A method of paired comparison is adapted for use in estimating economic measures of value. The method elicits multiple binary choices for paired items in a choice set. Probability distributions and economic values are estimated nonparametrically and parametri-cally. The method is applied in an experimental context with a choice set composed of four private goods and several sums of money. The sample's median value estimates for the goods are generally not different than the market prices for these goods. People who are in the market for a good value it higher than those not in the market for the good.

When Siegrist (1989) derived an expression for the probability that player A wins a game that consists of a sequence of Bernoulli trials, the winner being the first player to win n trials and have a lead of at least k, he noted the desirability of giving a direct probabilistic argument. Here we present such an argument, and extend the domain of applicability of the results beyond Bernoulli trials, including cases (such as the tie-break in lawn tennis) where the probability of winning each trial cannot reasonably be taken as constant, and to where there is Markov dependence between successive trials.

Pearl millet, Pennisetum americanum L. occupies a large proportion of the area growing millets in Africa. Consequently the insect pests that attack this species have received attention over other millets. A list of the major species is presented. Actual data on losses due to insect pests on pearl millet are not readily available. Crop loss assessment methods using incidence and damage ratios are discussed. Quantitative losses determined from insecticide trials at research station are also presented.

Consider the number Xm of comparisons made in a sequence of comparisons between two opponents, which terminates as soon as one opponent wins m comparisons. The convergence of Xm to the normal variable is completely characterized. The normal approximations to the probability function and to the distribution function of Xm are obtained for any sufficiently large m, together with estimates of the errors in these approximations. Similar results are obtained for the negative binomial distribution as well. Finally, some simple estimates of the mean, variance and the incomplete beta function with equal arguments are constructed.

The co-twin control model using paired-comparison analysis provides an extremely powerful and cost-effective experimental design for clinical research. This paper suggests the possibility of using sequential analysis to further increase the efficiency and specificity of cotwin control studies.

A discrete random variable describing the number of comparisons made in a sequence of comparisons between two opponents which terminates as soon as one opponent wins m comparisons is studied. By equating two different expressions for the mean of the variable, a closed form for the incomplete beta function with equal arguments is obtained. This expression is used in deriving asymptotic (m-large) expressions for the mean and variance. The standardized variate is shown to converge to the Gaussian distribution as m→ ∞. A result corresponding to the DeMoivre-Laplace limit theorem is proved. Finally applications are made to the genetic code problem, to Banach's Match Box Problem, and to the World Series of baseball.