COURSE REVIEW WHAT HAVE WE LEARNED, ANYWAY? PS 30: Winter 2005

COURSE REVIEWWHAT HAVE WE LEARNED,ANYWAY?PS 30: Winter 2005

THE 3-PRONGED APPROACH • Logic and principles of statistical analysis (lectures) • Uses of software (sections and labs) • Applications in political science: • Course Reader (lectures) • Student Projects (sections, labs, etc.)

Cross-Tabulation Review Voting Intention by Gender: Chile, 1988 ___Gender (X)____ _M_ _F_ Σ Intention (Y) Yes 320 340 660 No 620 420 1040 Σ 940 760 1700

Steps in Analyzing Cross-Tabulation • Check levels of measurement • Check array of table—X as column variable and Y as row variable, and “low-low” cells (if relevant) in upper left-hand corner • Check marginal frequencies • Compute and compare percentages (down the columns) • Form and strength: distribution of % and/or summary measure such as gamma • Significance: X2, which is a function of N and strength of relationship

Computing and Comparing Percentages _____Gender______ __M__ __F__ Σ Intention Yes 34.044.7 38.8 No 66.055.3 61.2 Σ 100.0 100.0 100.0

γ = (ad-bc)/(ad+bc) = - .221 X2 = Σ[(fo – fe)2 /fe] = 20.2 p < .001 Confidence bands at .05 level: ± 2.4%

Regression Review Illegitimacy and Employment Y = % births outside marriage X = % economically active Unit of analysis: Scottish districts R = .666 R Square = .443 Adjusted R Square = .424 Standard Error of Estimate = 5.888

Regression Coefficients: Intercept a = 106.570 Std error = 14.966 t = 7.121 p < .000 Slope b = -.922 Std error = .189 Beta = -.666 t = -4.884 p< .000 BOM = 106.570 - .922 EAP

Steps in Analyzing Regression Coefficients • Strength: • Check values for r and (especially) r2 • Scrutinize scattergram • Form: • Write out full equation • Impose regression line on scattergram • Note signs of b coefficients • To observe predicted values of Y, plug in maximum and minimum values of X, mean value of X, and X values one standard deviation above and below mean of X

Significance: • Check significance levels for F (or t) • Place confidence bands around b coefficient— • multiply standard error by ±1.96 • Ask yourself: Is this a function of the strength of • the observed relationship or of the N? • Multiple Regression: • Compare beta weights (standardized regression coefficients) • Note: interpretation of dummy variables

TYPES OF RELATIONSHIPAND MULTIPLE REGRESSION • With Y as dependent variable: • Spurious: Association (coefficient) between X1 and Y vanishes (approaches zero) when X2 enters the equation • Enhancement: Total R2 for X1 plus X2 greatly exceeds r2 for either X1 or X2 (and X1 and X2 are not highly interrelated) • Specification: Difference in slopes, as determined through use of dummy variables

COURSE REVIEW WHAT HAVE WE LEARNED, ANYWAY? PS 30: Winter 2005