Control TablesControl Tables

March 7, 2011March 7, 2011

ObjectivesObjectivesBy the end of this meeting, you should By the end of this meeting, you should

be able to:be able to:

a)a) Explain the concept of statistical Explain the concept of statistical control.control.

b)b) Differentiate intervening (mediator) Differentiate intervening (mediator) and interacting (moderator) and interacting (moderator) variables.variables.

c)c) Appropriately choose control Appropriately choose control variables in data analysis.variables in data analysis.

d)d) Compute a control table.Compute a control table.

Think AboutThink About

a) When analyzing the relationship between variables, what does it mean to “control” for a variable?

b) We cannot always use experimental data in political science.

Control VariablesControl Variablesa)a) Frequently when we observe a Frequently when we observe a

relationship between two variables, relationship between two variables, causally there may be a third variable causally there may be a third variable acting as well. acting as well.

b)b) Therefore we must statistically Therefore we must statistically ‘‘controlcontrol’’ for that variable to see if a for that variable to see if a relationship continues between our relationship continues between our initial two variables.initial two variables.

c)c) Imagine that we believe that ideology Imagine that we believe that ideology leads to vote choice. Does that finding leads to vote choice. Does that finding still hold if partisanship is controlled?still hold if partisanship is controlled?

Intervening and Interacting Intervening and Interacting VariablesVariables

a)a) An intervening variable is one where the An intervening variable is one where the third variable occurs between the third variable occurs between the independent and the dependent variable. independent and the dependent variable.

b)b) An interacting variable is one that An interacting variable is one that moderates, in a casual sense, the effect of moderates, in a casual sense, the effect of the independent variable on the dependent the independent variable on the dependent variable. The effects of interacting variables variable. The effects of interacting variables can be very different.can be very different.• Sometimes an effect may be negative for one Sometimes an effect may be negative for one

value but positive for anothervalue but positive for another• Sometimes an effect may be stronger (but in the Sometimes an effect may be stronger (but in the

same direction) for one value of the variable than same direction) for one value of the variable than another. another.

Intervening and Interacting Intervening and Interacting VariablesVariables

a)a) In the previous example with In the previous example with ideology and vote choice, what type ideology and vote choice, what type of variable is partisanship?of variable is partisanship?

b)b) There are two general ways to There are two general ways to answer that question.answer that question.• TheoreticallyTheoretically• EmpiricallyEmpirically

Antecedent VariablesAntecedent Variablesa)a) It is also important to identify if the It is also important to identify if the

control variable is antecedent to the control variable is antecedent to the independent variable, i. e. does it independent variable, i. e. does it occur before. occur before.

b)b) If the control variable is antecedent If the control variable is antecedent and including it in the model and including it in the model eliminates the effect of the eliminates the effect of the independent variable then the initial independent variable then the initial relationship must be considered relationship must be considered spurious.spurious.

SpuriousnessSpuriousnessa)a) While control variables may help us While control variables may help us

eliminate relationships that are spurious, it eliminate relationships that are spurious, it is important to look for relationships that is important to look for relationships that are specified by the control variable. are specified by the control variable.

b)b) In these cases, there is a relationship In these cases, there is a relationship between the independent and dependent between the independent and dependent variable but it only occurs at one level of variable but it only occurs at one level of the control variable. the control variable.

c)c) For instance, you might discover that the For instance, you might discover that the relationship between race and turnout is relationship between race and turnout is spurious when education is considered spurious when education is considered except for Native Americans.except for Native Americans.

How Many Control Variables to How Many Control Variables to Use?Use?

a)a) Parsimony vs. accuracyParsimony vs. accuracy• Achen and the rule of threeAchen and the rule of three• The medical field: rule of thirtyThe medical field: rule of thirty

b)b) Make sure to use only those that have Make sure to use only those that have a relationship with both the a relationship with both the independent and dependent variable.independent and dependent variable.• If the variable does not have a relationship If the variable does not have a relationship

with both the independent and dependent with both the independent and dependent variable, then it is a poor control.variable, then it is a poor control.

How Many Control Variables to How Many Control Variables to Use?Use?

c)c) When testing for spuriousness only When testing for spuriousness only look at those variables that precede look at those variables that precede both the independent and dependent both the independent and dependent variablevariable• Remember if a control occurs between Remember if a control occurs between

the independent and dependent variable the independent and dependent variable (i.e. is intervening) then it cannot render (i.e. is intervening) then it cannot render the initial relationship spurious.the initial relationship spurious.

d)d) When in doubt follow the trend of the When in doubt follow the trend of the literature.literature.

For Next TimeFor Next Timea)a) Read WKB chapter 14, pp. 298-313Read WKB chapter 14, pp. 298-313

b)b) Answer questions 1, 2, & 3 on page Answer questions 1, 2, & 3 on page 324.324.