7: Diseussion 1 Chapter 7: Discussion 1 Nate Silver 2012 Election Nathaniel (Nat

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7: Diseussion 1 Chapter 7: Discussion 1 Nate Silver 2012 Election Nathaniel (Nate) Silver is a popular statistician and writer. He first gained recognition for developing a system forecast the performance of Major League Baseball players. More recently he gained further accolades by correctly predicting the winner of the 2012 presidential elections in all 50 states. The methods he used were more numerous and sophisticated than this demonstration can present. However, this demonstrative example gives some insight as to how he was able to predict a winner when everyone else was saying Too Close to Call. The data in this demonstration is contrived though it represents the idea behind a relatively simple concept called aggregate pollng. 1. Individual Polls: Suppose there were three separate pre-election polls by three diferent polling firms in a given swing state. n-1600 | 99% interval 95% interval 90% interval 80% inteval (0 466, 0.514)|(0.469, 0.511)| (0.474, 0501 Obania?.491 (0.458, 0.522) omney 45 (0.418, 0.482) (0.426, 0.474) (0.430, 0.470) (0.434, 0.466) Pollster 2 Confidence Intervals (0.418 0.3 22)1 0.430.0.51 0)1(0.436,0.504)-110.444-0496) Confidence Intervals (0.456, 0.504) (0.461, 0.499) (0.464, 0.496) (0.468, 0.492) n600 0.436, 0.504) (0.444 Obama ..47 Romney 48 (0.427, 0.533) (0.440, 0.520) (0.446, 0.514) (0.454, 0.506) 99R interval T95%intervalT90% interval-180% inteval? n?2800T Obama 48 Looking at each of these individually, why would it be difficult to predict a winner? 2. Aggregate Poll: Assuming each poll was conducted properly (strict adherence to simple random sampling) you can aggregate the polls into one. This is done by getting a weighted average of the individual proportions where the weights are the sample sizes. Now you have an aggregate poll where n is a lot bigger Aggregate Poll 50001-p-t99%?ntervalT 95% interval T 90%intervall 80% inteval (0.464, 0.500) (0.468, 0.496) (0.470, 0.494) (0.473, 0.491) 45 0.435, 0.472) (0.440, 0.467) (0.442,0.465) (0.445, 0.463 Looking at the aggregate confidence intervals, is it easier to predict a winner? Who would you pick and how confident are you?

Explanation / Answer

Question 1

At looking the poll results of three different pollsters, we see that

for pollster 1 we are only confident when we use 80% confidence interval that Obama is clear winner as obama's confidence interval is higher than Romney's at 80% significance level.  

for pollster 2 : None of the confidence interval shows a difference between Obama and Romeney so by going through this pollster we can't predict who is the winner here.

for pollster 3 : we are only confident when we use 80% confidence interval that Obama is clear winner as obama's confidence interval is higher than Romney's at 80% significance level.  

so as we can see that it is very difficult here to predict a clearcut winner even taking samples of size above 1000.

Question 2

Here as we can see that for the aggregate poll where n = 5000 , we see that for 80% , 90% & 95% confidence level, there is significance difference between Obama's and Romeny's Confidence interval. But for 99% confidence level, we can't be sure that Obama's clear winner here. So, in comparison we can see that it is easier now to predict a winner as compared to previous polls. We will definitely pick the second one, the aggregate poll and here we are at least 95% confident but not 99% confident that Obama would be winner.

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