Statistical procedures used

Upper confidence limit (UCL) A statistical procedure used to estimate whether the true value is higher than the measured value. 

If you cannot find what you need in an output data set from the statistical procedure, use ODS OUTPUT to send your statistics to a data set. To determine... 

This model assumes that any dosage effect has the same mechanism as that which causes the background incidence. Low-dose linearity follows directly from this additive assumption, provided that any fraction of the background effect is additive no matter how small. A best fit curve is fitted to the data obtained from a long-term rodent cancer bioassay using computer programs. The estimates of the parameters in the polynomial are called Maximum Likelihood Estimates (MLE), based upon the statistical procedure used for fitting the curve, and can be considered as best fit estimates. Provided the fit of the model is satisfactory, the estimates of these parameters are used to extrapolate to low-dose exposures. 

Correlations were observed for exposure levels and duration. This study is limited, however, by lack of blinding and failure to report control mercury levels the statistical procedures used for confounders (use of traditional Chinese medicines) were not reported. 

Data used for the assessment of analytical uncertainty by ICP/MS were obtained over a time period of two years. The statistical procedure used to assess the uncertainty of the different elements by ICP/MS, taking into account the matrix effect and level of concentrations, is described below. 

A statistical procedure used in analyzing sampling data to estimate the probability that the true value of the sampled quantity is lower than that obtained. 

In sampling analysis, a statistical procedure used to estimate the likelihood that a particular value is above the obtained value. 

The statistical procedures used in this thesis are summarized in this subsection together with hints for further literature. PASW Statistics 18 and Microsoft Office Excel were used for computations. T-tests and Mann-Whitney tests were performed to assess internal relationships between binary and continuous explanatory variables, particularly vehicle impact speed. Pearson and Spearman correlations were used to assess possible correlations among continuous variables. 

The statistical procedures used with instrumental analysis methods must provide as always information on the precision and accuracy of the measurements. They must also reflect the technical advantages of such methods, especially their ability to cover a great range of concentrations (including very low concentrations), and to handle many samples rapidly. (In this chapter we shall not cover methods that facilitate the simultaneous determination of more than one analyte. This topic is outlined in Chapter 8.) In practice the results are calculated and the errors evaluated in a particular way that differs from that used when a single measurement is repeated several times. 

The direct method is a mathematical process in which diffrent phase and amplitudes of the molecular transform are related to the contribution of individual atoms. This method is based on statistical procedures used to extract the phase information. The missing phase information is believed to be present in the statistical intensity distribution. One of the most well-known statistical proposals was offered by Karle and Hauptmann (1986). These authors assumed that the Fourier transform of the intensity represents the probability of finding interatomic distances in a molecule and that the transform is nonnegative. 

Corrosivity in complex environments. Experimental design techniques were also used to develop models for understanding the effects of complex environments on materials considered for the operation of different processes such as wood pyrolysis, gas desulfurization, and continuous digestion. In these studies, it was demonstrated that to reduce the complexity of the environments (solution variables, constraints, etc.) to a manageable level, designed experiments are essential. When such studies are properly done, the results can be used to predict the corrosion performance of alloys as a function of solution composition. For the interested reader, reference 54 gives additional details on the actual statistical procedures used for a few typical designs for complex corrosion. 

The forecast errors distributions depend on previous errors (e ) and on how many periods ahead the forecast is being done. If the correct forecasting model has been chosen, and if the statistical procedure used to estimate parameters in the model yields unbiased estimates, then the expected forecast error will be zero. When the forecasting error (e) is assumed to be normally distributed (7V(0, forecasting error for the period ahead can be calculated by means of Eq. (7.57). This approximation holds even for non-normally distributed errors. For more details about estimation of forecast errors, please refer to Montgomery et al. (1990). 

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