Tuesday, November 12, 2013

State Outliers in the 2012 Election


Question:  In a recent post analyzing the 2012 election results I found that several states which were crucial to President Obama reelection were decided by a relatively small margin.   By contrast, Governor Romney tended to win by large margins in red states.
http://economicmemos.com/2013/11/12/state-outcomes-from-2012-implications-for-2016/
Below I present information on the average and standard deviation of the margin of victory for the two candidates.   The statistics in this chart reveal that the average margin for the Romney win is only a bit larger than the average margin for the Obama win.   The standard deviation of the Obama win is much larger than the standard deviation of the Romney win.

Obama Wins
Romney Wins
Average Margin
0.179
0.211
Standard Deviation of Margin
0.172
0.111

Is the chart above consistent with my post?
Answer:  Let's put it this way.  If I only looked at the average and standard deviation of the margin of victories for the two candidates  I would not have written a post stating that margins in many important blue states were relatively small   Statisticians need to look at the data and not just rely on summary statistics.
Information on  the victory margins in blue states is presented below.
D. C.
0.852
Hawaii
0.434
Vermont
0.365
New York
0.286
Rhode Island
0.280
Maryland
0.266
California
0.237
Massachusetts
0.236
Delaware
0.189
New Jersey
0.180
Connecticut
0.175
Illinois
0.172
Maine
0.157
Washington
0.153
Oregon
0.125
New Mexico
0.106
Michigan
0.096
Minnesota
0.079
Wisconsin
0.070
Nevada
0.068
Iowa
0.059
New Hampshire
0.057
Colorado
0.055
Pennsylvania
0.055
Virginia
0.039
Ohio
0.030
Florida
0.009


Note that President Obama's huge margin in the District raises the simple average of his victory margins.   Three big states -- FL, Oh, and Va were very close.  

Below are statistics on victory margins in Red states.


Utah
0.493
Wyoming
0.423
Oklahoma
0.335
Idaho
0.328
West Virginia
0.273
Arkansas
0.243
Kentucky
0.231
Alabama
0.224
Nebraska
0.223
Kansas
0.221
Tennessee
0.207
North Dakota
0.202
South Dakota
0.184
Louisiana
0.175
Texas
0.160
Alaska
0.146
Montana
0.141
Mississippi
0.116
South Carolina
0.106
Indiana
0.104
Missouri
0.096
Arizona
0.092
Georgia
0.079
North Carolina
0.021
Utah, the state with the largest margin for Governor Romney  had a margin that was around half of the margin in DC.   Only one state -- North Carolina --- was closely contested.

The average and the standard deviation of the state victory margins for President Obama are deceptive because of an outlier -- DC.   This outlier also affects the difference in the average state victory margins for the two candidates.

Statisticians must always beware of outliers !!!!!

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