Description frequency distribution

With the aid of the power density spectrum, we can now give a complete description of how a linear, time-invariant filter affects the frequency distribution of power of the input time function X(t). To accomplish this, we must find the relationship between the power... 

Table 4.30. Statistical frequency distributions of electron countsa, common formulasa, and localized bonding descriptions (in terms of number of metal-centered lone pairs, 2c/2e bonds, tu bonds, and average sd hybridization) for organometallic complexes of groups 3-10...

The analytical plan of epidemiological studies should use descrip tive and analytical techniques in describing the sample and results. Descriptive statistics, such as frequency distributions, cross-tabulations, measures of central tendency, and variation, can help explain underlying distributions of variables and direct the assessment of appropriateness of more advanced statistical techniques. Careful weighing of study findings with respect to the design and methods helps to ensure the validity of results. 

The purpose of most practical work is to observe and measure a particular characteristic of a chemical system. However, it would be extremely rare if the same value was obtained every time the characteristic was measured, or with every experimental subject. More commonly, such measurements will show variability, due to measurement error and sampling variation. Such variability can be displayed as a frequency distribution (e.g. Fig. 37.3), where the y axis shows the number of times (frequency,/) each particular value of the measured variable (T) has been obtained. Descriptive (or summary) statistics quantify aspects of the frequency distribution of a sample (Box 40.1). You can use them to condense a large data set, for presentation in figures or tables. An additional application of descriptive statistics is to provide estimates of the true values of the underlying frequency distribution of the population being sampled, allowing the significance and precision of the experimental observations to be assessed (p. 272). 

The appropriate descriptive statistics to choose will depend on both the type of data, i.e. whether quantitative, ranked or qualitative (see p. 65) and the nature of the underlying frequency distribution. 

Three important features of a frequency distribution that can be summarized by descriptive statistics are ... 

Iodine excretion and serum T4 are markedly lower in the iodine-deficient group than in the control group. The effects of treatment with Lipiodol are disappointing the mean urinary I before and after treatment is nearly the same and there is no difference in the frequency distributions. In each group more than half of the children are excreting less than 40 xg/L. The plasma T4 did not change either, with 19 Z of the treated children and 17 Z of the iodine-deficient children having values lower than 6 xg/dl. There is no difference between T4 mean values, or between frequency distributions. For a more detailed description of this study see Escobar del Rey et al. (33). 

Descriptive statistics for each item, including percentage frequency distribution, mean and standard deviation are presented. 

This brief and rather incomplete description of frequency distributions and their relationship to probability distribution has been for the purpose of introducing the normal distribution curve. The normal or Gaussian distribution is the most important of the distributions that are considered in statistics. The height of a normal distribution curve is given by... 

In Sect. 2.8 we saw that the mean lifetime r, of a molecular level E/, which decays exponentially by spontaneous emission, is related to the Einstein coefficient Ai by Ti = 1/A/. Replacing the classical damping constant y by the spontaneous transition probability A/, we can use the classical formulas (3.9-3.11) as a correct description of the frequency distribution of spontaneous emission and its linewidth. The natural halfwidth of a spectral line spontaneously emitted from the level Ei is, according to (3.11),... 

The first approach represents an individual molecule by the frequency distribution of the interatomic distances in its distance matrix the similarity between a pair of molecules can then be calculated by the goodness-of-fit between the two frequency distributions. Given a distance matrix, DA, the method involves sorting the elements DA(I,J) (l N(A)-l I J N(A)) into increasing order of distance and representing them as a frequency distribution FA such that the TT-th element of FA, FA(K)y contains the number of elements of DA that occur in the K-th distance range that has been defined. The reader is referred to the paper elsewhere in these proceedings by Artymiuk et for a detailed description of the way in which this is carried out. 

Our data were submitted to descriptive analysis in terms of mean values, range and frequency distributions. Since the distributions of lead exposure parameters were skewed, a log transformation of values was applied. Pearson s correlation coefficients were calculated to evaluate the association between neuropsychological impairments and lead exposure. The level of significance assumed was p < 0.05 (one-tailed). To evaluate the influence of potential confounding variables on measured parameters, analysis of variance (ANOVA) was performed. In addition, we estimated the variance of psychometric tests explained by covariates (ALA-D, PbB, PbH, PbT) after regressing out the effects of demographic variables (ANCOVA). 

Nature In monitoring a moving threadhne, one criterion of quality would be the frequency of broken filaments. These can be identified as they occur through the threadhne by a broken-filament detector mounted adjacent to the threadhne. In this context, the random occurrences of broken filaments can be modeled by the Poisson distribution. This is called a Poisson process and corresponds to a probabilistic description of the frequency of defects or, in general, what are called arrivals at points on a continuous line or in time. Other examples include ... 

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