What Is a Variance

Variances from the Occupational Safety and Health Administration (OSHA) standards are authorized under sections 6 and 16 of the Occupational Safety and Health Act of 1970 (OSHAct), and the implementing rules contained in the Code of Federal Regulations (29 CFR 1905). A variance may be requested by an employer or by a class of employers for specihc workplaces. 

Requests for variance should be made as follows for permanent variance [authorized by section 6(d) of the OSHAct] the requirements of 29 CFR 1905.11 are to be followed, while for temporary variance [authorized by section 6(b)(6)(A) of the OSHAct] the requirements of 29 CFR 1905.10 are applicable. There are also provisions in section 16 of the OSHAct (29 CFR 1905.12) for National Defense variances, and in section 6(b)(6)(C) of the OSHAct for variances allowing authorized experimentation. Each type variance is summarized below. 

A permanent variance authorizes an alternative to a requirement of an OSHA standard as long as the applicant s employees are provided with employment and a place of employment equivalently safe and healthful. Two factors that must be addressed in the application are proof that the alternative is safe and healthful as the standard 

The final determination by the Assistant Secretary for grant of permanent variance is based upon the employer s application and evidence, an on-site visit to the workplace by OSHA representatives, as deemed necessary, and comments by employees and other interested parties. If the request is granted, the final order details the differences between the requirements of the standard and the alternative, and specifies the employer s responsibilities and requirements. 

The Assistant Secretary may issue a time-limited interim order pending the decision on the temporary variance, if such an order was requested by the applicant. 

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Collaborative testing provides a means for estimating the variability (or reproducibility) among analysts in different labs. If the variability is significant, we can determine that portion due to random errors traceable to the method (Orand) and that due to systematic differences between the analysts (Osys). In the previous two sections we saw how a two-sample collaborative test, or an analysis of variance can be used to estimate Grand and Osys (or oJand and Osys). We have not considered, however, what is a reasonable value for a method s reproducibility. 

A mean square residuals is equal to 1.395. If the model contained po and five additional parameters, and if the model was fit to data from twelve experiments, what is the variance of residuals The sum of squares of residuals ... 

Random and Ordered Mixtures The accompanying figure shows two samples of mixtures of black-and-white squares. One is a black-and-white checkered board and the other was obtained by tossing a coin for each square if it showed heads, the square was colored black, (a) If we take a large number of black-and-white particles of equal numbers and place the mixture in a V-blender, which sample will the mixture resemble (b) If we take a large number of small testing samples from sample 1 and sample 2, and measure the fraction of black particles in each sample, what type of distribution would be expected in each case (c) What is the variance of each distribution ... 

S. A system composed of ethane hydrate, water, and ethane is classed aa a two-component system when Gibbs phase rule is applied since it could be formed from water and ethane. What is the variance of this system when a solid, a liquid, and a vapor phase coexist in equilibrium If the temperature of this three-phase system is specified, would it be possible to alter the pressure without the disappaaranoe of a phase ... 

I dr the same capillary as in part (g), what is the variance o of a typical peak ... 

Statistics in general is a discipline dealing with ideas on description of data, implications of data (relation to general pharmacological models), and questions such as what effects are real and what effects are different Biological systems are variable. Moreover, often they are living. What this means is that they are collections of biochemical reactions going on in synchrony. Such systems will have an intrinsic variation in their output due to the variances in the... 

As Equations 10-1 and 10-2 show, the variance (s2) can lay claim to being a more fundamental variable than the standard deviation. In any event, when s2 significantly exceeds sc2, there may be several important sources of variation. It is then advisable to discover what these sources are. Because analysis of variance is a systematic procedure for making this discovery, it is expedient to use it, and to stop thinking exclusively in terms of the standard deviation. 

The discrepancy would be resolved if about 4.8 eV were the actual work function of clean Hg. In this case, however, it would be difficult to understand why 4.50 eV has been consistently measured it is hard to imagine what kind of contamination is responsible for such a highly reproducible situation. On the other hand, if 4.80 eV were the value of for clean Hg, then most of the other metals would show a decrease in work function upon water adsorption less negative than Hg, which is at variance with the expected chemistry of metal surfaces (see later discussion). 

In conclusion, there is very little evidence that even if changes are found in the rhizosphere, the.se changes will remain and actually change the wide biological potential of. soils. A major concern is the lack of reference samples—i.e. what is the natural variance in biodiversity and what are the rates of change as they occur, for example, under intensification of agricultural land u.se. 

Levenspiel and Smith Chem. Eng. Sci., 6 (227), 1957] have reported the data below for a residence time experiment involving a length of 2.85 cm diameter pyrex tubing. A volume of KMn04 solution that would fill 2.54 cm of the tube was rapidly injected into a water stream with a linear velocity of 35.7 cm/sec. A photoelectric cell 2.74 m downstream from the injection point is used to monitor the local KMn04 concentration. Use slope, variance, and maximum concentration approaches to determine the dispersion parameter. What is the mean residence time of the fluid ... 

Now we ask ourselves the question If we calculate the standard deviation for a set of data (or errors) from these two formulas, will they give us the same answer And the answer to that question is that they will, IF (that s a very big if , you see) the data and the errors have the characteristics that statisticians consider good statistical properties random, independent (uncorrelated), constant variance, and in this case, a Normal distribution, and for errors, a mean (fi) of zero, as well. For a set of data that meets all these criteria, we can expect the two computations to produce the same answer (within the limits of what is sometimes loosely called Statistical variability ). 

The analysis of rank data, what is generally called nonparametric statistical analysis, is an exact parallel of the more traditional (and familiar) parametric methods. There are methods for the single comparison case (just as Student s t-test is used) and for the multiple comparison case (just as analysis of variance is used) with appropriate post hoc tests for exact identification of the significance with a set of groups. Four tests are presented for evaluating statistical significance in rank data the Wilcoxon Rank Sum Test, distribution-free multiple comparisons, Mann-Whitney U Test, and the Kruskall-Wallis nonparametric analysis of variance. For each of these tests, tables of distribution values for the evaluations of results can be found in any of a number of reference volumes (Gad, 1998). 

This graph has several important features. It reaches saturation at d0bs of about 0.93, which means that the model predicts that one will never see a pair of proteins that are less than 7% identical. At this level of distance, a substitution will restore an amino acid identity just as likely as generate a new difference. Real sequences will sometimes exceed this level of observed distance and then the correction is not applicable. This is especially likely to occur with short sequences. If such distances are encountered in a real data set, then the sequences are so distant that the analysis will be difficult anyway. No matter what is done, it will be difficult to estimate the true number of substitutions. A further problem arises when one considers the possible variance or error of the distance estimates. A difference in the observed distance of just one identity more or less will have very little effect when dobs is small but will make an enormous difference to D when dobs is more than 0.80. 

Equation 4.4 is a general equation for calculating the variance of residuals. Equation 3.4 is a specific equation for calculating the variance of residuals. What is the model that gives rise to Equation 3.4 ... 

There is a problem with this approach, however - a problem with the residuals. The residuals are neither parameters of the model nor parameters associated with the uncertainty. They are quantities related to a parameter that expresses the variance of the residuals, The problem, then, is that the simultaneous equations approach in Equation 5.25 would attempt to uniquely calculate three items (P, r, and r,2) using only two experiments, clearly an impossible task. What is needed is an additional constraint to reduce the number of items that need to be estimated. A unique solution will then exist. 

To use what is termed universal kriging, it is assumed that Z(2 ) is an intrinsic random function of order k. But the problem of identifying the drift and the semi-variogram when they are both unknown is still present. However, Matheron (11) defined a family of functions called the generalized covariance, K(h). and the variance of the generalized increment of order k can be defined in terms of K(h ). That is. 

Although molecular orbital predictions (Section III, A) are often at variance with each other, they are generally agreed that substitution should not take place exclusively at the 2-position. The calculations of Kikuchi do in fact predict the order 2 > 4 > 3,1, which is what is actually observed in the two cases described above. 

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