A quick and dirty proof that Perot didn't cost Bush the 1992 election

[Nym90]

In fact, according to my calculations, he hurt Clinton more than Bush.

Now, as the subject says, this is a simple calculation. It took me all of about 15 minutes of data entry at a website where you can enter x and y variables and the site will calculate the correlation coefficient: http://www.socscistatistics.com/tests/pearson/Default2.aspx. It does not account for the fact that there may be other reasons why some areas of the country saw a greater or lesser Democratic trend in 1992, or other reasons why Perot would have done better or worse in a state....it also is not as comprehensive of an analysis as could be done if one burrowed down to the county, or even better, the precinct level, as opposed to looking only at the statewide level. I encourage others to expound on this.

But it was based on a common sense hypothesis. If Perot cost Bush more votes than Clinton, we would expect the states where Perot performed best to also be the states where there was the greatest Democratic "trend" in Atlas-speak. In other words, where there was the greatest drop off in the Republican vote from 1988 to 1992, relative to the Democratic vote. So if Perot was taking votes disproportionately from Bush, we should have seen Bush's vote percentage decrease the most in Perot's strongest states, and hold up better in states where Perot ran worse.

However, plugging in the data for the 50 states and DC, plotting Perot's percentage of the vote on the x axis vs. the Democratic trend on the y axis (using the Democratic trend as opposed to the Republican trend, because we expect the D tend to be positively correlated with Perot's vote such that as one is greater, the other should be greater as well.), we actually find a slight negative correlation (!), albeit not one of statistical significance.

So in layman's terms, Perot did better in the states that had a Republican trend, where Bush's vote total held up better, as opposed to the ones that saw Bush's performance drop more, but we can't say with statistical certainly that Perot actually cost Clinton more votes than Bush.

However what we can say with a pretty high degree of certainty is that Perot most certainly didn't take twice as many votes from Bush as Clinton, which is what would have more or less been required for Perot to cost Bush the election, if you look at the national percentage margins and the percentage margins in the closest states.

"The value of R is -0.1327. Although technically a negative correlation, the relationship between your variables is only weak (nb. the nearer the value is to zero, the weaker the relationship).

The value of R2, the coefficient of determination, is 0.0176."

--------------------------------

For those who wish to double check my work, here are the x values for Perot's percentage of the vote in each state, and the associated y values for the Democratic trend, and the full calculations and text explanations that the site spat out.

The value of R is: -0.1327.

Explanation of results

As you have probably already noticed, the output of this calculator is... verbose. Although most of the information provided below is self-explanatory, there are a few things worth noting. There is more than one way to calculate the R value, but these are all mathematically equivalent, so you shouldn't worry if you don't recognize the equation used here. In the "Result Details & Calculations" box, you'll find what we've called a cross-check value, which is the R value calculated using an algorithm supplied by the Meta Numerics statistical library. This should be identical to the value that we've calculated.

Perot     D trend

30.44   6.54
28.43   0.86
27.34   2.18
27.04   -0.83
26.99   -5.2
26.19   10.28
26.11   -4.9
25.55   3.66
24.21   -8
23.96   -8.67
23.79   5.97
23.68   -3.44
23.63   -9.51
23.32   -1.25
23.16   -6.98
23.07   -12.26
23.01   -5.26
22.8     -2.62
22.78   5.93
22.56   14.09
22.01   -4.16
21.8           -10.46
21.69   0.84
21.58   -1.75
21.51   -12.55
20.98   -0.6
20.63   3.67
20.44   7.31
19.82   7.19
19.77   0.76
19.3           2.01
18.71   -17.49
18.2           -1.95
16.64   3.04
16.12   0.23
15.92   -5
15.75   -1.54
15.61   2.73
14.22   -11.41
14.18   3.8
13.7           2.19
13.66   1.56
13.63   2.85
13.34   7.56
11.81   1.54
11.55   2.49
10.85   -0.75
10.43   18.61
10.09   7.71
8.72          -1.38
4.25          -6.08

Result Details & Calculation

Key

X: Perot percentage
Y: Dem trend
Mx: Mean of Perot percentage
My: Mean of Dem trend
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores

X values
∑ = 994.97
Mean = 19.509
∑(X - Mx)2 = SSx = 1684.288

Y Values
∑ = -18.44
Mean = -0.362
∑(Y - My)2 = SSy = 2394.611

X and Y Combined
N = 51
∑(X - Mx)(Y - My) = -266.552

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -266.552 / √((1684.288)(2394.611)) = -0.1327

Meta Numerics (cross-check)
r = -0.1327

[Nym90]

If there is interest, I may expand this to look at other third party candidates, in other years. I also encourage anyone with more of a statistical background than I to help us understand how the correlation coefficient translates to what percentage of votes were likely taken from each of the two major party candidates, or what percentage likelihood each major party candidate was hurt by the third party candidate.

[/]

I think it's very interesting! I would love to see if you could try to calculate other years and candidates, particularly Nader and Johnson in 2000 and 2012.

[mencken]

I did this once a few years ago. The problem was that the opposite trend emerged when I looked at county level trends for most states, although it still did not flip enough states to the Bush column to swing the election

[Nym90]

I'm not surprised there would be the opposite trend at the county level. For starters, of the counties that Perot won, only three went on to vote for Clinton in 1996 (the three in Maine), the rest for Dole, and all had voted for Bush in 1988.

[Nym90]

Nader in 2000 actually produces a negative correlation with Republican trend, which surprised me. But Nader's support was much lower than Perot's nationally, so I would expect the results to be less reliable for candidates with a smaller spread of support between states.

The value of R is: -0.119.

Explanation of results

As you have probably already noticed, the output of this calculator is... verbose. Although most of the information provided below is self-explanatory, there are a few things worth noting. First, the five text boxes spread across the middle of the page represent the calculations that would be required if you were to calculate the R value in stages. Second, there is more than one way to calculate the R value, but these are all mathematically equivalent, so you shouldn't worry if you don't recognize the equation used here. Third, in the "Result Details & Calculations" box, you'll find what we've called a cross-check value, which is the R value calculated using an algorithm supplied by the Meta Numerics statistical library. This should be identical to the value that we've calculated.

Note: If you want to calculate a P value from your R score, we have a calculator here (before clicking, remember to note your r score and record any calculation details you require).

X Values (Nader percentage)

10.07
6.92
6.42
6.12
5.95
5.88
5.70
5.25
5.24
5.20
5.04
4.65
4.42
4.14
3.90
3.82
3.62
3.58
3.55
3.52
3.37
3.29
2.98
2.97
2.65
2.54
2.50
2.46
2.45
2.23
2.19
2.17
2.15
2.12
2.10
1.99
1.65
1.63
1.63
1.50
1.47
1.46
1.16
1.10
0.95
0.84
0.82
0.52
0
0
0
  Y Values (Republican trend)

5.42
4.33
-1.91
-4.18
14.19
-1.04
7.75
-1.01
-8.35
5.74
-0.35
11.41
-7.32
-1.04
3.22
-6.91
2.11
-4.15
-0.73
2.29
-5.4
12.79
0.5
-5.98
-8.4
-5.82
1.87
-3.43
13
2.03
-2.51
-1.92
8.39
19.08
-2.97
0.08
13.07
-2.29
1.64
8.09
1.89
14.38
11.74
-0.09
-1.73
2.05
3.79
2.51
0.14
6.07
11.27
 
Result Details & Calculation

X Values
∑ = 157.88
Mean = 3.096
∑(X - Mx)2 = SSx = 211.469

Y Values
∑ = 113.31
Mean = 2.222
∑(Y - My)2 = SSy = 2213.189

X and Y Combined
N = 51
∑(X - Mx)(Y - My) = -81.393

R Calculation
r = ∑((X - My)(Y - Mx)) / √((SSx)(SSy))

r = -81.393 / √((211.469)(2213.189)) = -0.119

Meta Numerics (cross-check)
r = -0.119 Key

X: X Values
Y: Y Values
Mx: Mean of X Values
My: Mean of Y Values
X - Mx & Y - My: Deviation scores
(X - Mx)2 & (Y - My)2: Deviation Squared
(X - Mx)(Y - My): Product of Deviation Scores
The value of R is -0.119. Although technically a negative correlation, the relationship between your variables is only weak (nb. the nearer the value is to zero, the weaker the relationship).

The value of R2, the coefficient of determination, is 0.0142.

[Oldiesfreak1854]

Well done.  I've suspected all along that spoiler effects are exaggerated.