The term LION is an acronym for Long Ionization Chamber. This is a distributed ion chamber which is used to monitor secondary ionization along the shield walls of a beam line resulting from incorrectly steered charged particle beams in lieu of the use of many discrete ion chambers. A cone of ionizing radiation emanating from a point source as a result of incorrect steering intercepts a portion of 1-5/8 inch Heliax cable (about 100 meters in length) filled with Argon gas at 20 psi and induces a pulsed current which is proportional to the ionizing charge. This signal is transmitted via the cable to an integrator circuit whose output is directed to an electronic comparators, which in turn is used to turn off the accelerated primary beam when preset limits are exceeded. This device is used in the Stanford Linear Accelerator Center (SLAC) Beam Containment System (BCS) to prevent potentially hazardous ionizing radiation resulting from incorrectly steered beams in areas that might be occupied by people. This paper describes the design parameters and experience in use in the Final Focus Test Beam (FFTB) area of the Stanford Linear Accelerator Center.

This paper concerns comparisons of the efficiency of several diagnostic tests, as characterized by the measures of sensitivity (xi), specificity (eta) and predictive value (rho). We show that hypotheses concerning the equality of predictive values relate only to hypotheses concerning xi and eta and that we can test these by approximate chi 2 statistics. Data for the cases of t = 2 or 3 diagnostic tests illustrate the method.

The authors (1968) have previously given tables of the percentage points of the range (= w ) of r samples from a multinomial distribution of r cells each with probability r −1 , r = 2(1)10. This paper presents the small sample power of w for r = 2(1)6 under alternatives H to the null hypothesis H 0 of a symmetric multinomial distribution. The alternatives are of the form H: p i =r −1 + c 1 n 1/2 i = 1, …, r , where the c 's are such that ∑ c i =0, i. e. H consists of a set of multinomial probabilities approaching H 0 of 0(n −1/2 ). Table 1 gives values of the power of the range test, and Table 2 consists of selected comparisons of the power with respect to the X 2 index of dispersion.

This paper discusses statistical methods for situations in which two or more ( k + 1) exposure groups, including a reference one, are compared with respect to rate ratios, or incidence density ratios (IDR) (e.g. MIETTINEN, 1976). Data are assumed available on population times (PT) experienced in the exposure groups. The logit transformation or its generalizations (e.g. Cox, 1970 are utilized in order to obtain suitable tests for the hypotheses involved. Three examples illustrate these methods, including approximate and exact confidence limits for the IDR's ( k = 1). For the case of ( k + 1) groups a linear contrast for the hypothesis of a trend is derived as well as its standard error.

In multiple assays a ‘Standard’ preparation is compared in a single assay with two or more ‘Test’ preparations (Finney, 1978, ch. 11). In addition to the estimation of the relative potency of the ‘Test’ preparations the question arises as to simultaneous confidence limits, or else a joint confidence region for these relative potencies. This paper compares a joint confidence region using a LR statistic with separate limits based on Fieller's theorem. These results are presented in an Example on a multiple assay of two tuberculin preparations A, B compared with a Standard one (data of Wadley, Finney, 1978, Table 11.1).

This note is in continuation of the author's results on ’classical‘ confidence regions for relative potencies in multiple assays (Bennett, 1987). It is shown by the use of a Bonferroni inequality (e.g. Miller, ch. 2, 1980) that approximate confidence regions for the relative potencies { M i } i = 1, …, p may also be obtained directly. A comparison with the classical regions is made for the case: p = 2 using Finney's example (1978, ch. 2).

This paper discusses the analysis of data on proportions in contingency tables. The X 2 ‘index of dispersion test’ (e.g. Fisher, 1954) is developed in these situations and compared with the use of the ‘logit’ transformation. An example using Osborn's (1979) data is given, illustrating the estimation of one or more missing observations.

The problem of estimation of, and statistical tests for, the relative risk (=α) from samples in which there is matching on covariates have been discussed by various authors (Cox, 1970; MANTEL and HAENSZEL, 1959) using the approach of conditional variates. This paper discusses log LR (likelihood ratio) tests of hypotheses concerning α, as based on one or more sets of matched samples. Approximate X 2 tests are also developed for the hypotheses concerning α. An example is presented which illustrates the proposed tests of significance (Table 1).

AbstractA series of papers by FIELLER, PEARSON et al. (1957, 1961, 1962) were concerned with the use of FISHER'S tanh−1 transformation (=z) for SPEARMAN'S ‘rho’ and KENDALL'S ‘tau’ rank correlation coefficients. Under the assumption of bivariate normal samples, empirical results on the means and variances for z were obtained.This paper presents results on the z transformation for small samples under a more general trivariate normal model, and reviews the accuracy of the variance and covariance approximations for z, as well as considerations on the resulting power of the tests using the z‐transformation.

If { U i } i = 1, …, k is a sequence of binary responses of n i subjects at each of k successive dose levels x i , there is the problem of the statistical treatment of the observed proportions P i = U i/ni when neither the probit nor the logit transformation may be assumed. This paper considers the use of the midranks of the responses for point and interval estimation of relative potency in the case of parallel line assay in particular. More generally the problem of combining the results of several independent estimates using ranks is discussed. Several examples illustrate the method.

A reparametrization of the multivariate normal distribution is introduced in order to consider LR tests of significance for the hupothesis of homogeneity of relative errors, or generalized coefficients of variations (c. v.) θ This is in continuation of the author's results (Bennett, 1978) on tests of the equality of univariate c. v. 's from successive experiments based on a normal distribution.

This article is in continuation of a previous one on properties of diagnostic indices (Bennett, 1976). Results are presented on biases in sample estimates of the sensitivity (ξ) and specificity (η) of a diagnostic test T for a disease, as well as their asymptotic variances.The problem of combining estimates of ξ, η from various clinical centres and obtaining appropriate confidence limits is also discussed. A numerical example is also given. (Tables 1a, b). The log‐linear model for ξ, η is also discussed.

The usual definitions of sensitivity, specificity and predictive value of a diagnostic test T refer only to the situation of the presence or absence of disease. There is then question of the appropriate extensions of these definitions in cases where there are more than two diagnostic categories, especially with ordered or graded responses. This paper deals with some aspects of this problem. An example with the data of B ERGESON and S TEINFELD (1974) on gradings of fever in children by palpation is analyzed, using the methods discussed in this paper.

The use of the negative binomial, or the method of inverse sampling (e.g. (1), (2)), is suggested for prospective studies. This method usually has the advantage of fostering an early decision on the statistical significance of some etiological factor in examining successive patient records. Several limiting situations for the distribution are discussed regarding the prevalence of a disease. An example illustrates the method.

The sample matrix [vij] of generalized coefficients of variation, or relative errors, is defined by\(v_{ij} = s_{ij} /\bar x_i \bar x_j \) (i, j=1, …,p) in terms of the sample means\(\bar x_i \) and variances/ covariances sij from a p normal population. In this paper the joint distribution of the v′s is derived, using a result of Tallis (1961) on the moment generating function of the truncated multinormal distribution. This note generalizes the results obtained for the case: p=2 (Bennett, 1977).

SUMMARY For a bivariate normal distribution with variances and covariance given multiples of an unknown σ2, methods are presented for the combination of several separate estimates of the ratio of means, and for assessing confidence limits when an estimate of σ2 is available. A numerical example is presented of the application of this method in combining estimates of relative potency based on several parallel line assays of insulin.

Categorical data on n patients are classified according to the results on an initial clinical test T , and also with respect to a subsequent and definitive diagnosis D. In this paper the sensitivity (=), specificity (=) and predictive values (= v ) are discussed with reference to the tetrachoric correlation model based on the bivariate normal density (e.g. PEARSON, 1901; KENDALL and STUART, 1972, II, p. 317). The result of HAMDAN (1970) concerning the equivalence of the tetrachoric r t and the maximum likelihood estimate of the correlation coefficient is utilized in this paper to obtain a test of significance concerning r t , and also the relation between the tetrachoric function w and the relative risk ψ for the 2X2 table.

This paper reviews the distribution of the sample coefficient of variation (c. v.),\(v = s/\bar x\) as presented here in closed form in terms of the derivatieves of the moment generating function (m.g.f.) of the normal distribution.