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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).