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PS 390.002 - SP 14 Week 5: Using the Normal Curve and Z-Scores Nick Davis (Teaching Assistant) Office: Bolton 656 Office Hour: Wed. 4-5pm Web page: http://democracyobserver.org/390 Data for Week • this week you will use the ANES 2008 dataset for the lab exercises: http://democracyobserver.org/data/nes2008.dta • recall that Stata commands . describe and . codebook varname allow you to learn more about the data, where varname is a variable name Getting Add-ons for Stata • you need zcalc to calculate z-scores • the code . findit zcalc will open a viewer window, scroll to where it says “1 package found” and click the link to install • to learn what zdemo2 needs, use . help zcalc Normal Curve 400 the assumption that our variables take on a normal distribution (looks like a bell-curve) underlies our statistical analysis 0 100 Frequency 200 300 • 0 10 20 30 40 50 60 70 Feeling thermometer: CONGRESS 80 90 100 Description to Inference • we need to be able to describe before we can make inferences about variables and their relationships with each other • normality (and mean, standard deviation) allow us to precisely describe empirical distributions • normality allows us to make credible statements about data, since a normally distributed variable will always have 99.72% of the distribution in 3 standard deviations (+/-) from the mean of that variable Z-Scores • a z-score for a value of a variable tells you where where that observation fits on the curve (and how many observations lie above or below that point) • get the summary statistics of a variable using . tabstat varname, s(n mean sd) by(varname2) Comparing Distributions • zdemo2 allows you to compare two distributions by entering the mean and standard deviation of each group: . zdemo2 60.79 20.2 47.29 21.89 Two Normal Distributions Republican -40.27 Democrat 47.29 60.79 Congress Feeling Thermometer 141.59 Calculating Z-Scores • if you want to know how many observations lie above and below a given point (respondent answers 75 out of 100) get the z-score: . zcalc x mean sd! ! ! ! • the z-score here is 0.94, which we can then use to find the proportion of area under the normal curve below and above 75 Area Under Normal Curve • proportion of the area under the normal curve that lies below z=0.94: . display normprob(value)! • proportion of the area under the normal curve that lies above z=0.94: . display 1 - normprob(value) Area Under Normal Curve • proportion of the area under the normal curve that lies below z=0.94: . display normprob(value)! • proportion of the area under the normal curve that lies above z=0.94: . display 1 - normprob(value) Lab Exercises • use any data set other than ANES 2008 and find two different variables for which you would like to calculate z-scores • pick a value for each variable and find its z-score • find the area of the normal cure above and below that value’s zscore • lab manual data sets can be found at: http://democracyobserver.org/390