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Poli Sci 3N06 - JAN 22 2014

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Political Science
Todd Alway

Political Science 3N06 Wednesday, 22 January, 2014 Political Science 3N06 Semester II 2014 Lecture 4a: Probability and the Normal Curve RECAP Description o Measure of central tendency (what is typical?) o Measure of dispersion o Need to be able to describe the shape of the distribution! LAST WEEK o Measures of dispersion o Interested in the variety  Within a particular variable • How far apart are the cases? • Is there a deal of spread? • How much variety? o Which measure of dispersion we can use. It’s based upon the level of measurement on the variable. o It’s whether it’s at the nominal, ordinal or interval  NOMINAL LEVEL - variation ration (proportion of cases not in the mode)  ORDINAL LEVEL - Range or the interquartile range • If have to make a determination whether range or interquartile range • BETTER MEASURE OF DISPERSION o Interquartile - We can eliminate the outlier o What gives us a better variety in the distribution? o Where do the majority of cases fall in between?  INTERVAL LEVEL RANGE - How can we do better? • Interquartile or range - Only uses two variables; we are still only building two scores within the variety. It does not give us a sense of how much variety there is with one another. • Better off going with measure of dispersion… Variance o Adding together deviations - will sum to zero! o Need to get rid of the negative signs by squaring the deviations o Add all of the deviations together (n) and get some indication of the variance! o How far on average are the cases from each other? o Problems with the square - It’s squaring all of our deviations! o When we square those numbers, we are also squaring those units! - Different methods of calculating the variance o Matters less and less the sample size o Small sample sizes it makes a difference whether dividing by∨n−1 o s standard deviation ∨s variance) 2 o σ standarddeviation ∨σ (variance) 1 Political Science 3N06 Wednesday, 22 January, 2014 CHAPTER 4 The normal curve is a theoretical distribution that happens to closely match many (although not all) real distributions - It is based on mathematics, not on something that can be seen 1 - p x = 2 √255σ - Normal curve resembles empirical distributions o Physical characteristics like height or weight tend to be normally distributed o Social variables are also distributed in an approximately normal way  Political extremism - Many social variables are sometimes NOT o Variables that are not normally distribute
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