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POL 51: Scientific Study of Politics

POL 51: Scientific Study of Politics. Prof. B. Jones Dept. of Political Science UC-Davis. Plots and Z-scores. How to do some of the “stuff” in HW 4 Multiple plots on a single page Creating z-scores and finding p -values Visualizing political data Data: Obama vote share by county.

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POL 51: Scientific Study of Politics

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  1. POL 51: Scientific Study of Politics Prof. B. Jones Dept. of Political Science UC-Davis

  2. Plots and Z-scores • How to do some of the “stuff” in HW 4 • Multiple plots on a single page • Creating z-scores and finding p-values • Visualizing political data • Data: Obama vote share by county

  3. dotchart(obamapercent, labels=row.names, cex=.7, xlim=c(0, 100), main="Support for Obama", xlab="Percent Obama") abline(v=50) Returns: Dot Chart: Obama Vote

  4. Interpretation? • Geographical Patterns? • Central Valley • Coastal • SoCal, NorCal? • Why might you observe these patterns? • Z-scores • NB: we’re doing this for learning purposes

  5. Z-scores • Easy: create mean, standard deviation • Then derive z-score using formula from last slide set: • R code on next slide

  6. Z-scores and R #Z scores for Obama meanobama<-mean(obamapercent) sdobama<-sd(obamapercent) zobama<-(obamapercent-meanobama)/sdobama

  7. Interpretation • Z-scores in metric of standard deviations • Large z imply the observation is further away from mean than observations with small z. • Z=0 means the observation is exactly at the mean. • Dotchart (code): par(mfcol=c(1,1)) dotchart(zobama, labels=row.names, cex=.7, xlim=c(-3, 3), main="p-values for Obama Vote Z-scores", xlab="Probability") abline(v=0) abline(v=1, col="red") abline(v=-1, col="red") abline(v=2, col="dark red") abline(v=-2, col="dark red")

  8. Probability Values • High Z-scores are probabilistically less likely to be observed than smaller scores. • Consult a z-distribution table • Probability area is given • Can think about probabilities in the “tails” • One-tail (upper or lower) • Two-tail (upper + lower) • R

  9. R code twotailp<- 2*pnorm(-abs(zobama)) #Gives us area in the upper and lower tails of z onetailp<- pnorm(-abs(zobama)) #Gives us 1-tail probability area; if #subtract this from 1, this give us the area #below this z score (if z is positive) or #area above this z score (if z is negative) zp<-cbind(county, onetailp, twotailp, zobama ); zp

  10. Plots • 4 plots on one page: par(mfcol=c(2,2)) boxplot(obamapercent, ylab="Vote Percent", main="Obama Vote: Box Plot", col="blue") hist(zobama, xlab="Obama Vote as Z-Scores", ylab="Frequency", main="Histogram of Standardized Obama Vote", col="blue") hist(obamapercent, ylab="Frequency", xlab="Vote Percent", main="Obama Vote: Histogram", col="blue") plot(zobama, onetailp, ylab="One-Tail p", xlab="Z-score", main="Z-scores and p-values", col="blue")

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