Deviation additive

The C-section ( litter ) values, i.e., gravid uterus weight, corpora lutea, total number of implants, and numbers of live and dead implants (including separate categories of dead implants) are presented as means, together with an indicator of variation, typically standard deviation. Additionally, pre- and postimplantation losses are calculated for each female ... 

The issue of goodness-of-fif with nonlinear regression is not straightforward. Numerous methods can be used to explore the goodness-of-fif of the model to the data (e.g., residual analysis, variance analysis, and Chi-squared analysis). It is always a good idea to inspect the plot of the predicted [y(x,)] versus observed y, values to watch for systematic deviations. Additionally, some analytical measure for goodness-of-fit should also be employed. 

Commonly used descriptive statistics include measures that describe where the middle of the data is. These measures are sometimes called measures of central tendency and include the mean, median, and mode. Another category of measures describes how spread out the data is. These measures are sometimes called measures of variability and include the range, variance, and standard deviation. Additional descriptive measures can include percentages, percentiles, and frequencies. In safety performance measurement, the safety professional must determine the format of the data (i.e., ratio, interval, ordinal, or categorical) that will be collected and match the data format to the appropriate statistic. As will be discussed in the following sections, certain descriptive statistics are appropriate for certain data formats. 

Descriptive Statistics statistical techniques that are used to describe the population or sample. Commonly used descriptive statistics include measures of central tendency mean, median and mode and measures of variability range, variance and standard deviation. Additional descriptive measures can include percentages, percentiles and frequencies. 

A few of the results for m = 5 show surprisingly large deviations. Additional calculations with all m in the range m = 3-11 and with both real and complex boundary conditions showed such instabilities only for m = 5 and— to a lesser... 

Normal variation is expected, and to discriminate between random variation and loss of process control, statistical analysis is performed on the results of the control standard. Random variation is expected and is out of the operator s control. Random variation is exhibited as distribution around the average (mean) of the values that conform to the normal distribution curve. The standard deviation of the results is an indicator of the level of control of the process. The smaller the standard deviation, the more controlled a process is. Statistically, in a controlled process approximately 95% of the values will fall within a range of the mean plus or minus two standard deviations, and 99.7% will fall within the mean plus or minus three standard deviations. Additionally when considered chronologically, the values should be randomly distributed on either side of the mean, and the further from the mean, the less frequent the occurrence. 

An additional advantage derived from plotting the residuals is that it can aid in detecting a bad data point. If one of the points noticeably deviates from the trend line, it is probably due to a mistake in sampling, analysis, or reporting. The best action would be to repeat the measurement. However, this is often impractical. The alternative is to reject the datum if its occurrence is so improbable that it would not reasonably be expected to occur in the given set of experiments. 

We have repeatedly observed that the slowly converging variables in liquid-liquid calculations following the isothermal flash procedure are the mole fractions of the two solvent components in the conjugate liquid phases. In addition, we have found that the mole fractions of these components, as well as those of the other components, follow roughly linear relationships with certain measures of deviation from equilibrium, such as the differences in component activities (or fugacities) in the extract and the raffinate. 

In addition, the mirrors are adjustable, so that unimportant areas can be ignored. Light re-emmited from the surfaee is detected, and the detector signal is transmitted to a computer programmed with acceptable deviation levels for comparison with a reference component. Tolerance levels can vary for different areas of the same test piece they may, for example, be higher on a ground section than on adjacent unmachined areas. 

A linear dependence approximately describes the results in a range of extraction times between 1 ps and 50 ps, and this extrapolates to a value of Ws not far from that observed for the 100 ps extractions. However, for the simulations with extraction times, tg > 50 ps, the work decreases more rapidly with l/tg, which indicates that the 100 ps extractions still have a significant frictional contribution. As additional evidence for this, we cite the statistical error in the set of extractions from different starting points (Fig. 2). As was shown by one of us in the context of free energy calculations[12], and more recently again by others specifically for the extraction process [1], the statistical error in the work and the frictional component of the work, Wp are related. For a simple system obeying the Fokker-Planck equation, both friction and mean square deviation are proportional to the rate, and... 

Another scheme for estimating thermocheraical data, introduced by Allen [12], accumulated the deviations from simple bond additivity in the carbon skeleton. To achieve this, he introduced, over and beyond a contribution from a C-C and a C-H bond, a contribution G(CCC) every time a consecutive arrangement of three carbon atoms was met, and a contribution D(CCC) whenever three carbon atoms were bonded to a central carbon atom. Table 7-3 shows the substructures, the symbols, and the contributions to the heats of formation and to the heats of atomization. 

The second step, the so called generation, created only those structures which complied with the given constraints, and imposed additional restrictions on the compounds such as the number of rings or double bonds. The third and final phase, the tester phase, examined each proposed solution for each proposed compound a mass spectrum was predicted which was then compared with the actual data of the compound. The possible solutions were then ranked depending on the deviation between the observed and the predicted mass spectra. 

In addition lo the cii ergy quan lilies HKIN, etc., il is possible to average and plot iheir standard deviations Id KKIN, etc, as described below. 

In addition to bein g able to plot sim pie in stan tan eous values of a quantity x along a trajectory and reporting the average, , HyperChem can also report information about the deviation of x from its average value. Ihese RMS deviations may have particular sign ifican ce in statistical tn ech an ics or just represen t lh e process of convergence of the trajectory values. 

As many as four plots are possible with colors red, green, blue and black. Each plot is scaled independent of the others and the colored labels identify the minimum and maximum of the plot and the name of the quantity being plotted. In addition to the values of X, the RMS deviation in x (Dx) can be plotted. The plot of Dx converges to the RMS deviation of x at the end of the run and represents the current value of the RMS deviation at any point in the plot. 

The intercept on the adsorption axis of the extrapolated linear branch gives the micropore contribution, and when converted to a liquid volume may be taken as equal to the micropore volume itself. It is sometimes convenient indeed to convert all the uptakes into liquid volumes (by use of the liquid density) before drawing the t-plots or the a,-plots. If mesopores are present (in addition to micropores) the plots will show an upward deviation at high relative pressures corresponding to the occurrence of capillary condensation (Fig. 4.12(6)). The slope of the linear branch will then be proportional to the area of the mesopore walls together with the... 

Precision is a measure of the spread of data about a central value and may be expressed as the range, the standard deviation, or the variance. Precision is commonly divided into two categories repeatability and reproducibility. Repeatability is the precision obtained when all measurements are made by the same analyst during a single period of laboratory work, using the same solutions and equipment. Reproducibility, on the other hand, is the precision obtained under any other set of conditions, including that between analysts, or between laboratory sessions for a single analyst. Since reproducibility includes additional sources of variability, the reproducibility of an analysis can be no better than its repeatability. 

Consider, for example, the data in Table 4.1 for the mass of a penny. Reporting only the mean is insufficient because it fails to indicate the uncertainty in measuring a penny s mass. Including the standard deviation, or other measure of spread, provides the necessary information about the uncertainty in measuring mass. Nevertheless, the central tendency and spread together do not provide a definitive statement about a penny s true mass. If you are not convinced that this is true, ask yourself how obtaining the mass of an additional penny will change the mean and standard deviation. 

The emission spectrum from a hollow cathode lamp includes, besides emission lines for the analyte, additional emission lines for impurities present in the metallic cathode and the filler gas. These additional lines serve as a potential source of stray radiation that may lead to an instrumental deviation from Beer s law. Normally the monochromator s slit width is set as wide as possible, improving the throughput of radiation, while being narrow enough to eliminate this source of stray radiation. 

The goal of a collaborative test is to determine the expected magnitude of ah three sources of error when a method is placed into general practice. When several analysts each analyze the same sample one time, the variation in their collective results (Figure 14.16b) includes contributions from random errors and those systematic errors (biases) unique to the analysts. Without additional information, the standard deviation for the pooled data cannot be used to separate the precision of the analysis from the systematic errors of the analysts. The position of the distribution, however, can be used to detect the presence of a systematic error in the method. 

The principal tool for performance-based quality assessment is the control chart. In a control chart the results from the analysis of quality assessment samples are plotted in the order in which they are collected, providing a continuous record of the statistical state of the analytical system. Quality assessment data collected over time can be summarized by a mean value and a standard deviation. The fundamental assumption behind the use of a control chart is that quality assessment data will show only random variations around the mean value when the analytical system is in statistical control. When an analytical system moves out of statistical control, the quality assessment data is influenced by additional sources of error, increasing the standard deviation or changing the mean value. 

In Chaps. 5 and 6 we shall examine the distribution of molecular weights for condensation and addition polymerizations in some detail. For the present, our only concern is how such a distribution of molecular weights is described. The standard parameters used for this purpose are the mean and standard deviation of the distribution. Although these are well-known quantities, many students are familiar with them only as results provided by a calculator. Since statistical considerations play an important role in several aspects of polymer chemistry, it is appropriate to digress into a brief examination of the statistical way of describing a distribution. 

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