model to test the theory Errors of Inference: 1. Overemphasis in statistical significance while neglecting substantive significance 2.Small Sample Size 3. Single Test Bias rather than multiple testing for reliability 4. Lakatos View: Your it till I find something better vs. Bayesian View-Cumulation of results 5.Garbage Can Models: Too many variables, attempt to limit the variables 6.Computer Error The Effects of Hegemony on Trade The Effects of Alliances, PTA, and Trade The Effects of Political Conflict on Trade 1970: 20% of Research in the IPE used Quantitative Methodology Other Research Methods Quant. 1980: 25% of Research in the IPE used Quantitative Methodology Other Research Methods Quant. 1990: 45% of all research in the IPE used Quantitative Methodology Other Research Methods Quant. Problem: How do you define, and operationalize Hegemony? Many have tried and failed to reject the Null Hypothesis: There is no relationship between Hegemony and Trade Until the definition of Hegemony was operationalized by viewing Benevolent and Malign Hegemony, and viewing the effect of alliances in Bi-polar and Multi-polar environment Reaffirming that Theory leads the Research Method Increased Trade with Non-Major Powers in Percentage No PTA/ Yes Ally Increased Trade with Non-Major Powers in Percentage Yes PTA/No Ally PTA/Alliance 0 50 100 150 Increased Trade with Major Powers in Percentage No PTA/ Yes Ally Increased Trade with Major Powers in Percentage Yes PTA/No Ally PTA/Alliance 0 50 100 150 Gravity Model of Distance and Trade with added variable for Diplomatic Relations Results: Cooperation stimulates trade; Threats had no statistical significance; War hampers trade 5 Central Themes of Research: The effect of economic development(IV), abatement costs(IV), and democracy(IV) on the pollutions patterns(DV) The effect of growing trade(IV) on environmental degradation(DV) The effect of regulatory issues(IV) on the environment(DV) The relationship between environmental factors(IV) and violent conflict(DV) The formation of effectiveness of international regimes(IV) and environmental degradation(DV) Larger and more comprehensive datasets relevant to International Environmental Policy are needed Small Sample Sizes making it difficult to ascertain reliability of studies Problem of conceptual consolidation: How do you unify different concepts of resource expenditures and problemsolving models Measuring Effectiveness Four Stages of International Disputes: Dispute Initiation Stage Challenge the Status Quo Stage Negotiation Stage Military Escalation Stage Appropriate Measurements, which unit of analysis to use, and mode of analysis: Crosssectional time series Selection Bias: one solution stratified random sampling using both conflict and non-conflict variables Non-Independent observations Inadequate Measurements-Solutions by Stage: Military Balance measure Dyadic Analysis https://controls.engin.umich.edu/wiki/ind ex.php/Basic_statistics:_mean,_median,_ average,_standard_deviation,_zscores,_and_p-value