1. THE PRINCIPLE OF PRE

2. READINGS Pollock, Essentials, chs. 4 and 6
Course Reader, Selection 2 (Licklider on Civil Wars)

3. OUTLINE Components of Statistical Association The Principle of PRE
PRE for Categorical Data
Benchmarks for PRE
Looking Ahead…

4. COMPONENTS OF STATISTICAL ASSOCIATION
1. Form (e.g., positive or negative, varies from – 1.0 to + 1.0)
2. Strength (how much X says about Y, varies from zero to 1.0)
Significance (i.e., probability of null
hypothesis, such as p < .05)

5. (PROPORTIONAL REDUCTION OF ERROR)
THE PRINCIPLE OF PRE
(PROPORTIONAL REDUCTION OF ERROR)
Where X = independent variable and Y = dependent variable
State a rule for estimating each value of Y without knowing the respective value on X. These guesses, or “predictions,” are usually based on the appropriate measure of central tendency (mean, median, or mode).
Define, and measure, the total amount of error resulting from these predictions. This quantity is E1.

6. THE PRINCIPLE OF PRE (continued)
State a rule for estimating each value of Y given knowledge of respective values on X. These rules vary according to the level of measurement and the measure of association.
Define, and measure, the total amount of error resulting from this procedure. This quantity is E2.
Then measure the proportional reduction of error as:
PRE = (E1 – E2)/E1

7. PRE FOR CATEGORICAL DATA
Coefficient = Lambda-b = λ-b = PRE
= (E1 - E2)/E1
= (N - Mode) – (N – Σ col Modes)/ N – Mode
= PRE
Sample Computation

8. Gun Control Attitudes and Gender
Example:
Gun Control Attitudes and Gender
________Gender______
Gun Ban?___ Male Female Total
Oppose
Favor
Total ,514

9. Guessing Y without knowing X
Guessing Y with knowledge of X
= E2 = 1,514 – ( ) = 584
PRE = (E1 – E2)/E1 = ( )/707 = .174

10. BENCHMARKS FOR PRE < .10 = weak > .10 but < .20 = moderate
> .20 but < .30 = moderately strong
> .30 = strong
> .40 = very strong
> .50 = exceptionally strong

11. Rearranging Table 6-8:
Campaign Interest, by Level of Education
__________Level_________ __ Σ __
Interested?___ Low Medium High
Not Very
Somewhat
Very
Totals ,711
Lambda = 0
Gamma = > Kendall’s tau-b = > tau-c = +.152

12. LOOKING AHEAD Categorical variables: PRE rule based on mode
Ordered nominal variables: PRE rule based on “pairs”
Interval-scale variables: PRE rule?