foo.html

<p><a href = "http://gerrymander.princeton.edu"><b>Gerrymandering analyzer from Prof. Sam Wang, Princeton University</b></a></p>
<p></p>
<p>
Election to be analyzed:  U.S. House election of 2016 in ['AZ']</p>
<p>
Districts to be sampled for fantasy delegations:  U.S. House 2012</p>
<p></p>
<p>
The AZ delegation has 9 seats, 4 Democratic/other and 5 Republican.</p>
<p>
Uncontested races are assumed to have been won with 75% of the vote.</p>
<p>
The average Democratic share of the two-party total vote was 48.4% (raw)
.</p>
<p></p>
<p>
<b>Analysis of Intents</b></p>
<p></p>
<p>
If a political party wishes to create for itself an advantage, it will pack its opponents to win overwhelmingly in a small number of districts, while distributing its own votes more thinly, but still to produce reliable wins. 
</p>
<p></p>
<p>
Partisan gerrymandering arises not from single districts, but from patterns of outcomes. Thus a single lopsided district may not be an offense - indeed, single-district gerrymandering is permitted by Supreme Court precedent, and may be required for the construction of individual districts that comply with the Voting Rights Act. Rather, it is combinations of outcomes that confer undue advantage to one party or the other.
</p>
<p></p>
<p>
The following two tests provide a way of quantifying any such advantage in a set of election results.
</p>
<p></p>
<p>
<b>First Test of Intents: Probing for lopsided win margins (the two-sample t-test):</b> 
To test for a lopsided advantage, one can compare each party's winning margins and see if they are systematically different. 
This is done using the <a href="http://vassarstats.net/textbook/ch11pt1.html">two-sample t-test</a>. 
In this test, the party with the <i>smaller</i> set of winning margins has the advantage.</p>
<p></p>
<p>
The difference between the two parties win margins does not meet established standards for statistical significance. 
The probability that this difference or larger could have arisen by partisan-unbiased mechanisms is 0.48.
</p>
<p></p>
<p>
<IMG SRC="foo_Test1.png" border="0" alt="Logo"></p>
<p>
<b>Second Test of Intents: Probing for asymmetric advantage for one party (mean-median difference and/or chi-square test):</b> 
The choice of test depends on whether the parties are closely matched (mean-median difference) or one party is dominant (chi-square test of variance).</p>
<p></p>
<p>
When the parties are closely matched in overall strength, a partisan advantage will be evident in the form of a difference between the mean (a.k.a. average) vote share and the median vote share, calculated across all districts. </p>
<p></p>
<p>
The mean-median difference is 5.3 % in a direction of advantage to the Republican Party. 
The mean-median difference would reach this value in 13.1 % of situations by a partisan-unbiased process. 
This difference is not statistically significant (p>0.05). 
</p>
<p></p>
<p>
<IMG SRC="foo_Test2a.png" border="0" alt="Logo"></p>
<p></p>
<p>
When one party is dominant statewide, it gains an overall advantage by spreading its strength as uniformly as possible across districts. The statistical test to detect an abnormally uniform pattern is the <a href="http://www.itl.nist.gov/div898/handbook/eda/section3/eda358.htm">chi-square test</a>, in which the vote share of the majority party-controlled seats are compared with nationwide patterns.</p>
<p></p>
<p>
The standard deviation of the Republican majoritys winning vote share is 7.3 %. 
At a national level, the standard deviation is nan %. 
This difference is not statistically significant (p>0.05). 
</p>
<p>