Hypothesis Testing with Lot Quality Assurance Sampling (LQAS) Using the Normal Approximation of the Binomial

• Activity Number: 547
• Type: Contributed
• Date/Time: Thursday, August 2, 2007 : 10:30 AM to 12:20 PM
• Sponsor: Social Statistics Section
• Author(s): David Fitch*+ and Roberto Molina Cruz
• Companies: Universidad del Valle de Guatemala and Universidad Del Valle de Guatemala
• Keywords: LQAS ; Lemeshow ; Valadez ; USAID ; Evaluation

Abstract

Lemeshow and coauthors have papers on using probabilities from the binomial distribution to test a null hypothesis, e.g., that the child vaccination rate is not >80%. It would be more efficient to use normal approximations of binomial probabilities. With sample sizes of 28, probabilities for b(28, .8) are approximated using N[28x.8,28x.8(1-.8)] = N[22.4, 4.48]. The binomial probability of 27 or more vaccinated (1 or fewer unvaccinated) where the population rate is .8 or greater is .02 or less, hence Ho would be rejected using binomials, but with only 26 vaccinated it would not, the probability being .06. But using the normal, z=(26-22.4)/2.1166, = 1.70, and thus Ho would be rejected, the relevant probability being .0446. A concern is to see that correct statistics are being used to save children's lives. This is not the case with the Valadez LQAS method widely supported by USAID.