Binomial Confidence Limits Research Articles

Binomial confidence limits adjusted for a confounding variable

A simple transformation of classical binomial confidence limits provides exact confidence limits in situations where a confounding variable is present. An example is the multiple-choice test, where a correct answer may represent either knowledge or guesswork, the latter being the confounding variable.

Statistical Tables for the Design of Clinical Trials.

Basic design considerations The normal distribution Comparing two binomial proportions Testing equivalence of two binomial proportions Confidence limits for a binomial proportion Post-marketing surveillance Comparing two means Significance of the correlation coefficient Comparing two survival curves (Logrank comparisons) Comparing two survival curves (exponential survival) Phase II trials (Gehan's method) Phase II trials (Fleming's single stage procedure) Randomization Bibliography of other statistical tables and texts.

Approximate binomial confidence limits

SUMMARY A quick procedure of good accuracy is proposed for obtaining approximate binomial confidence limits. Numerical investigations are made to compare the accuracy of the new method with those of other procedures.

Radiation-Sterilization of Food: Treating Scanty Data from Inoculated Packs

This paper is about the mathematical methods used in calculating the 12D radiation-dose for a food which has been subjected to an inoculated pack. It concerns the case in which only one partial-spoilage data point is obtained from the experiment. A simple, partly graphical procedure is described. This method is based on binomial confidence limits and furnishes an estimate that lies above the (unknown) true 12D value with probability greater than 90%. The method is applied to an inoculated pack for low-level nitrite/nitrate ham described by Anellis et al. (2).

Microbiological Safety of Radappertized Beef

To assure microbiological safety and stability of irradiated meats, inoculated pack studies are performed with each meat. These studies are designed to provide partial spoilage data for computation of that dose required to reduce the number of viable spores of a single most resistant strain of Clostridium botulinum by 12 log cycles. A beef inoculated pack had only one significant partial spoilage “point” at 22 kGy. Therefore, the binomial confidence limit method was used to compute a 12D dose of 41.2 kGy. This 12D dose, together with a prveious thermal treatment of inactivate autolytic enzymes, provides a wide margin of microbiological safety and stability to packaged meats stored without refrigeration.

Finite Population Correction for Binomial Confidence Limits

Abstract This article examines the accuracy of the finite population correlation ordinarily applied to binomial confidence limits, suggests a more accurate FPC and describes a procedure, based on a computer program for hypergeometric probabilities, for obtaining exact confidence limits and exact confidence level.

Finite Population Correction for Binomial Confidence Limits

Abstract This article examines the accuracy of the finite population correlation ordinarily applied to binomial confidence limits, suggests a more accurate FPC and describes a procedure, based on a computer program for hypergeometric probabilities, for obtaining exact confidence limits and exact confidence level.

Close approximations of binomial confidence limits at 10 confidence levels

Approximate binomial confidence limits with relative accuracy of at least .999 may be obtained at 10 confidence levels for sample sizes of 20 or more and sample proportions to .5, using simple formulas that employ Poisson confidence limits and a table of correction terms.

Editor's Correction to Approximating the Lower Binomial Confidence Limit

Editor's Correction to Approximating the Lower Binomial Confidence Limit

Editor's Correction to Approximating the Lower Binomial Confidence Limit

Editor's Correction to Approximating the Lower Binomial Confidence Limit

Approximating the Lower Binomial Confidence Limit

Abstract An earlier article [1] presented two formulas for approximating the upper binomial confidence limit from a sample of size n with c “defectives” drawn randomly from an infinite population with probability p of a defective. The present article presents two complementary formulas for approximating the lower binomial confidence limit p, based on m, the lower confidence limit for the paramater m of a Poisson distribution. These approximations are easy to calculate and have precisely specified bounds on their error over stated ranges of n and c/n. The error of the simpler formula is guaranteed to be within .1% of the exact binomial confidence limit when n ≥ 16 and c/n ≤ 1/8. The relative error of the second formula is not more than .1% when n ≥ 16 and . Values of m for small values of c are readily available from tables of the Poisson and chi-square distributions. For c ≥ 50, a simple formula permits approximating m with no more than .069% relative error. A procedure is given for approximating p when , which produces relative accuracy of at least .999 except possibly when p falls below ; then the guaranteed relative accuracy is at least .998. (Approximation of the upper confidence limit when , with relative accuracy of at least .999, is also discussed.)

Approximating the Upper Binomial Confidence Limit

Abstract When a sample of size n with c “defectives” is drawn randomly from an infinite population with probability p of a defective, the upper binomial confidence limit can be approximated by two formulas based on , the upper confidence limit for the parameter m of a Poisson distribution. The approximations are easy to calculate and have precisely specified bounds on their error over a stated range of n and c/n. The error of the simpler formula is guaranteed to be within .1% (with trivial deviations) of the exact binomial confidence limit when n≥ 40 and c/n ≤ 1/10. The relative error of the second formula is not more than .1% (with no deviations) when n ≥ 20 and . Values of for small values of c are readily available from tables of the Poisson and chisquare distributions. For c ≥ 50, a simple formula permits approximating with no more than .045% relative error.

Approximating the Upper Binomial Confidence Limit

Abstract When a sample of size n with c “defectives” is drawn randomly from an infinite population with probability p of a defective, the upper binomial confidence limit can be approximated by two formulas based on , the upper confidence limit for the parameter m of a Poisson distribution. The approximations are easy to calculate and have precisely specified bounds on their error over a stated range of n and c/n. The error of the simpler formula is guaranteed to be within .1% (with trivial deviations) of the exact binomial confidence limit when n≥ 40 and c/n ≤ 1/10. The relative error of the second formula is not more than .1% (with no deviations) when n ≥ 20 and . Values of for small values of c are readily available from tables of the Poisson and chisquare distributions. For c ≥ 50, a simple formula permits approximating with no more than .045% relative error.

Muscular Fatigue and Mortality in Troll-Caught Chinook Salmon (Oncorhynchus tshawytscha)

Blood samples were analyzed for lactic acid from 66 troll caught chinook salmon after from zero to 103/4 hours of rest. Fish were held in a live box aboard a trolling vessel. During the course of the experiment 22 individuals died. Analysis of these data indicate a general response of blood lactic acid comparable with results of other experiments. The typical response is a gradual increase of blood lactic acid to high levels in the third and fourth hours, followed by a general decline. Death is strongly associated with high blood lactic acid. The level of lactic acid response is not significantly increased with more than 10 minutes of vigorous exercise nor is it significantly affected by the size of the fish within the ranges sampled in this experiment. Mortality rate is estimated at 71% with 95 percent binomial confidence limits of 40% and 86%.

STATISTICAL METHODS IN MEDICAL RESEARCH: I. QUALITATIVE STATISTICS (ENUMERATION DATA)

This article is designed to help investigators in applying to qualitatively classified clinical and laboratory data the appropriate statistical treatment—tests of significance in binomial and multinomial distributions, estimation of confidence limits, analysis of contingency tables, and estimation of sample sizes required for further investigation. Section A is a brief introduction (definitions and principles). Section B comprises 40 examples classified so that the investigator can choose data and problems comparable to his own. Questions that arise in the examples, regarding experimental design (especially random sampling) and the interpretation of the tests, are discussed in Section C (Notes).Because the standard deviation of the binomial and the chi square contingency test are often used without appreciation of the risk entailed, tables, which can be used also in nonmedical investigation, are presented: binomial confidence limits (with graphs) and exact probabilities for small-sample fourfold contingency tables. For samples not covered by the tables, precautions and rules regarding the use of chi square have been derived from more than five hundred comparisons between chi square and the exact method. To help in the exact computation of probabilities where that is necessary, four-decimal logarithms of factorials of numbers up to 1000 are given.