THE PRINCIPLE OF PRE

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

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

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)

(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.

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

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

Gun Control Attitudes and Gender Example: Gun Control Attitudes and Gender ________Gender______ Gun Ban?___ Male Female Total Oppose 449 358 807 Favor 226 481 707 Total 675 839 1,514

Guessing Y without knowing X Guessing Y with knowledge of X = E2 = 1,514 – (449 + 481) = 584 PRE = (E1 – E2)/E1 = (707-584)/707 = .174

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

Rearranging Table 6-8: Campaign Interest, by Level of Education __________Level_________ __ Σ __ Interested?___ Low Medium High Not Very 81 161 156 398 Somewhat 108 263 475 846 Very 41 124 302 467 Totals 230 548 933 1,711 Lambda = 0 Gamma = + .273 > Kendall’s tau-b = +.167 > tau-c = +.152

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