THE PRINCIPLE OF PRE READINGS Pollock Essentials chs
- Slides: 12
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 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) 3. Significance (i. e. , probability of null 4. hypothesis, such as p <. 05)
THE PRINCIPLE OF PRE (PROPORTIONAL REDUCTION OF ERROR) Where X = independent variable and Y = dependent variable 1. 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). 2. Define, and measure, the total amount of error resulting from these predictions. This quantity is E 1.
THE PRINCIPLE OF PRE (continued) 3. 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. 4. Define, and measure, the total amount of error resulting from this procedure. This quantity is E 2. 5. Then measure the proportional reduction of error as: PRE = (E 1 – E 2)/E 1
PRE FOR CATEGORICAL DATA Coefficient = Lambda-b = λ-b = PRE = (E 1 - E 2)/E 1 = (N - Mode) – (N – Σ col Modes)/ N – Mode = PRE Sample Computation
Example: Gun Control Attitudes and Gender ____Gender______ Gun Ban? ___ Male Female Total Oppose 449 358 807 Favor 226 481 707 675 839 1, 514 Total
Guessing Y without knowing X = E 1 = 1, 514 - 807 = 707 Guessing Y with knowledge of X = E 2 = 1, 514 – (449 + 481) = 584 PRE = (E 1 – E 2)/E 1 = (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_____ Interested? ___ Low Medium High __ Σ __ Not Very 81 161 156 398 Somewhat 108 263 475 846 41 124 302 467 230 548 933 1, 711 Very Totals 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?
