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Use of the Poisson distribution to estimate the quality of random mixtures was evaluated as a measure of the highest attainable degree of dose uniformity of tablets. Ingredient A was assumed to have a large particle size as compared to diluent B. In contrast to the more precise binomial distribution, for the simple Poisson approach no experiments are necessary to investigate the mean proportions of the apparent volume, av and bv, which A and B assume within the powder samples in the die. The range of volume ratios was defined where the Poisson distribution is valid. Accepting an error of 5% of the random content variation of A per sample, av may amount to up to 0.1 (10%). In terms of the proportion by mass of A, a, this range is wider, and commonly of the order of 0.2 or higher. This approach was tested with tablets prepared from mixtures of coarse sucrose A and a fine Avicel/talc diluent B at A:B (m:m) ratios from 10:90 to 50:50. Even with the 30:70 tablets, the variations of the sucrose content were still in good agreement with the content variations of the random mixtures as estimated from the Poisson distribution. Estimates of the 50:50 ratio, however, deviated from the Poisson distribution.
Earlier reports indicated that sperm from 25% of patients from infertile couples, but not from normal or fertile donors, show deviations from the theoretical Poisson distribution of the number of sperm penetrating zona-free hamster ova. Using semen samples from 15 grandfathers (aged 60 to 84 years) and 24 young fathers (aged 25 to 36 years), this study analyzed whether age also has an effect on the distribution. It was found that the overall fit to the Poisson distribution of the samples from grandfathers was very poor; in contrast, the samples from young fathers fit well. The observed deviations from the Poisson distribution among grandfathers may be a consequence of their long periods of sexual abstinence. Decrease in sexual activity produces age-different populations of sperm that probably differ in penetrating ability. Samples from older fathers also show a worse fit to the Poisson distribution than do those from younger fathers. These results suggest that the duration of sperm storage in the genital tract after maturation has an effect on sperm function.
Vital cells number (VCN) in the sampling of E. coli populations was experimentally measured and distribution histograms were obtained. In most cases distributions show considerable deviation from Poisson model. VCN distribution histograms are polymodal, dispersion/arithmetical mean ratio may essentially differ from 1. The more essential differences from Poisson distribution were observed for populations with the higher cell concentration. Computer simulation of the VCN histograms indicated that additional parameters (such as those describing cellular interaction of different nature and/or other factors that influence random behaviour of cells) should be introduced into Poisson model to explain observed variations in VCN distribution histograms.
A truncated Poisson distribution provides a closer fit to observed caries in a sample of 10- to 11-year-old children than a previously reported chain binomial distribution. Operations research techniques are used in estimating a parameter.
Computer simulations are used to examine the significance levels and powers of several tests which have been employed to compare the means of Poisson distributions. In particular, attention is focused on the behaviour of the tests when the means are small, as is often the case in ecological studies when populations of organisms are sampled using quadrats. Two approaches to testing are considered. The first assumes a log linear model for the Poisson data and leads to tests based on the deviance. The second employs standard analysis of variance tests following data transformations, including the often used logarithmic and square root transformations. For very small means it is found that a deviance-based test has the most favourable characteristics, generally outperforming analysis of variance tests on transformed data; none of the latter appears consistently better than any other. For larger means the standard analysis of variance on untransformed data performs well.
Minature end-plate potentials (MEPP's) were recorded from frog (Rana pipiens) sartorius muscle cells of 60--80 mum diam; MEPP frequency remained constant up to 3 h and was 100 times greater in 80-mum cells than in 6-mum cells. Rapid cooling or heating of preparations initiated or accentuated bursts of MEPP's. Records from cells under control conditions and from cells where the MEPP population had been reduced to the small mode showed many instances of small clusters of MEPP's occurring within 100-ms intervals, indicating quantal release interdependencies. Some small cells initially generated many large MEPP's 2 or more times the average amplitude and fewer small clusters. Analysis of the occurrence of both large- and small-mode MEPP's for both 1.0-s and 100-ms nonoverlapping bins demonstrated a highly significant deviation from a Poisson distribution with significance increasing with decreasing cell diameter and/or MEPP frequency. It is suggested that doublet MEPP's are generated from one release site and that large bursts results from the activity of several release sites, since the size of bursts decreases with cell diameter (junctional area). It is concluded that release characteristics are the same for large-mode (classical) and small-mode MEPP's and that the occurrence of MEPP's is not Poisson.
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Data on the distribution of dicentrics and acentrics observed when human lymphocytes are cultured for 48 h after irradiation by X-rays, gamma-rays, and neutrons are presented. Analysis shows that for dicentrics, the observed distribution for X-rays, gamma-rays, and fission neutrons may be described by Poisson statistics but for higher energy neutrons overdispersion is observed. The phenomenon of overdispersion is also observed for acentrics irrespective of the radiation used. The possibility that overdispersion results from the variations of dose in sensitive sites leads to the conclusion that for dicentrics the site size is considerably larger than the 1--2 micrometer diameter derived by applying the dual action theory to the dose effect relationships. This larger site may well be the cell nucleus.
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The microculture plaque titration of virus shows an important disadvantage : the reduction of the areas observation brings out plaque convergence and prevents from their exact enumeration. Nevertheless, a method, proposed by Moore, enables the estimation of virus title. The influence of the dilution and repetition factors on the title precision has been investigated. Two examples are treated.
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In analyzing standardized mortality ratios (SMRs), it is of interest to calculate a confidence interval for the true SMR. The exact limits of a specific interval can be obtained by means of the Poisson distribution either within an iterative procedure or by one of the tables. The limits can be approximated in using one of various shortcut methods. In this paper, a method is described for calculating the exact limits in a simple and easy way. The method is based on the link between the chi 2 distribution and the Poisson distribution. Only a table of the chi 2 distribution is necessary.
In evaluating factor-VIII activity it should be noted that regarding the remaining activity of deficient plasma a linear reference curve is achieved. In the standard population factor-VIII activity and factor-VIII associated protein are distributed approximately lognormally. Due to this distribution certain results have been gained for the optimal choice of localisation and dispersion measures. It is assumed that the proportions of neutralized factor-VIII activity in plasma are distributed according to Poisson. The applicability of the Poisson distribution was also proved for the free factor-VIII activity portion. Due to the Poisson distribution the antibody unit is clearly defined, thus eliminating a further discussion on the establishment of an arbitrary standardized antibody unit.
We studied urinary beta 2-microglobulin levels in a total of 29 apparently healthy relatives (aged 0.8-70 years) of 8 male patients with asymptomatic low-molecular-weight proteinuria in six families. The frequency of levels above the age- and sex-associated 95% confidence limit was 7 of 29 (24%), 4 of 12 (33%) in first-degree relatives, 2 of 6 (33%) fathers, and 2 of 6 (33%) mothers. These frequencies were significantly above those in the general population (P less than 0.01, by a normal distribution test, a binomial distribution, and Poisson distribution test for the sample proportion). The increased frequency in fathers argues against an X-linked pattern of inheritance for this entity, suggesting that there is heterogeneity in the inheritance.