Presentation on theme: "Measures of Association Quiz"— Presentation transcript:
1 Measures of Association Quiz What do phi and b (the slope) have in common?Which measures of association are chi square based?What do gamma, lambda & r2 have in common?When is it better to use Cramer’s V instead of lambda?
2 In-Class Exercise Creating causal hypotheses X YWrite down a factor that you hypothesize to influence each of the following dependent variables:__________ causes criminality.__________ influences one’s happiness in marriage__________ plays a role in one’s opinion about Gov Pawlenty
3 Statistical Control Conceptual Framework Elaboration for Crosstabs (Nom/Ord)Partial Correlations (IR)
4 3 CRITERIA OF CAUSALITYWhen the goal is to explain whether X causes Y the following 3 conditions must be met:AssociationX & Y vary togetherDirection of influenceX caused Y and not vice versaElimination of plausible rival explanationsEvidence that variables other than X did not cause the observed change in YSynonymous with “CONTROL”
5 CONTROLExperiments are the best research method in terms of eliminating rival explanationsExperiments have 2 key features:Manipulation. . .Of the independent variable being studiedControl. . .Over conditions in which the study takes place
6 CONTROL VIA EXPERIMENT Example:Experiment to examine the effect of type of film viewed (X) on mood (Y)Individuals are randomly selected & randomly assigned to 1 of 2 groups:Group A views The Departed (drama)Group B views Little Miss Sunshine (comedy)Immediately after each film, you administer an instrument that assesses mood. Score on this assessment is D.V. (Y)
7 CONTROL VIA EXPERIMENT BASIC FEATURES OF THE EXPERIMENTAL DESIGN:1. Subjects are assigned to one or the other group randomly2. A manipulated independent variable(film viewed)3. A measured dependent variable(score on mood assessment)4. Except for the experimental manipulation, the groups are treated exactly alike, to avoid introducing extraneous variables and their effects.
8 CONSIDER AN ALTERNATIVE APPROACH… Instead of conducting an experiment, you interviewed moviegoers as they exited a theater to see if what they saw influenced their mood.Many RIVAL CAUSAL FACTORS are not accounted for here
9 STATISTICAL CONTROL Multivariate analysis simultaneously considering the relationship among 3+ variables
10 The Elaboration Method Process of introducing control variables into a bivariate relationship in order to better understand (elaborate) the relationshipControl variable –a variable that is held constant in an attempt to understand better the relationship between 2 other variablesZero order relationshipin the elaboration model, the original relationship between 2 nominal or ordinal variables, before the introduction of a third (control) variablePartial relationshipsthe relationships found in the partial tablesThe elaboration method the process of introducing control variables into a bivariate relationship in order to better understand (elaborate) the relationship.The third variable enhances (or elaborates) the understanding of a two-variable relationship.Control variable a variable that is held constant in an attempt to understand better the relationship between 2 other variablesAnother way to think about control variables:When you control for a variable, you are subtracting the effects of that variable to see what a relationship would be without it.
11 3 Potential Relationships between x, y & z 1. Spuriousnessa relationship between X & Y is SPURIOUS when it is due to the influence of an extraneous variable (Z)(X & Y are mistaken as causally linked, when they are actually only correlated)SURVEY OF DULUTH RESIDENTS BICYCLING PREDICTS VANDALISM (Does bicycling cause you to be a vandal?)extraneous variablea variable that influences both the independent and dependent variables, creating an association that disappears when the extraneous variable is controlledAGE relates to both bicycling and vandalism Controlling for age should make the bicycling/vandalism relationship go away.
12 Examples of spurious relationship ZYa. X (# of fire trucks) Y ($ of fire damage)Spurious variable (Z) – size of the fireb. X (hair length) Y (performance on exam)Spurious variable (Z) – sex (women, who tend to have longer hair) did better than men
13 “Real World” ExampleResearch Question: What is the difference in rates of recidivism between ISP and regular probationers?Ideal way to study: Randomly assign 600 probationers to either ISP or regular probation.300 probationers experience ISP300 experience regularFollow up after 1 year to see who recidivatesProblem: CJ folks do not like this idea—reluctant to randomly assign.
14 “Real World” ExampleIf all we have is preexisting groups (random assignment is not possible) we can use STATISTICAL controlBivariate (zero-order) relationship between probation type & recidivism:RecidivismRegularISPTotalsYes100 (33%)135 (45%)235No2001653653006002 = 8.58 (> critical value: )CONCLUSION FROM THIS TABLE?
15 “Real World” Example 2 partial tables that control for risk: LOW RISK (2 = 0.03)Recid.RegularISPTotalsYes30 (17%)15 (17%)45No1507122018086266HIGH RISK (2 = 0.09)Recid.RegularISPTotalsYes70 (58%)120 (56%)190No5094144120214334
16 “Real World” ExampleConclusion: after controlling for risk, there is no causal relationship between probation type and recidivism. This relationship is spurious.Instead, probationers who were “high risk” tended to end up in ISP
17 IN OTHER WORDS…. X Z Y X = ISP/Regular Y = Recidivism Z = Risk for Recidivism
18 3 Potential Relationships between x, y & z #2Identifying an intervening variable (interpretation)Clarifying the process through which the original bivariate relationship functionsThe variable that does this is called the INTERVENING VARIABLEa variable that is influenced by an independent variable, and that in turn influences a dependent variableREFINES the original causal relationship; DOESN’T INVALIDATE it
19 Intervening (mediating) relationships X Z YExamples of intervening relationships:a. Children from broken homes (X) are more likely to become delinquent (Y)Intervening variable (Z): Parental supervisionb. Low education (X) crime (Y)Intervening variable (Z): lack of opportunity
20 3 Potential Relationships between x, y & z #3Specifying the conditions for a relationship – determining WHEN the bivariate relationship occursaka “specification” or “interaction”Occurs when the association between the IV and DV varies across categories of the control variableOne partial relationship can be stronger, the other weaker. AND/OR,One partial relationship can be positive, the other negative
21 Example Interaction Effect An interaction between treatment and risk for recidivismTreatment had an impact on recidivism for high risk offenders, but not low risk offendersLow RiskTreatment = 30% recidivismControl = 30% recidivismHigh RiskTreatment = 45%Control = 75%
22 Limitations of Table Elaboration: Can quickly become awkward to use if controlling for 2+ variables or if 1 control variable has many categoriesGreater # of partial tables can result in empty cells, making it hard to draw conclusions from elaboration
23 Partial Correlation “Zero-Order” Correlation Correlation coefficients for bivariate relationshipsPearson’s r
24 Statistical Control with Interval-Ratio Variables Partial CorrelationPartial correlation coefficients are symbolized as ryx.zThis is interpreted as partial correlation coefficient that measures the relationship between X and Y, while controlling for ZLike elaboration of tables, but with I-R variables
25 Partial Correlation Interpreting partial correlation coefficients: Can help you determine whether a relationship is direct (Z has little to no effect on X-Y relationship) or (spurious/ intervening)The more the bivariate relationship retains its strength after controlling for a 3rd variable (Z), the stronger the direct relationship between X & YIf the partial correlation coefficient (ryx.z) is much lower than the zero-order coefficient (ryx) then the relationship is EITHER spurious OR intervening
26 Partial CorrelationExample: What is the partial correlation coefficient for education (X) & crime (Y), after controlling for lack of opportunity (Z)?ryx (r for education & crime) = -.30ryz (r for opportunity & crime) = -.40rxz (r for education and opp) = .50ryx.z = -.125Interpretation?
27 Partial CorrelationBased on temporal ordering & theory, we would decide that in this example Z is intervening (X Z Y) instead of extraneousIf we had found the same partial correlation for firetrucks (X) and fire damage (Y), after controlling for size of fire (Z), we should conclude that this relationship is spurious.
28 Partial Correlation Another example: What is the relationship between hours studying (X) and GPA (Y) after controlling for # of memberships in campus organizations(Z)?ryx (r for hours studying & GPA) = .80ryz (r for # of organizations & GPA) = .20rxz (r for hrs studying & # organizations) = .30ryx.z = .795Interpretation?