Date: Dec 27, 2012 10:10 AM
Author: Luis A. Afonso
Subject: Polio, Salk vaccine

Quoting 

www.tamiu.edu/~cferguson/Ferguson PPRP.pdf - -
An Effect Size Primer: A Guide for Clinicians and Researchers Christopher J. Ferguson
Texas A&M International University

. . . Rosnow and Rosenthal (2003) discuss the effectiveness of the Salk vaccine on polio. From a treatment group (n = 200,745) receiving the Salk vaccine, 33 later had polio develop. From a control group (n = 201,229), polio developed in 115.
_______________

Let be
__X0= 115, n0=201228
__X1= 33, n1=200475
And
_____z = (x0/n0 - x1/n1)/sqrt [pp*(1-pp)*(1/n0+1/n1)]
pp=(x0+x1)/(n0+n1)
_____z= 6.71880, which gave a p-value1E-11 (z=6.70602, Abramowitz, Stegun, Handbook of Mathematical Functions).
COMMENT
If is accepted that proportions can be treated as asymptotically normal (even very away from p=0.5, which is uppermost risky) one can safely state that the vaccine is effective.
Performing a No-NHST one can state that by million of children it was expected that 571 be infected. If vaccinated at least 50.4% will not be infected (5% significance level). At late 1940´s, in Portugal, I got a full hand of high school colleagues.


Luis A. Afonso