PubMed Health⌕ Search

SEARCH · PubMed Health

Results for “Normal Distribution”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 19 recordsLinked to original sources
PubMed1992

Evidence that dyslexia may represent the lower tail of a normal distribution of reading ability.

BACKGROUND: Dyslexia is now widely believed to be a biologically based disorder that is distinct from other, less specific reading problems. According to this view, reading ability is considered to follow a bimodal distribution, with dyslexia as the lower mode. We hypothesized that, instead, reading ability follows a normal distribution, with dyslexia at the lower end of the continuum. METHODS AND RESULTS: We used data from the Connecticut Longitudinal Study, a sample survey of 414 Connecticut children who entered kindergarten in 1983 and were followed as a longitudinal cohort. Dyslexia was defined in terms of a discrepancy score, which represents the difference between actual reading achievement and achievement predicted on the basis of measures of intelligence. Data were available from intelligence tests administered in grades 1, 3, and 5 and achievement tests administered yearly in grades 1 through 6. For each child there were 108 possible discrepancy scores ([3 x 3 years] x [2 x 6 years]) based on combinations of the ability scores (full-scale, verbal, and performance IQ) in each of three years and two achievement scores (reading and mathematics) in each of six years. We demonstrated that each of the discrepancy scores followed a univariate normal distribution and that the interrelation of two different discrepancy scores followed a bivariate normal distribution. At most, only 9 of 108 discrepancy scores (8.3 percent) and 171 of 3402 pairs of discrepancy scores (5.0 percent) were significantly different (at the 5 percent level) from the expected scores--well within the expected values for data with univariate and bivariate normal distributions, respectively. We also examined the stability of dyslexia over time. The normal-distribution model predicted (and the data indicated) that only 7 of the 25 children (28 percent) classified as having dyslexia in grade 1 would also be classified as having dyslexia in grade 3. CONCLUSIONS: Reading difficulties, including dyslexia, occur as part of a continuum that also includes normal reading ability. Dyslexia is not an all-or-none phenomenon, but like hypertension, occurs in degrees. The variability inherent in the diagnosis of dyslexia can be both quantified and predicted with use of the normal-distribution model.

Child↗
PubMed1977

[Log-normal distributed plasma cortisol levels of four daily measurements in normal subjects. A comparison of the fluorescence method after de Moor with a radioimmuno assay of plasma cortisol (author's transl)].

The present paper describes the plasma cortisol concentrations on four daily measurements in normal subjects assayed with the fluorescence method after de Moor and with a radioimmuno assay. A comparison of these two methods shows that the determinations of plasma cortisol with the fluorescence method always yielded higher values. Both methods are sensitive enough to detect the circadian rhythm of cortisol secretion. For the purpose of routine diagnostics it is sufficient to measure the maximal and minimal concentrations of plasma cortisol in blood samples taken at 8 a.m. and 8 p.m., respectively. The plasma cortisol measurements should only be attempted after allowing a few days of adaption to the hospital situation. Table 2 shows that the normal plasma cortisol levels are represented only by log-normal distributed values. These concentrations are lower than the linear distributed levels reported so far.

Adult↗
PubMed1978

Estimation of the mixing proportion in a mixture of two normal distributions from simple, rapid measurements.

A mixture of two or more normal distributions often provides an adequate model for the distribution of a population consisting of varying proportions of component subpopulations. We consider here the problem of estimating the mixing proportion in a mixture of two normal distributions, the parameters of which can be assumed known. Very large samples may be needed if reasonably precise estimates are to be obtained, thus bringing into consideration the cost or time involved in obtaining large numbers of exact measurements and computing the estimates from them. Simple estimators based on simple, rapidly obtained measurements may then be attractive alternatives provided efficiency losses are not too great. Three such estimators studied here are based on (a) the number of observations less than a fixed point r, (b) the nembers less than s and greater than t, and (c) the sample mean. Optimal choices of the points r, s and t are considered, and the efficiencies of the estimators relative to maximum likelihood estimators (MLE) using the full data are obtained. The simple estimators often perform sufficiently well to make the collection of full data not worthwhile in practice.

Genetics, Population↗
PubMed1992

Estimation, reference ranges and goodness of fit for the three-parameter log-normal distribution.

The three-parameter log-normal distribution (3PL) is an appropriate model for many of the continuous variables encountered in medicine. It is shown how to obtain different types of estimate and approximate (sometimes conservative) confidence intervals for the parameters of the 3PL and for certain functions of them, particularly in the calculation of reference ranges of clinical measurements. A simple non-iterative estimate of the shift parameter is described. The Shapiro-Wilk test of non-normality is modified to allow it to be used for testing for departure from the 3PL. Its power is compared with that of other well-known tests. The methods are illustrated using several data sets.

Algorithms↗
PubMed1975

Log normal distribution of gonadotropins and ovarian steroid values in the normal menstrual cycle.

In the statistical analysis of the values of luteinizing hormone, follicle-stimulating hormone, estradiol, and progesterone obtained from normal menstrual cycles, a depature from normality was noted. Chi square, W test, and linear transformation were used to check the normality of the distributions. The results of this investigation showed that the distributions were not normal (Gaussian) but log-normal. By plotting the probit of the percentages of cumulative frequency on a log scale (probit-log), linearity of the data was obtained. This resulted in direct graphical estimations of values with a useful clinical range, which included the mean and the 95 per cent confidence interval.

Adult↗
PubMed1976

[Logarithmo-normal distributions of relative and absolute values of human lymphocytes forming spontaneous rosettes in presence of sheep and mouse erythrocytes in normal adult].

The percentages and absolute numbers of peripheral blood lymphocytes forming rosettes with sheep and mouse red blood cells were established in 135 normal human beings. We found SRFC values almost similar to the proportion of so called "active" rosettes, whereas the values of MRFC were low. SRFC and MRFC values had a logarithmico-normal distribution. The absolute number of the two types of rosettes was decreased in the subjects more than 70 years old.

Age Factors↗
PubMed1975

[Disaccharidases of the small intestine mucosa in infants and children. "Normal values", log normal distribution and age dependence].

In 63 infants and children with a histological normal mucosa of the duodenum, without an isolated defect of enzyme and with a normal increase of xylose and glucose in serum after a combined xylose-lactose loading test the activities of disaccharidases were log normal distributed. The asymmetric distributions were transformed into symmetric ones and the geometric mean (x) as well as the range (+/- 2 s) of maltase, saccharase, isomaltase, lactase and trehalase were calculated. Only the activity of lactase shows a significant dependency on age. In the first year of age the lower limit (x -- 2 s) of this enzyme is much higher than later.

Age Factors↗
PubMed1978

Log normal distribution of ovarian and placental steroid values in early human pregnancy.

Concentrations of estradiol, progesterone, 17OH-progesterone were measured by radioimmunoassay in individual serum samples obtained from a group of 304 women with normal gestations between the 4th and 17th week of pregnancy. Values obtained underwent statistical analysis in order to determine the arithmetic mean and the 95% normal range (+/- two standard deviations). It was noted hereby that the spread of values above the mean was greater than that below the mean, and that very often the mean minus two standard deviations was either close to zero or negative. Therefore, the data for each hormone were analyzed for normality of the distributions by the chi-square test. For each hormone the chi-square test was significantly different (p less than 0.001) from the normal distribution (Gaussian). Subsequently, linear transformation by rankit analysis revealed the log-normal distribution of our data. Furthermore, rankit analysis was used as a graphical method to delineate a useful clinical range, which includes the mean and meaningful 95% confidence limits for estradiol, progesterone, and 17OH-progesterone in early normal pregnancies.

Estradiol↗
PubMed1992

Estimation of direct formulation effect under log-normal distribution in bioavailability/bioequivalence studies.

This paper considers estimation of a measure of relative bioavailability of a test formulation to a reference formulation, on the original scale, under the assumption of a log-normal distribution for the data from a 2 x 2 crossover bioavailability/bioequivalence study. We propose the minimum variance unbiased estimator which is equal to the maximum likelihood estimator adjusted for bias by a correction factor. We also derive the variance of the minimum variance unbiased estimator and its unbiased estimator. We derive the biases and mean square errors of the maximum likelihood estimator, the ratio of the least square means, and the least squares mean of individual subject ratios, with respect to this measure, and compare them in a simulation study. Both theoretical and empirical results strongly suggest that one always consider the minimum variance unbiased estimator. A numerical example illustrates the proposed estimation procedure.

Bias↗
PubMed1978

Amino acids in parenteral feeding. I. The normal distribution of serum amino acids in healthy subjects.

Questions as to the utilisation of intravenously supplied amino-acids are answerable by determining nitrogen balances and by ascertaining the pattern of amino-acids in the serum of plasma. In a first study, the normal distribution was established for the individual serum amino-acids in 150 fasting test persons with a healthy metabolism. Sex-specific differences in concentration became clearly evident for the majority of amino-acids present in the serum.

Adolescent↗
PubMed1978

Use of overlapping normal distributions in genetic counselling.

If a numerical variable can be assumed to be normally, but differently, distributed in each of two or more populations, then for an 'unknown' individual whose numerical value is known the relative probability of his belonging to each of the populations can be simply calculated. We briefly review the method and its application in genetic counselling.

Genes↗
PubMed1978

The mucosa-associated microflora of the rat intestine: a study of normal distribution and magnesium sulphate induced diarrhoea.

Specimens of intestinal mucosa of rats were examined closely to determine the distribution of the mucosa-associated microbial flora. Six distinct zones were found along the length of the intestinal tract. The first zone, in the small intestine 50 cm or more from the ileocaecal junction, had no associated flora: however, each of the five other zones had different populations of microorganisms associated with the mucosa. Some of these organisms have not been reposted previously. Treatment of rats with oral doses of the purgative magnesium sulphate resulted in dramatic changes in the distribution of these mucosa-associated microorganisms. The normal flora of ileal and caecal crypts disappeared, while the organisms in colonic crypts were unchanged. Large numbers of mucosa-associated bacteria appeared in the stools of treated animals.

Animals↗
PubMed1992

Multiple-trait restricted maximum likelihood for simulated measures of ovulation rate with underlying multivariate normal distributions.

A data set that was used to estimate covariance components with REML for an animal model with eight measures of ovulation rate treated as separate traits was used as a template to simulate data sets of eight multivariate normal traits that were then truncated to binomial traits. The model for simulation included eight measures on 610 animals with 1,071 animals in the numerator relationship matrix. Heritabilities were equal for the eight measures, and both genetic and phenotypic correlations among the measures were equal. Ten replications for each combination of heritability (.15, .25, and .35) and genetic correlation (.50, .66, and .90) were simulated on the normal scale. For each replicate, estimates of the eight heritabilities and 28 genetic correlations were obtained by multiple-trait REML. The usual transformation of heritability estimated on the binomial scale overestimated heritability on the normal scale. Genetic correlations on the binomial scale seriously underestimated the correlations on the normal scale. Standard errors of the estimates obtained by replication were somewhat larger than the approximate SE from REMLPK (the multi-trait REML program of K. Meyer). A final set of 10 simulated replications with heritability of .25 and genetic correlation of 1.00 resulted in average estimates of .18 for heritability and of .66 for genetic correlation that agree closely with those from the analysis of measures of ovulation at eight estrous cycles used as a template; averages for heritability of .16 and for genetic correlation of .66 were obtained.

Animals↗
PubMed1978

Normal distribution of acetylation phenotypes in systemic lupus erythematosus.

Previous reports have indicated that idiopathic systemic lupus erythematosus (SLE), like drug-induced lupus, is more frequent in "slow" hepatic acetylators. Using dapsone acetylation rate to determine phenotypes, we found that of the 18 SLE patients studied, 9 were fast acetylators, 8 were slow, and 1 was indeterminate. This result (53% fast) is similar to acetylator phenotypes in our normal controls (50% fast) and in the population at large (52%).

Acetylation↗