MetaAnalysis Of The Final 1996 Pre-Election Presidential Campaign Polls:

The Odds Calculated Here Are The Odds Against A Chance Explanation Of Poll Prediction Failures.


Poll n Clinton
(pC)
Dole
(pD)
Clinton-Dole
(pC - pD)

Std. Error
of
(pC - pD)

Z-score

P(Z) Probability
(2-tailed)
Odds
(1-p)/p
Rounded
Odds
CBS/NY Times 1519 0.53 0.35 0.18 0.0236 3.9954 0.999968 0.000065 15479 15,000
to 1
Pew Research 1211 0.49 0.36 0.13 0.0262 1.6893 0.954423 0.091155 9.97 10 to 1
ABC/Washington Post 703 0.51 0.39 0.12 0.0355 0.9581 0.830986 0.338027 1.96 2 to 1
Harris 1339 0.51 0.39 0.12 0.0257 1.3358 0.909196 0.181607 4.51 5 to 1
NBC/Wall St. Journal 1020 0.49 0.37 0.12 0.0288 1.1890 0.882771 0.234458 3.27 3 to 1
CNN/USA Today/Gallup 1200 0.52 0.41 0.11 0.0277 0.8791 0.810326 0.379348 1.64 2 to 1
Hotline/Battleground 1000 0.45 0.36 0.09 0.0283 0.1497 0.559482 0.881037 0.14 1 to 7
Reuters/Zogby 1200 0.44 0.37 0.07 0.0259 -0.5728 0.716617 0.566766 0.76 1 to 1
Actual Vote 96,211,883 0.493 0.407 0.0853
Combination of Probabilities 3.7138 0.999898 0.000204 4,896 4900 to 1
Note 1: The standard error of the difference between two categories of a multinomial distribution (here tabulated as the standard error of pC - pD) is derived in Kish, L. (Survey Sampling, 1965, Wiley, pp. 497-501).
It is: STD.ERROR = SQRT((1 - (n/96,211,883))*(pC + pD - ((pC - pD)^2))/(n - 1))
Note 2: The computation of a Z-score follows Snedecor, G.W. and Cochran, W.G. (Statistical Methods, 6th Ed., 1967, Iowa State University Press, pp. 211-212).
It is: Z = (ABS((pC - pD) - 0.0853) - (1/(2*n)))/STD.ERROR
Note 3: Probabilities were combined by the weighting method described by Rosenthal, R. (Meta-Analytic Procedures for Social Research, Rev. Ed., 1991, Sage Publications, Ch. 5).
Combined Z = SUMPRODUCT(n, Z)/SQRT(SUMSQ(n)).
Note 4: The P(Z) values associated with the two most extreme Z values were double checked against entries in the normal probability table in Abramowitz, M. and Stegun, I.A. (Eds.) (Handbook of Mathematical Functions, 1964, U.S. Government Printing Office, p. 972).

© 1997 Gerald S. Wasserman