POLS-3328 Fall 2009-- Lecture Outline

October 27, 2009


Readings:

Chapter 12. Bivariate Data Analysis (Johnson and Reynolds) (pp 431-462) 
Chapter 6 Tests of Significance and Measures of Association (Pollock) (144-151) 
Chapter 10 Doing Your Own Political Analysis (Pollock Workbook)

Bring your CD's to Class from the Pollock workbook 


Measures of Association with Nominal Variables

Chi-Square enables you  to estimate whether a relationship exists, but how do you know how strongly the variables are related?  This is done through a battery of statistical tests that measure both the magnitude of the relationship (how strong is it) and the significance of the relationship/measure.  
 
 Measures of association summarize efficiently the existence, and strength of the relationship.

Level of Measurement

Measure of Association

Range

Characteristics

Nominal Variables

Lambda

0 - 1.0

may underestimate, but a PRE measure

Phi

0- 1.0

Use for a 2x2 table only and is chi-square based

Cramer's V

0 -1.0

chi-square based and the compliment to PHI.  

LAMBDA-  this measures the strength of the relationship between two nominal (or a nominal/ordinal) variables.  

Relationship strengths With Lambda

  • .000 to .10  none

  • .10-.20 very weak

  • .20-.30 moderate

  • .30-.40 moderate-strong 

  • .40 and above-  there is a strong relationship

 Problems With Lambda
Lambda can Underestimate relationships, even when there are significant chi-square values. This is especially true when you have many values clustered around 1 response.  When this is the case, use ......

  • Cramers V-  similar to lambda, except that one cannot use it as a P-R-E measure.  It only describes the strength of the relationship. You should try to use lambda, unless you believe one of your variables is skewed.  As with Lambda we go from 0 to 1.

    • .00  no effect

    • .10  small effect

    • .30  medium effect

    • .50 large effect

  • Phi-  only if you have a 2x2 table. 

Here we can say with a .808 Cramer's V, that we have a very strong relationship between our independent and dependent variables.
 
How to do it in
PASW

Select the Proper Statistic and continue with the cross-tabs!

Here is a case where Lambda may be Underestimating

COMPARING TWO ORDINAL VARIABLES

 If you are using nominal level data, you must use nominal level measures of association.  The exception to this is if you are using dichotomous  variables, you can treat these as ordinal!

MANY OF THE RELATIONSHIPS YOU WILL BE TESTING INVOLVE ORDINAL VARIABLES.  Tests with Ordinal variables allow:

  1. strength

  2. significance

  3. direction- This allows us to determine if we have a positive or negative relationship between our variables.  

When we have two ordinal variables- the measures that we usually use are Kendall's Tau, Goodman and Kruskal's Gamma and Somer's d..

  1. all three are PRE measures. 

  2. each has a possible range of -1 to 1.  As we approach -1 or 1 the stronger our relationship. A value of 0 (zero), means no relationship.

  3. A positive number indicates a positive relationship, a negative value means a negative relationship. 

In variables that have ordinal variables, we can determine if we have a positive or negative relationship between our variables.  This gives us greater statistical power than simply saying that there is a relationship.

Level of Measurement

Measure of Association

Range

Characteristics

Two Ordinal Variables

Gamma

-1.0 to 1.0

Tends to be generous

Kendall's Tau B

-1.0 to 1.0

For square tables

Kendall's Tau C

-1.0 to 1.0

For rectangular

Somer's D -1.0 to 1.0 If you know the D.V.

When to choose? Each one provides different estimates of the value.  .

A POSITIVE RELATIONSHIP

A NEGATIVE RELATIONSHIP

This exists when changes in the independent variable are associated with changes in the reverse direction in the dependent variable.  As the numbers increase in the i.v., the numbers in the category of the dependent variable decrease!

 

As the independent variable increases, the dependent variable decreases. 

 The Tests of Significance

How the output looks

IGNORE THE ASYMP STD. ERROR AND THE APPROX T.!!!

WHAT THIS MEANS

Somer's D on the same test

A negative value does not mean a weak relationship. LOOK AT THE ABSOLUTE VALUE!!!!

From the 80's: In 1984, Ronald Reagan asked Americans if they were "better off now, than they were 4 years ago". The assumption here is that those who were would reward Reagan with 4 more years. Below is a cross-tab of this relationship.

From 2006

Opinions on Iraq and vote choice

 


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