Lecture5_2005 - Green / Statistics The Mechanics of...

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Green // Statistics The Mechanics of Multiple Regression One of the most important concepts in statistics is the idea of “controlling” for a variable. This lecture is designed to give you a feel for what “controls” are and how they are implemented in the context of multiple regression. Let’s begin by considering an example. In the weeks leading up to the November 2003 election, a group called ACORN sought to bolster support for a ballot proposition in Kansas City. The measure authorized a rise in sales tax in order to fend off cuts to public transportation. ACORN canvassed voters in a predominantly black section of Kansas City, targeting registered voters who had voted in at least one of the five most recent elections. The campaign consisted primarily of door-to-door canvassing conducted during the final two weeks before Election Day. I was asked to evaluate the effectiveness of this campaign. ACORN identified 28 precincts of potential interest to their campaign; I randomly assigned 14 to the treatment group and 14 to the control group. After the election, voter turnout records were gathered. Voting rates among those living in the treatment and control precincts were calculated. The data may be found at Kansas City Dataset The data may be modeled in a few different ways. The simplest model describes the voter turnout rate (Y) as a linear function of the experimental treatment (X) plus a disturbance term: Y = a + bX + U. Here is an “individual value plot” of the data. Note that all of the X values are either 0 (control) or 1 (treatment), but the plot scatters them a bit in order to make the individual values easier to see.
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TREATMEN VOTE03 1.00 0.00 0.50 0.45 0.40 0.35 0.30 0.25 0.20 I ndividual Value Plot of VOTE03 vs TREATMEN Using regression, we obtain the following results: Regression Analysis: VOTE03 versus TREATMEN The regression equation is VOTE03 = 0.289 + 0.0355 TREATMEN Predictor Coef SE Coef T P Constant 0.28884 0.01778 16.24 0.000 TREATMEN 0.03554 0.02515 1.41 0.169 S = 0.0665291 R-Sq = 7.1% R-Sq(adj) = 3.6% The critical numbers here are .036, which suggests that the expected rate of turnout increases by 3.6 percentage-points as we move from control to treatment, and .025, which conveys the uncertainty surrounding this experimental effect. The p-value of .169 tells us that there is a 16.9% chance of observing a treatment effect as large as this in absolute value even if the true experimental effect were zero. Ordinarily, we would use a 1-tailed test here, because one would suppose that canvassing would increase turnout; in that case, the one-tailed p-value is approximately .09. For what it’s worth, that falls a bit short of the conventional statistical significance threshold of .05. (Note that it is just a coincidence that the estimated treatment effect of .036 coincides
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This note was uploaded on 04/07/2008 for the course STAT 102 taught by Professor Jonathanreuning-schererdonaldgreen during the Fall '05 term at Yale.

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Lecture5_2005 - Green / Statistics The Mechanics of...

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