[Normal distribution, zeta punctuation and percentiles].
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Bronchoalveolar lavage (BAL) is used to obtain inflammatory cells from the lung. For clinical research, parametric statistics are frequently used to compare cells present in BAL of patients with lung disease with cells present in BAL of normal subjects. To determine if these populations can be compared in this manner we performed BAL on 111 never-smoking, normal volunteers and determined: (1) the mean, median, standard deviation, and range of the cells in BAL; (2) whether the data are normally distributed and satisfy the criteria for use of parametric statistical analysis. The BAL cellularity was expressed as a percentage of total cells, cells per milliliter return, and total cells per lavage. Regardless of the means of expression, no measure of BAL cellularity (total cells, macrophages, lymphocytes, neutrophils, or eosinophils) conformed to the normal (bell-shaped) distribution when tested for goodness of fit with the G statistic (all p < 0.001). The lack of fit to the normal distribution was not substantially altered by either the method of expressing the data (i.e., cells per milliliter, total cells, or percent of cells) or log transformation of the data. The poor fit in all cases resulted from clumping of the data about the mean and large tails. The percent of cells were, therefore, tested for goodness of fit to the Poisson distribution, a distribution of discrete variables. The neutrophil and eosinophil percentages resulted in an excellent fit to the Poisson distribution, but macrophage and lymphocyte percentages did not.(ABSTRACT TRUNCATED AT 250 WORDS)
Many statistical textbooks lend themselves readily to the analysis of physical and chemical data. This is due to the material gathered from such analyses, following, in most cases, normal distribution. Normally distributed data can be examined over time to allow the obtained profile to be studied for variation. Microbiological data rarely follows such distribution. However, such approaches can be adapted for non-normally distributed (or skewed) microbiological data. This paper applies Shewhart Control Charts to the trend analysis of microbiological data from two different pharmaceutical water systems.
The aim of this study was to describe the normal distribution of the water content in several regions of the rat brain and furthermore to determine if global ischemia results in a variable increase in water content in these regions. Water content was determined in 40 regions; in 8 unaffected brains by gravimetry and in 9 unaffected brains by estimation of the wet/dry weight ratio. In addition, 6 rats underwent 6 h of moderate global brain ischemia in order to evaluate the sensitivity of the investigated brain areas to develop a cytotoxic brain edema. The impermeability of the blood-brain barrier to proteins was evaluated by staining with Evans blue. Physiological differences in water content between the several brain regions ranged from 72.57 +/- 0.77% (mean +/- S.D.) in the medulla oblongata to 84.83 +/- 0.52% in the hypothalamus. Generally, the water content of the grey matter was higher than that of the white matter and increased from the frontal to the occipital and from the parietal to the basal cortex. Even adjacent cortical regions showed differences in the amount of brain water of up to 3.41%. In the ischemic animals, the impermeability of the blood-brain barrier to proteins was not compromised, but an increase in the amount of brain water was found in the frontoparietal cortex of 1.17 +/- 0.37% and hippocampus of 1.49 +/- 0.39% (P < 0.05). This ischemic increase in the brain water content was small in comparison to the normal variance in regional brain water content. Similar results were obtained by determining the wet/dry weight ratio and by gravimetry. Gravimetry led to more consistent results. In conclusion, the study shows great differences in normal water content between the several brain areas in comparison to an only slight increase of water content due to the development of cytotoxic brain edema. The determination of an early state of an increased brain water content requires an adequate and differentiated measurement of different brain areas. The gravimetry fulfills this demand.
The normal distribution of Tc-99m sulfur colloid is described in 100 patients with no clinical or radiographic evidence of hip disorders. Two-thirds of the patients had uptake in the femoral neck and some uptake in the femoral head. In the other one-third, no uptake was detected in either femoral head. A high degree of symmetry was noted. Judging both the symmetry and pattern of uptake in both hips is important in evaluating femoral head vasculature after a fracture.
In adaptive radiotherapy, measured patient-specific setup variations are used to modify the patient setup and treatment plan, potentially many times during the treatment course. To estimate the setup adjustments and re-plan the treatment, the measured data are usually processed using Kalman filtering or by computing running averages. We propose, as an alternative, the use of Bayesian statistical methods, which combine a population (prior) distribution of systematic and random setup errors with the measurements to determine a patient-specific (posterior) probability distribution. The posterior distribution can either be used directly in the re-planning of the treatment or in the generation of statistics needed for adjustments. Based on the assumption that day-to-day setup variations are independent and identically distributed Normal distributions, we can efficiently compute parameters of the posterior distribution from parameters of the prior distribution and statistics of the measurements. We illustrate a simple procedure to apply the method in practice to adaptive radiotherapy, allowing for multiple adjustments of treatment parameters during the course of treatment.
The structure of CN(4)H(7)ZrF(5) reported by Bukvetskii et al. [Koord. Khim. (1992). 18, 576-579] has been independently redetermined on the basis of measurements on three different crystals. Assuming all four resulting structures are drawn from a normal distribution, normal probability analysis of the atomic coordinates taken in pairs reveals joint standard uncertainties that are underestimated by factors as large as 16.5 for the x(Zr) coordinate. Unit-cell parameters in the four crystals similarly have joint uncertainties, under the same assumption, that are underestimated by factors as large as 83.0 for the b axis. The variations in axial lengths from crystal to crystal and the declines in standard reflection intensities by 13-15% in at least two of the crystals measured are consistent with the inference that the distribution is not normal. Rather, the differences observed may be assumed to be caused by small but highly significant radiation-induced structural changes. The large underestimations hence reflect physical differences among the four irradiated crystals. The determinations show that the CN(4)H(7)(+1) cation is exactly planar except for the two H atoms bonded to the terminal N atom; the plane of this NH(2) group is normal to that of the cation. The average length of the three independent C-N bonds is 1.318 (11) A; the N-N bond length is 1.397 (3) A. Distorted ZrF(7) pentagonal bipyramids share edges, forming chains linked by N-H...F bonds to the CN(4)H(7)(+1) ions.
Twenty-four listeners received 20 dichotic listening runs of 30 pairs of natural CV nonsense syllables per run. Left- and eight-ear responses are represented by two partially overlapping normal distributions with equal variance. Observed ear advantages across listening runs are also distributed normally. The means of the distribution of ear advantage are listener specific, but the standard deviations are 10.8% +/- 2.5. The origin of reversals in direction of ear advantage among listening runs is statistical--a small mean/sigma ratio--and approximately six listening runs (180 listening trials) are required to achieve a split-half reliability coefficient of + 0.90.
To clarify the hemodynamic state of an apparently small heart; i.e., a small cardiac silhouette on chest radiography, chest radiographic and echocardiographic studies, physical fitness tests (a battery of tests consisting of vertical jump, side step, floor push-up, and modified Harvard step test) and graded uninterrupted bicycle exercise test were performed. 1. The cardiothoracic ratio (CTR) in 3,461 newly-enrolled university students (18.7 +/- 1.2 years old: mean +/- SD) distributed normally and the mean value +/- SD was 40.2 +/- 3.6%. No difference was observed between male and female students. 2. A small heart was defined as one having a cardiothoracic ratio (CTR) less than or equal to 35% which comprised the lower 10% of the normal distribution. There was no significant difference in results of physical fitness tests between students with small heart (n = 134) and normal controls (n = 136, 45% less than or equal to CTR less than or equal to 50%). 3. A maximal bicycle exercise test was performed in 14 male students with small heart (S: CTR = 31.9 +/- 2.1%) and nine normal controls (C: CTR = 46.5 +/- 1.0%). a) Body weight (S: 57 +/- 7, C: 69 +/- 8 kg, p less than 0.001) were less in students with small heart; Body height was similar in both categories (S: 171 +/- 5, C: 175 +/- 7 cm, NS). b) All controls finished 200 W workload, whereas all students with small heart ceased exercise earlier than the control subjects (three at 125 W, three at 150 W, eight at 175 W). c) Resting heart rate was higher in cases with small heart (S: 92 +/- 14, C: 77 +/- 10 beats/min, p less than 0.02). Left ventricular end-diastolic dimension was smaller in small heart (S: 39 +/- 4, C: 48 +/- 4 mm, p less than 0.001). d) During exercise, blood pressure and oxygen intake at the same workload were similar in both groups, but peak oxygen uptake was higher in the controls (S: 43 +/- 5, C: 50 +/- 7 ml/kg/ml, p less than 0.05). Heart rate and blood lactate concentration were higher throughout exercise in students with small heart (lactate at 175 W; S: 12.7 +/- 1.6, C: 7.8 +/- 2.0 mmol/L, p less than 0.001) (heart rate at 175 W; S: 194 +/- 6, C: 173 +/- 21 beats/min, p less than 0.05). We concluded that hemodynamic conditions at rest and during low grade exercise are preserved in students with small heart.(ABSTRACT TRUNCATED AT 400 WORDS)
OBJECTIVE: The purpose of this study was to establish data for normative distributions for pudendal and perineal nerve compound muscle action potential data in healthy women across a wide age range and varied history of vaginal deliveries. STUDY DESIGN: We studied 42 continent women, aged 20 to 67 years, including 29% nulliparous women with a disposable St. Mark's electrode to stimulate the pudendal nerve at the ischial spine by a transvaginal approach. The pudendal terminal motor latency and amplitude were detected with the use of surface patch electrodes overlying the external anal sphincter; the perineal responses were measured with the use of a surface ring electrode at the proximal urethra. RESULTS: None of the data were distributed normally and required the use of negative inverse and cube root transformations to create a normal distribution. Clinical correlations were found with advancing age and vaginal delivery. CONCLUSION: The collection of these data allows for the definition of normal limits and begins the study of clinically important variables on test results and clinical outcomes.
We retrospectively assayed plasma corticosterone (B) in 143 dexamethasone suppression tests (DST) given serially to 19 depressed patients during the course of their hospitalization. A total of 424 blood samples from these 19 patients were analyzed for both plasma cortisol (F) and B. Concentrations of plasma B were not distributed normally. To establish a cut-off point for a positive B value in the DST, we log transformed the values for B to approximate a normal distribution. Using this approach we determined that a value of 1.3 ng/ml is the most sensitive cut-off point for the plasma B-DST in our laboratory. The serial DST's were performed weekly during the patients' stay and plasma B values were compared with plasma F values. Severities were assessed by weekly Hamilton ratings (17 items). In general, the B values closely parallel the F values. The sensitivity of F-DST was 53% (20/38) and the sensitivity was 56% (20/36) for B-DST. During treatment, both B and F normalized in parallel and this correlated strongly with improvements in the patients' severity ratings. These data confirm the fact that plasma B is as good (but not better) a marker for depression as plasma F in the DST.
The half-lives and withdrawal times of the veterinary drugs Toltrazuril and Enrofloxacin in trout have been assessed by statistical analysis. Confidence intervals were computed using a normal distribution of residual data and an empirical distribution by the Bootstrap method. Both methods produced similar statistics for the two drugs. Simulation of the residue data according to the regression lines of the decay curves has shown that the Bootstrap method is better for use when the residue patterns are not distributed normally. Using confidence intervals, a statistical mean of withdrawal times can be assessed. Taking into account the decays of the individual antibiotics in all treated trout, tolerance intervals for the regression lines are obtained: the calculated 10-20% longer withdrawal time includes values for which the antibiotic concentration in 95% of the treated trout is decreased below the tolerance level of Toltrazuril or Enrofloxacin.
Neutrophil leucocytes are known to migrate actively into 3-dimensional gels of collagen or fibrin. In this paper, we have used such gels to study chemotaxis of human blood neutrophils towards gradient sources of formyl-methionyl-leucyl-phenylalanine (FMLP) using 2 assay systems. The first resembled the micropore filter assay in that neutrophils on the upper surface of collagen gels were allowed to invade in the presence of either an isotropic concentration or a gradient of FMLP. Neutrophils invaded the gel vigorously in both cases. The effect of the gradient was assessed by determining the population distribution at different levels in the gel. Cells moving randomly should be distributed normally, and directional locomotion should cause deviation from normal distribution. Such a deviation was seen, but was of marginal significance. A more direct demonstration of chemotaxis was achieved by the second assay in which an agarose slab containing FMLP was incorporated into a gel, and the paths of nearby neutrophils were filmed. These cells showed an unequivocal directional response to the FMLP gradient. Protein gels can thus be used in the same way as both the presently used filter assays and visual assays using plane substrata, but with the advantage of providing a more physiological environment for the study of chemotaxis than either.
Recognition and matching trials were designed for the Rey-Osterrieth Complex Figure Test (ROCFT). Following pilot testing and expert review, they were standardized using 90 community-dwelling adults (58% female, ages 30 to 88). Recognition has 30 multiple-choice items for different figural elements; scores distributed normally with strong item-total correlations and with normally distributed item difficulties. Cronbach alphas were .84,.61, and .81 for the Total, Global, and Detail Scales. Recognition correlated .81 with ROCFT recall and .65 with Visual Reproductions. Matching has 10 multiple-choice items; scores were negatively skewed with a substantial ceiling effect. Alpha for Matching was .58, limited in part by few items. Matching correlated .68 with Judgment of Line Orientation and .74 to .90 with copy trials. Both Recognition and Matching discriminated 34 patients with intractable epilepsy from 34 matched controls. Overall, Recognition appeared to be reliable and showed evidence of validity. By comparison, Matching reliability and validity were less impressive and warrant further examination.