Lecture4_2005

Lecture4_2005 - Prof. Green Stat 102 From T-Tests to...

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Prof. Green Stat 102 From T-Tests to Regression to Multiple Regression The T-test provides an instructive way to get acquainted with the idea of “degrees of freedom.” In contrast to the Z-test, where numbers like 1.65 and 1.96 have magical qualities regardless of the number of observations in question, the T-test requires one to look up critical values in a table. (Note that if the degrees of freedom are greater than 120, the Z-test and T-test become equivalent, in which case you can once again rejoice at the simple elegance of 1.65 and 1.96.) The T-test also provides a handy way to compare two samples drawn from normal populations with an unknown variance. However, anything a T-test can do, regression can do, too. The advantage of regression is that it can do lots of other cool stuff. In this lecture, I demonstrate the equivalence of regression and T-tests in two important cases, unmatched and matched experimental comparisons. The (simulated) data presented below were inspired by recent experiments designed to see how voters respond to political campaigns in 2002. These hypothetical data are meant to approximate the never-made-public but much-discussed experiments that inspired the Republican “72 Hour Campaign.” (For results from always-made-public experiments, see Green, Donald P., and Alan S. Gerber. 2004. Get Out The Vote! How to Increase Voter Turnout . Washington, D.C.: Brookings Institution Press.) Here’s the experiment. Prior to the 2002 campaign, ten voting precincts of 100 voters apiece were grouped into pairs. Each pair consisted of two precincts that had cast the same proportion of votes for Republican candidates in 1998. For each pair, a coin is tossed, one member of the pair was placed in the treatment group. The treatment group received attention from the “ground campaign” – canvassers and local phone banks. The question is whether this treatment increased the number of voters casting Republican ballots. The data may be found in the following dataset . The control group is denoted treatment=0; the treatment group is treatment=1. Notice that the dataset contains a precinct pair identification number. The pairs happen to vary widely in terms of past GOP voting. Some leaned Republican in the past; others had low GOP voting rates. Let’s begin by treating the data as though they had been randomized without pairing. After all, flipping a coin for each pair still produces random assignment of 5 observations to treatment and control groups, so this is still a randomized experiment. By
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ignoring pairing now and taking it into account later, we can appreciate the importance of this aspect of the research design. To analyze whether the treatment and control groups differ, we might begin by looking at the 5-number summary for the two groups: Descriptive Statistics: GOP Vote in 2002 by Treatment Variable Treatmen N Mean Median TrMean StDev GOP Vote 0 5 39.80 41.00 39.80 18.36 1 5 42.00 42.00 42.00 18.91 Variable Treatmen SE Mean
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Lecture4_2005 - Prof. Green Stat 102 From T-Tests to...

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