Showing papers on "Confidence interval published in 1978"
TL;DR: In this paper, three methods of obtaining confidence intervals for the risk ratio offailure in two independent binomial samples are compared, and it is concluded that Method A is reasonable but conservative, Method B is erratic and should not be used, aszd Method C is reasonable and less conservative than Method A.
Abstract: Three methods of obtaining confidence intervals for the risk ratio offailure in two independent binomial samples are compared. The three are (A) the method of Thomas and Gart (1977), (B) an adaptation of the method of Fieller using the normal distribution, and (C) a proposed method using a logarithmic transformation. On the basis of extensive simulations we have concluded that Method A is reasonable but conservative, Method B is erratic and should not be used, aszd Method C is reasonable and less conservative than Method A. Method C, cotnputationally the simplest, is recommended.
378 citations
TL;DR: In this paper, a procedure that reduces the effect of population skewness on the distribution of the t variable so that tests about the mean can be more correctly computed is proposed.
Abstract: This article considers a procedure that reduces the effect of population skewness on the distribution of the t variable so that tests about the mean can be more correctly computed. A modification of the t variable is obtained that is useful for distributions with skewness as severe as that of the exponential distribution. The procedure is generalized and applied to the jackknife t variable for a class of statistics with moments similar to those of the sample mean. Tests of the correlation coefficient obtained using this procedure are compared empirically with corresponding tests determined using Fisher's z transformation and the usual jackknife estimate.
367 citations
TL;DR: Cutler and Ederer illustrated how the life table approach could provide considerably more information on 5-yr survival than would be available from only those subjects followed for at least 5 yr.
290 citations
TL;DR: In this paper, a method for obtaining confidence intervals following sequential tests is described, where an order relation is defined among the points on the stopping boundary of the test and confidence limits are determined by finding those values of the unknown parameter for which the probabilities of more extreme deviations in the order relation than the one observed have prescribed values.
Abstract: SUMMARY A method is given for obtaining confidence intervals following sequential tests. It involves defining an order relation among points on the stopping boundary and computing the probability of a deviation more extreme in this order relation than the observed one. Particular attention is given to the case of a normal mean with known or unknown variance. A comparison with the customary fixed sample size interval based on the same data is given. The purpose of this paper is to describe a method for obtaining confidence intervals following sequential tests. An order relation is defined among the points on the stopping boundary of the test. The confidence limits are determined by finding those values of the unknown parameter for which the probabilities of more extreme deviations in the order relation than the one observed have prescribed values. To facilitate understanding the proposed procedures, most of the paper is restricted to estimating the mean of a normal population with known variance following the class of sequential tests recommended by Armitage (1975) for clinical trials. The case of unknown variance is discussed briefly in ? 4. It is easy to see that the proposed method is valid more generally, although the probability calculations required to implement it depend on the specific parent distribution and stopping rule. A closely related method was proposed by Armitage (1958), who studied the case of binomial data numerically by enumeration of sample paths. Let xl, x2, ... be independent and normally distributed with unknown mean ,u and known variance cr2. Let sn =x1 + .. . + xn, and for given b > 0 consider the stopping rule
151 citations
TL;DR: In this paper, an approximate confidence interval for the parameter is presented as a function of the three mean squares of the analysis of variance table summarizing the results: between subjects, between raters, and error.
Abstract: When the raters participating in a reliability study are a random sample from a larger population of raters, inferences about the intraclass correlation coefficient must be based on the three mean squares from the analysis of variance table summarizing the results: between subjects, between raters, and error. An approximate confidence interval for the parameter is presented as a function of these three mean squares.
144 citations
TL;DR: In this article, the accuracy of the large sample standard error of weighted kappa appropriate to the non-null case was studied by computer simulation, and it was shown that only moderate sample sizes are required to test the hypothesis that two independently derived estimates of the same value are equal.
Abstract: The accuracy of the large sample standard error of weighted kappa appropriate to the non-null case was studied by computer simulation. Results indi cate that only moderate sample sizes are required to test the hypothesis that two independently de rived estimates of weighted kappa are equal. How ever, in most instances the minimal sample sizes re quired for setting confidence limits around a single value of weighted kappa are inordinately large. An alternative, but as yet untested procedure for set ting confidence limits, is suggested as being poten tially more accurate.
136 citations
TL;DR: In this article, a method for determining the sample size required for a specified precision simultaneous confidence statement about the parameters of a multinomial population is described, based on a simultaneous confidence interval procedure due to Goodman.
Abstract: A method is described for determining the sample size required for a specified precision simultaneous confidence statement about the parameters of a multinomial population. The method is based on a simultaneous confidence interval procedure due to Goodman, and the results are compared with those obtained by separately considering each cell of the multinomial population as a binomial.
107 citations
TL;DR: In this paper, the authors present a review of methods of constructing confidence intervals for parameters or other characteristics of the Weibull or extreme value distribution, with emphasis on the flexibility of the method and on the computations which are necessary to use it.
Abstract: This paper reviews methods of constructing confidence intervals for parameters or other characteristics of the Weibull or extreme value distribution. The conditional method of obtaining confidence intervals is stressed, with emphasis on the flexibility of the method, and on the computations which are necessary to use it.
97 citations
TL;DR: The authors discusses properties of several statistical parameters that are useful in judging the quality of least squares fits of experimental data and in interpreting least-squares results, including the standard error of estimate, the standard deviations of slopes and intercepts, the correlation coefficient, and the degree of correlation between the least squares slope and intercept.
Abstract: This paper discusses properties of several statistical parameters that are useful in judging the quality of least-squares fits of experimental data and in interpreting least-squares results. The presentation includes simplified equations that emphasize similarities and dissimilarities among the standard error of estimate, the standard deviations of slopes and intercepts, the correlation coefficient, and the degree of correlation between the least-squares slope and intercept. The equations are used to illustrate dependencies of these parameters upon experimentally controlled variables such as the number of data points and the range and average value of the independent variable. Results are interpreted in terms of which parameters are most useful for different kinds of applications. The paper also includes a discussion of joint confidence intervals that should be used when slopes and intercepts are highly correlated and presents equations that can be used to judge the degree of correlation between these coefficients and to compute the elliptical joint confidence intervals. The parabolic confidence intervals for calibration cures are also discussed briefly.
77 citations
TL;DR: Monte Carlo experiments have been used to test the robustness of distribution-free confidence limits for the parameters of the Michaelis-Menten equation and when used in conjunction with the modified form of the direct linear plot they prove to be more robust than least-squares confidence limits.
72 citations
TL;DR: Tolerance limits and confidence limits on reliability are proposed for the two-parameter exponential distribution in this paper, with the advantage that solutions to both the tolerance limit problem and the confidence limit problem can be written explicitly.
Abstract: Tolerance limits and confidence limits on reliability, which closely approximate exact limits. are proposed for the two-parameter exponential distribution. These approximations have the advantage that solutions to both the tolerance limit problem and the confidence limit problem can be written explicitly.
TL;DR: A method for obtaining approximate confidence limits around the exposure-specific rates is presented and the equivalence of odds ratio to rate ratio requires no "rare disease assumption;" this permits estimation of exposure- specific illness rates when the overall rate is known.
Abstract: The methods used for selecting subjects yield three types of case-control studies: 1) incident cases are compared to non-cases chosen to be representative of the exposure distribution among the person-years which produced the cases. In this type of study the exposure-odds ratio equals the incidence density ratio; 2) incident cases are compared to residual non-cases at the end of the risk period (exposure-odds ratio = cumulative incidence-odds ratio); 3) prevalent cases are compared to non-cases (exposure-odds ratio = prevalence odds ratio). In study type 1 the equivalence of odds ratio to rate ratio requires no "rare disease assumption;" this permits estimation of exposure-specific illness rates when the overall rate is known. In study types 2 and 3 the exposure-odds ratio equals the corresponding rate ratios only when exposure-specific rates are low. Nonetheless, exposure-specific rates can be calculated without making any rare disease assumption using Bayes' theorem and information on the overall disease rate. A method for obtaining approximate confidence limits around the exposure-specific rates is presented.
TL;DR: A table to determine symmetrical confidence intervals for bioequivalence trials, according to Westlake’s method is presented allowing instant knowledge of the necessary constants and avoiding the usual trial and error method.
Abstract: A table to determine symmetrical confidence intervals for bioequivalence trials, according to Westlake’s method is presented allowing instant knowledge of the necessary constants and avoiding the usual trial and error method.
TL;DR: Results of computing coherence estimate confidence bounds for stationary Gaussian signals are presented and new computationally difficult examples are given for 80 and 95 percent confidence with independent averages.
Abstract: In many applications, two received signals are digitally processed to estimate coherence. Results of computing coherence estimate confidence bounds for stationary Gaussian signals are presented. New computationally difficult examples are given for 80 and 95 percent confidence with independent averages of 8, 16, 32, 64, and 128.
TL;DR: In this article, a method for the construction of exact confidence intervals on nonnegative linear combinations of variance components from nested classification models is proposed, and the robustness of these confidence intervals to model breakdown is discussed.
Abstract: Methodology is proposed for the construction of exact confidence intervals on nonnegative linear combinations of variance components from nested classification models. Examples are given for the one-fold and two-fold classifications. The robustness of these confidence intervals to model breakdown is also discussed.
TL;DR: In this article, a simple naive estimator of the failure rate function is proposed, which is asymptotically unbiased but not consistent, and can be smoothed by using any band limited window.
Abstract: : In this paper we propose a simple naive estimator of the failure rate function This estimate is asymptotically unbiased but not consistent It can be smoothed by using any band limited window We show that this smoothed estimate is equivalent to estimates obtainable from the modified sample hazard function, as in Rice and Rosenblatt (1976) We obtain the asymptotic distribution of the global deviation of the smoothed estimate from the failure rate function, which can then be used to construct uniform confidence bands We illustrate the rate of convergence of our estimator by a Monte-Carlo simulation
TL;DR: In this paper, a method for setting a distribution-free lower confidence limit for the mean of a nonnegative random variable is developed, and compared with the procedure which relies on asymptotic normality of the distribution of the sample mean.
Abstract: SUMMARY A method for setting a distribution-free lower confidence limit for the mean of a nonnegative random variable is developed, and compared with the procedure which relies on asymptotic normality of the distribution of the sample mean. Some key word8: Distribution-free confidence limit; Nonparametric; Robustness.
TL;DR: In this paper, the problem of estimating the parameter of an exponential distribution is described and techniques for constructing the estimates of this parameter and their confidence intervals under conditions of poor statistics are given.
TL;DR: In this article, a set of recurrences is developed for computing the probability content of any prior or posterior confidence bands for a distribution function assuming the parameter of the prior Dirichlet process known.
Abstract: A set of recurrences is developed for computing the probability content of any prior or posterior confidence bands for a distribution function assuming the parameter of the prior Dirichlet process known. When the prior parameter is unknown and is estimated from the sample, nonparametric estimates of the probability content of the posterior bands are obtained.
01 Jul 1978
TL;DR: A processing technique for computing arbitrary confidence bounds for stationary Gaussian signals is presented and new computationally difficult examples are given for 80 to 95% confidence with independent averages.
Abstract: In underwater acoustics where signals are digitally processed at the outputs of two or more receiving sensors, it is desirable to estimate the coherence spectrum, both for detection and position estimation. A processing technique for computing arbitrary confidence bounds for stationary Gaussian signals is presented. New computationally difficult examples are given for 80 to 95% confidence with independent averages of 8, 16, 32, 64 and 128. A discussion of the computational difficulties together with algorithmic details are presented.
TL;DR: In this article, the authors deal with the problem of constructing a confidence band over the real line for a polynomial regression curve of known degree, which involves successive and correlated measurements, say, in time, on the same objects.
Abstract: This paper deals with the problem of constructing a confidence band over the real line for a polynomial regression curve of known degree. The situation involves successive, and therefore in general, correlated measurements, say, in time, on the same objects. Two methods for constructing these bands are developed when the measurements are assumed to be multivariate normal. They are then compared to determine when one provides narrower bandwidths than the other. The confidence level I – α is, in general, a lower bound.
TL;DR: In this paper, an extended T-type procedure for one-way layouts with only two different sample sizes is presented. But it is strictly shorter for some of them than the original T procedure.
Abstract: Some improvements and clarifications of extended T-type procedures of multiple comparisons for unbalanced designs are given. In view of the general discussion, we obtain a procedure particularly tailored for one-way layouts with only two different sample sizes. In all such designs, the given procedure yields confidence intervals which are not longer than those obtained by Spjotvoll and Stoline's (1973) method for all pairwise comparisons and are strictly shorter for some of them. For moderately unbalanced designs, the new procedure is also superior to Hochberg's GT2 method using the average confidence interval length for all pairwise contrasts as criterion.
TL;DR: In this paper, a general approach for converting a certain class of nonparametric tests into confidence intervals for suitably defined parameters is discussed, which comprises but is not limited to lineair rank tests for the one-sample, two-sample and linear regression problems.
Abstract: Summary A general approach for converting a certain class of nonparametric tests into confidence intervals for suitably defined parameters is discussed. The class of tests comprises but is not limited to lineair rank tests for the one-sample, two-sample, and linear regression problems.
TL;DR: Mean time interval (with 95 per cent confidence limits) for the ECGs of 32 2-tooth Romney rams were: P wave duration, 0.054s (0.044s--0.065s) and PR interval,0.110s ( 0.081s)--0.139s.
TL;DR: The authors used the likelihood ratio test of the complete model including both zero and positive observations and an approximate confidence interval for the ratio of mean values over all seeded and non-seeded experimental units.
Abstract: A recurring problem in single-area randomized seeding experiments has been the assessment of statistical significance over all experimental units, such as days, when some of the units receive no precipitation. The present paper solves the problem in two ways: 1) the likelihood ratio test of the complete model including both zero and positive observations and 2) an approximate confidence interval for the ratio of mean values over all seeded and non-seeded experimental units. The results are obtained for both log-normal and gamma distributions. They are illustrated by numerical examples from the 1972–74 National Hail Research Experiment randomized seeding experiment.
TL;DR: In this article, confidence regions are based on a two-sided generalisation of this inequality and the results are illustrated by estimating the parameters of some elementary random models, such as balanced randoiu models.
Abstract: Earlier investigations used a one-sided inequality to consltuct confidence regions for the variance ratios or balanced randoiu models. In this study, confidence regions are based on a two-sided generalisation of this inequality and the results are illustrated by estimating the parameters of some elementary random models.
TL;DR: In this paper, the authors devised transformations to accelerate convergence to normality for maximum likelihood estimators of the reliability of complex systems, and used them to improve confidence intervals in cases where other methods were not appropriate.
Abstract: Transformations are devised to accelerate convergence to normality for maximum likelihood estimators of the reliability of complex systems. Improved confidence intervals follow from probability statements concerning the transformed estimator. Comparisons are made with intervals given by exact procedures and also by generating test results from a system of given reliability, enabling the confidence property of intervals obtained using the transformation to be assessed. Results using other methods, including the log odds transformation for binomial subsystem test data, are also given. The generality of the approach is illustrated by using the transformations to improve confidence intervals in cases where other methods are not appropriate.
TL;DR: As the point of intersection in linear-branch titration curves results from two optimized linear regressions, the value of the equivalence volume V(e) has the character of an estimated average V (e) hence a confidence interval is associated with it.
TL;DR: In this article, a method to obtain confidence intervals from nonlinear regression and demonstrates the use of a BASIC program employing this algorithm for computing confidence intervals for any nonlinear function regardless of the regression method.
Abstract: In psychological experiments linearity is desirable and usually realized. Some models, however, cannot avoid the nonlinearity of the underlying processes, or, for descriptive models, the obvious coordinate systems (log-log, semilog, probit, etc.) which leave the data nonlinear have been tried and failed. In any case, nonlinear regression becomes appropriate. Recent examples of parameters that appear in intrinsically nonlinear equations are arousal constants (Killeen, 1975), expectancy thresholds (Gibbon, 1977), transfer parameters (Davis & Levine, 1977), intellectual growth parameters (Zajonc & Markos, 1975), generalization factors (Blough, 1975), coupling constants (Staddon, 1977), cost parameters (Staddon, in press), consolidation parameters (Wickelgren, 1976), salience parameters (Rescorla & Wagner, 1972), and search constants (Norman & Rumelhart, 1970). Unless a large amount of data variance is accounted for or confidence intervals are established, the relationships or critical differences between parameters cannot be assessed. This paper briefly outlines a method to obtain confidence intervals from nonlinear regression and demonstrates the use of a BASIC program employing this algorithm for computing confidence intervals for any nonlinear function regardless of the regression method. Confidence Intervals for Nonlinear Regression. Suppose observations from an experiment arise as (y. ,td, (Y2,t2)·.· (Yn,tn). The standard regression model is of the form