1. The document discusses different types of statistical relationships between variables and measures used to quantify the strength of these relationships. 2. Some key relationship types are general association, monotonic relationships (positive and negative), and linear relationships (positive and negative). 3. Measures of association that quantify relationship strength include correlation coefficients and regression coefficients. These measures make assumptions about variable levels and relationship forms.

1. Correlations Is there a correlation between spending on athletics and wins? One would think so, but check out this outlier: College Basketball Budgets (2007) – 339 DI Teams 1. Kentucky -- $9,204,755 339. VMI -- $99,285 VMI won the game 111-103. Up this weekend: 112. Delaware State -- $1,796,416

2. Homework Assignment Note If you are using the SPSS Student Edition you cannot open datasets with more than 50 variables. Therefore, you need to use: NES2004A_Student.sav Let me know which file you used on the homework.

3. Homework Assignment Note The variable names are virtually the same: Ideology Measure: v_140a is libcon7 Party ID: partyid3 is the same 2004 Vote: who_2004 is who04_2

4. Statistical Relationships Andrew Martin PS 372 University of Kentucky

5. Statistical Relationships Generally speaking, a statistical relationship between two variables exists if the values of the observations for one variable are associated with the observations for the other variable.

6. Statistical Relationships Knowing two variables are related allows political scientists to make predictions.

9. Levels of Measurement

10. Types of Relationships General association. Exists when the values of one variable, X, tend to be associated with specific values of the other variable.

11. Monotonic Relationships Positive monotonic correlation. High values of one variable (X) are associated with high values of another (Y), and conversely, low values (X) are associated with low values (Y). Negative monotonic correlation. High values of X are associated with low values of Y; low values of X are associated with high values of Y.

12. Monotonic Relationships In a positive monotonic relationship, the data curve never goes down once on its way up. In a negative monotonic relationship, the data curve never goes up once on its way down.

21. Measures of Association Measures of association are statistics that summarize the relationships between two variables. These measures are typically used to support theoretical or policy claims.

22. Measures of Association However, a note of caution: These coefficients (1) assume a particular level of measurement – nominal, ordinal, interval and ratio (2) rest on a specific conception of association To interpret its numerical value one has to grasp the kind of association being measured.

23. Important Properties of Coefficients (1) Null value: Zero typically indicates no association, but there are exceptions. (Ex: Difference of the means) (2) Maximum values: Some coefficients have a maximum values. Many are bounded, with the typical lower bound being 0 and the upper bound being 1. (Ex: Correlation)

24. Important Properties of Coefficients (3) Strength of the relationship. Subject to lower and upper boundaries, a coefficient's absolute numerical value increases with the strength of the association. (Ex: Regression coefficient) (4) Level of measurement. Nominal, ordinal and quantitative variables require their own type of coefficient. (Ex: Stats for quantitative data)

25. Important Properties of Coefficients (5) Symmetry. A symmetric measure keeps the same value no matter which variable is treated as dependent or independent. With an asymmetric measures. The coefficient calculated with Y as dependent variable may be differ from the same indicator using X as the dependent variable. (Ex: Correlations)

26. Important Properties of Coefficients Standardized vs. Unstandardized The measurement scale affects the numerical value of most coefficients of association. Sometimes statisticians transform variables into standardized coefficients so that they all have variances of 1. (Ex: Standard errors)