What is an additive relationship? The control variable is a cause of the dependent variable but it only defines a small compositional difference across X; Z is only an auxiliary, ''additional'' component of the the independent variable X. What is a compositional difference? any quality that changes across the categories of an independent variable (ex: Gender represents a compositional difference in the support of gun control between Democrats and Republicans) What is a controlled comparison? A comparison accomplished by examining the relationship between and independent and a dependent variable, while holding constant other variables suggested by rival explanations and hypotheses. What is an interaction relationship? The relationship between X and Y depends on the value of Z; oftentimes, line representations of the data will show an intersection of the two lines for Z.

 What is a spurious relationship? A relationship between two variables caused entirely by the impact of a third variable. What is a controlled comparison table? a cross-tabulation table between the original independent and dependent variables for each value of the control variable (Z); it is a cross-tab with more depth, another dimension. It reveals controlled effects of X on Y. What is a controlled effect? effect of X upon Y, taking Z into account (ie. controlled for Z) What is a partial effect? numerical value that summarizes a relationship between an X and a Y after taking a Z into account (after controlling for Z)

 What is a partial relationship? The relationship between an explanatory variable and a dependent variable, taking into account how other, rival explanations account for variation in the dependent variable. What is the rule of direction for nominal relationships? A rule guiding the presentation and interpretation of statistical results. For nominal variables for which there is no greater or lower values (i.e. gender), the value of the variable that defines the left-most column of a cross-tabulation is the base category and effects or differences are stated in relation to the base category. What is a zero-order relationship? simple comparison between two values in cross tabulation analysis (ex: Democrats' support for gun permits is 18 points higher that of Republicans.) What is a confounder? Pre-treatment variable that is related to both the treatment and the outcome.

 What is a controlled comparison design? Allows the researcher to observe the effect of the independent variable on the dependent variable while holding a constant other plausible causes of the dependent variable. What is a difference-in-differences design? Can be used when researchers suspect that variables other than the independent variable have changed in the before and after time periods but these “other factors” are numerous or not clearly known. Involves controlling for time-varying conditions. What are matching methods? Attempts to replicate random assignment in observational setting. Involves matching subjects that are alike in many ways but have contrasting treatment conditions.