• goal of bivariate analysis: measure association or relationship

• crosstabulation = cross-classification =      contingency table

• intersecting frequency distributions

• rows, columns
• cells
• marginals - row and column totals
• r x c designation of a table - # rows x # columns
• computing row or column percentages

1) is there a relationship?

statistical independence/dependence

• detecting relationship by comparing percentage distributions for one variable across different categories of a second
• almost always some relationship

• crude assessment: compare percentage difference across the different categories of i.v.

• if cases' values high on one variable, values on other variable high (positive) or low (negative)

• e.g., positive = height and weight

• e.g., negative = size of vehicle and gas mileage

• can be defined for ordinal and interval variables only

• inverse = negative

• "spurious" relationship - two variables related by their common association with another variable that each causes them, but the two original variables not causally linked, even indirectly

• e.g., ice cream sales and murder - positive association (weather = key)

• intervening relationship - third variable links the independent variable to the dependent variable

• e.g., sex and job status among executives and managers

• conditional relationship - strength and/or direction of relationship between two variables differs for different values on third variable

• e.g., lightning strikes and forest fires - positive when dry, weakly positive or none when wet
• statistical interaction or interactive relationship

• causal direction - can go either/both directions

• e.g., friends' behavior x own behavior

Elaboration/partial tables

• examine third variables that could account for association (either as spurious or intervening relationship) or explore conditional relationships

• create tables between two variables for cases that fall into particular categories of a third variable

Pitfalls in analyzing associations
 

Simpson's paradox

• direction or strength of relationship changes when aggregating across natural groups that should be treated individually

• "More pedestrians are killed crossing with the signal than against it."

• "More people get killed crossing streets with crosswalks than those without."

• "In 1993, juveniles arrested in Orange County, CA, were tested for drug use (urinalysis). Forty-three percent (43%) tested positive, and a newspaper stated that 'the results seemed to bolster beliefs that drug use and juvenile crime are related.'"