POS 3713 Chapter 6: K & W Chapter 6

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Florida State University
Political Science
POS 3713
William Berry

6.3.1 The Normal Distribution Often called a “bell curve” Special properties of the Normal Distribution 1. It is symmetrical about the mean, such that the mode, media, and mean are the same 2. The normal distribution has a predictable area under the curve within specified distances of the mean (68-95-99 rule) 1 standard deviation in each direction = 68% of the area under the curve 2 (specifically 1.96) standard deviations in each direction = 95% of the area under the curve 3 standard deviations in each direction = more than 99% of the total area under the curve Frequency distribution: the distribution of actual scores in a sample (represents the frequency of each value of a particular variable) Questions we can answer using the normal distribution What can we say about a sample? Calculate the mean Add up all of the scores and divide by the total number Calculation: Ybar=(Sigma^nsub”i”=1Ysub”i”)/n Calculate the standard deviation SsubY=radical(Sigma^nsub”i”=1Ysub”i”(Ysub”i”-Ybar)^2)/(n-1) Sigma(Ysub”i”-Ybar)^2 means: for each observation, we subtract its value from the mean, then square that difference, then add up all deviations from the mean Sampling distribution: a hypothetical distribution of sample means The mean of the sampling distribution would be equal to the true population mean The standard deviation of the sampling distribution is: ThetasubYbar =ssubY/radical”n” “n” = sample size Standard error of the mean (“standard error”): the standard deviation of the sampling distribution of sample means; is equal to the sample standard deviation divided by the square root on the sample size ThetasubY = standard deviation/square root of all outcomes Confidence interval: the confidence a survey has about the likely location of the population mean 1st: choose a degree of confidence (usually 95% or 2 standard deviations) Ybar plus/minus 2 x thetasubYbar Mean plus/minus (2 x standard error)
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