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.)

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

Cross-Tabulation Review

Steps in Analyzing Cross-Tabulation

1. Check levels of measurement

2. Check array of table—X as column variable and Y as row variable, and “low-low” cells (if relevant) in upper left-hand corner

3. Check marginal frequencies

4. Compute and compare percentages (down the columns)

5. Form and strength: distribution of % and/or summary measure such as gamma

6. Significance: X2, which is a function of N and strength of relationship

_____Gender________M__ __F__ Σ

Intention Yes 34.0 44.7 38.8

No 66.0 55.3 61.2

Σ 100.0 100.0 100.0

Computing and Comparing Percentages

γ = (ad-bc)/(ad+bc) = - .221

X2 = Σ [(fo – fe)2 /fe] = 20.2

p < .001

Confidence bands at .05 level: ± 2.4%

Illegitimacy and Employment

Y = % births outside marriageX = % economically active Unit of analysis: Scottish districts

R = .666R Square = .443Adjusted R Square = .424Standard Error of Estimate = 5.888

Regression Review

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:

1. Check values for r and (especially) r2

2. Scrutinize scattergram

Form:

1. Write out full equation2. Impose regression line on scattergram3. Note signs of b coefficients4. 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:

1. Check significance levels for F (or t)2. Place confidence bands around b coefficient— multiply standard error by ±1.963. Ask yourself: Is this a function of the strength of the observed relationship or of the N?

Multiple Regression:

1. Compare beta weights (standardized regression coefficients)

2. 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