Mean, statistical

Helfand and Tagami [75,76] introduced a model which considered the probability that a chain of polymer 1 has diffused a given distance into polymer 2 when the interactions are characterised by the Flory-Huggins interaction parameter x They predicted that at equilibrium the thickness , d c, of the interface would depend upon the interaction parameter and the mean statistical segment length, b, as follows ... 

Mixing correlation exponent, or empirical constant = Arithmetic mean (statistics)... 

In this case the interaction between neighbouring molecules is not only stronger but also orientation dependent. The mean statistical energy of dipole-dipole interactions 0dd also decreases with r 6, but depends on i2 (p dipole moment) according to 3>... 

Different letters mean statistical differences (Duncan test, P<0.001)... 

Conventionally a p (probability) value of < 0.05 is taken to mean statistical significance. This means that if p = 0.05 then the observed difference could occur by chance on 1 in 20 (5%) of occasions. In effect, this means a 5% chance of a false-positive result. 

Bias The systematic or persistent distortion of an estimate from the true value. From sampling theory, bias is a characteristic of the sample estimator of the sufficient statistics for the distribution of interest. Therefore, bias is not a function of the data, but of the method for estimating the population statistics. For example, the method for calculating the sample mean of a normal distribution is an unbiased estimator of the true but unknown population mean. Statistical bias is not a Bayesian concept, because Bayes theorem does not relay on the long-term frequency expections of sample estimators. 

This expression is essentially the same as that for a single mean statistic (constant x se). The rules for obtaining the multiplying constant however are slightly different. For the difference between two means we use Table 3.1 as before, but now we go into that table at the row + U2 — 2, where rii and 2 e the sample sizes for treatment groups 1 and 2 respectively. 

Mean Statistical parameter (%) relative error Hydrodynamic parameter AP/Z fit Deviation AP/Z fit Mean relative error AP/Z Bt Deviation AP/Z fi, ... 

The previous discussion of standard deviation and related statistical analysis placed emphasis on estimating the reliability or precision of experimentally observed values. However, standard deviation does not give specific information about how close an experimental mean is to the true mean. Statistical analysis may be used to estimate, within a given probability, a range within which the true value might fall. The range or confidence interval is defined by the experimental mean and the standard deviation. This simple statistical operation provides the means to determine quantitatively how close the experimentally determined mean is to the true mean. Confidence limits (Lj and L2) are created for the sample mean as shown in Equations 1.6 and 1.7. 

Earlier editions of this book had a complete chapter devoted to this subject which opened by commenting that it was tempting to claim that it was the most important chapter. The reasoning was that, whatever property we measure, whatever test method we use we end up with results and the question "What do the figures really mean " Results are useless unless we know their significance significance means statistics. However, at that time it was very unusual for statistical methods to be applied to rubber testing. 

By aggregate we mean a domain in which the concentration of one kind of block is considerably greater than average. We do not, however, mean statistical variations of concentration and anomalously high concentrations in isolated coils. Suitable methods for proving the existence of such aggregates have been reviewed (20). 

The bubble size detected by the probe is subject to a probability distribution [28,29] and only the mean statistical value of the bubbles is given by J32. The analysis of the bubble size distribution helps us understand the uniformity of the bubble sizes and its axial evolution. Fig. 11 shows the axial change of the bubble size distribution at r/R = 0 and r/R = 0.97, respectively. Below the internal, the peak... 

About 68 % of the area under the curve lies between z = 1 and z = +1 (one standard deviation on either side of the mean). Statistically, from Eq. (1.28) ... 

The arithmetic mean (statistical average) burning rate of pyrotechnic or propellants at specific pressures and temperatures. Dimension -length/time or mass/time. 

Adsorption isotherm equations can in principle be derived by first formulating the chemical potential of the adsorbate p° in terms of a model, then equating p to p. Although it is not impossible to derive expressions for p by thermodynamic means, statistical approaches are more appropriate because in this way the molecular picture can be made explicit. Moreover, adsorbates are not macroscopic systems, which is a prerequisite for applying thermodynamics, and statistical thermodynamics lends itself very well to the derivation of expressions for the surface pressure. Another approach is based on kinetic considerations expressions for the rates of adsorption and desorption are formulated at equilibrium the two are equal. 

Statistical methods are used for explaining the macroscopic properties of bodies from the point of view of thdr microscopic structure. The macroscopic physical quantities are then found to be mean statistical values of parameters characterizing the microscopic processes occurring in the system as a whole. The procedure of statistical physics consists in assunung some microscopic (classical or quantal) model of the body from which, by methods of statistics, we derive its equation of state and describe all its macroscopic, e.g. in the presort context, electromagnetic, properties. 

Finnigan, J J. (1979) Turbulence in waving wheat. I. Mean statistics and honami, Boundary-Layer Meteorol. 16, 181-211. 

This means statistically significant. To be of chemical significance, a component must also be statistically significant The reverse is not always true. There can be statistically significant differences, which are uninteresting from a chemical point of view. Aldehydes and ketones, for instance, are significantly different to each other in many respects, but in their reaction with lithium aluminum hydride they do not show any pronounced chemoselectivity. 

The term "statistical analysis" has two meanings. Statistical analysis, used in a general sense, can be regarded as a global description or plan of how data collected will be analyzed. The term "a statistical analysis" refers to an individual analytical technique that is used to describe and analyze numerical information. This book teaches you how to conduct a collection of statistical analyses that are appropriate for use in analyzing the results of clinical trials. 

When a compound was identified at least in most samples of a group, an analysis of variance with interaction by the General Linear Model procedure was performed to check the effect of salt content (lower and higher), sodium nitrite (presence, absence), added amino acids (control, cysteine and proline) and reaction time (7, 14 and 21 days). When significant and more than two levels in an effect, multiple comparison by the Tukey test were carried out to compare means. Statistic analyses were performed by means of the SPSS version 11.0. 

---