The State does not evaluate these situations, apparently due to its reliance on the

normal approximation to the binomial for the purpose of computing a confidence interval for the RAMR.

Normal Approximation to the Beta Posterior Distribution

Table 1 contains the descriptive statistics and results of the Mann-Whitney test and

normal approximations for differences in cranial measurements and cranial capacities between male and female T.

In light of these concerns, it is not surprising that the

normal approximation exhibits a slow convergence as a function of sample size.

Chatterjee [7] provides a rate of

normal approximation for the statistic [[??].sub.k] ([X.sub.1], ..., [X.sub.n]).

A hexagonal field of variation was calculated by means of

normal approximation including arithmetic means, standard deviations, and upper or lower confidence limits ([C.sub.U or L] = mean [+ or -] standard deviation x [t.sub.df:[alpha]/2]).

To assess the overall parameter variability of econometric models, a simple mean may be calculated: V = [sigma][V.sub.i]/L where [V.sub.i] is the

normal approximation to the reported F-test from the ith study, and a measure of the parameter variability on a common scale.

We can compute the

normal approximation of this binomial probability by solving for E(r) and [[sigma].sub.r] and using them to find the approximate normal area.

Therefore more than one third had values of the denominator that were too small for the

normal approximation to be adequate.

The mean number of species per 1-[m.sup.2] quadrat was significantly greater at the Givens site than the Domermouth site (Table 1; Wilcoxon Rank Sum Test,

normal approximation, z = 5.51, P [less than] 0.0001, n = 21 quadrats per site), as was the mean height of both the tall rescue (Table 1; t = 2.217, df = 40, P = 0.03) and horsenettle stems (Table 1; t = 12.01, df = 94, P [less than] 0.0001; analysis performed on log transformed variables).

In the StORQS I report, this information was presented as a 95 percent confidence interval (C.I.) for p using the

normal approximation to the binomial distribution (cf.