Within-variance

Selection alone cannot achieve an optimization towards the solution With mere scicction performed over a number of generations, one would get a population which comprises only the best chromosome of the original population. Therefore, an operator has to be applied which causes variance within the population, This is achieved by the application of genetic operators such as the crossover and the mutation operators. 

It is possible to compare the means of two relatively small sets of observations when the variances within the sets can be regarded as the same, as indicated by the F test. One can consider the distribution involving estimates of the true variance. With sj determined from a group of observations and S2 from a second group of N2 observations, the distribution of the ratio of the sample variances is given by the F statistic ... 

A second way to work with the data in Table 14.7 is to treat the results for each analyst separately. Because the repeatability for any analyst is influenced by indeterminate errors, the variance, s, of the data in each column provides an estimate of O rand- A better estimate is obtained by pooling the individual variances. The result, which is called the within-sample variance (s ), is calculated by summing the squares of the differences between the replicates for each sample and that sample s mean, and dividing by the degrees of freedom. 

Once a significant difference has been demonstrated by an analysis of variance, a modified version of the f-test, known as Fisher s least significant difference, can be used to determine which analyst or analysts are responsible for the difference. The test statistic for comparing the mean values Xj and X2 is the f-test described in Chapter 4, except that Spool is replaced by the square root of the within-sample variance obtained from an analysis of variance. 

This value of fexp is compared with the critical value for f(a, v), where the significance level is the same as that used in the ANOVA calculation, and the degrees of freedom is the same as that for the within-sample variance. Because we are interested in whether the larger of the two means is significantly greater than the other mean, the value of f(a, v) is that for a one-tail significance test. 

Hay and Pasquill (5) and Cramer (6, 7) have suggested the use of fluctuation statistics from fixed wind systems to estimate the dispersion taking place within pollutant plumes over finite release times. The equation used for calculating the variance of the bearings (azimuth) from the point of release of the particles, cTp, at a particular downwind location is... 

Work done by Wiesner [6] is a much more accurate approach. The subject has also been reported on more recently by Simon and Bulskamper [71. They generally agree with Wiesner that the variance of performance with Reynolds number was more true at low value that at high values. The additional influence above a Reynolds number of 10 is not much. It would appear that if a very close guarantee depended on the Reynolds number to get the compressor within the acceptance range (if the Reynolds number was high to begin with), the vendor would be rather desperate. 

Selection of which material should pass through tubes cannot be decided by fixed rules, because of factors at a variance with one another. When corrosive condensate is encountered, condensation within the tubes rather than the shell is usually desirable. 

Temporary variance An OSH A variance issued to an employer who is unable to comply with a standard by its effective date for reasons beyond their control. The employer must demonstrate a plan for coming into compliance within a period not to exceed one year and provide all available measures to protect the employees in the interim. 

An appropriate sampling program is critical in the conduct of a hcaltli risk assessment. This topic could arguably be part of the exposure assessment, but it has been placed within hazard identification because, if the degree of contamination is small, no further work may be necessary. Not only is it important that samples be collected in a random or representative manner, but the number of samples must be sufficient to conduct a statistically valid analysis. The number needed to insure statistical validity will be dictated by the variability between the results. The larger the variance, tlic greater the number of samples needed to define tire problem, ... 

Analysis of variance (ANOVA), a statistical procedure that quantifies differences between means of samples and the extent of variances within and between those means to determine the probability of there being a difference in the samples. 

The reason for that ambiguity is the fact that the l/V characteristics are Fitted with equations (see above) consisting of various fit parameters in a rather restricted voltage range, so that many different curves can model the l/V curves within a moderate variance range. 

So, we can discard the third eigenvector and, along with it, that portion of the variance in our spectra that displaced the data out of the plane of the noise-free data. We are in fact, discarding a portion of the noise without significantly distorting the spectra The portion of the noise we discard is called the extracted error or the residuals. Remember that the noise we added also displaced the points to some extent within the plane of the noise-free data. This portion of the noise remains in the data because it is spanned by the eigenvectors that we must retain. The noise that remains is called the imbedded error. The total error is sometimes called the real error. The relationship among the real error (RE), the extracted error (XE), and the imbedded error (IE) is... 

The mixing time will be that required for the mixture composition to come within a specified deviation from the equilibrium value and this will be dependent upon the way in which the tracer is added and the location of the detector. It may therefore be desirable to record the tracer concentration at several locations, and to define the variance... 

Note that the Kolmogorov power spectrum is unphysical at low frequencies— the variance is infinite at k = 0. In fact the turbulence is only homogeneous within a finite range—the inertial subrange. The modified von Karman spectral model includes effects of finite inner and outer scales. 

The mean and variance of the difference between B colla (from table) and B colu is determined for all 14 diets for each trial combination of dp, dpi and to, and the best values for dp, dpj and w chosen to minimize both the mean and the variance. These values turn out to be dp = +5, dN = +2 and CO = -0.75. Figure All.l shows a plot of the difference between the estimated and calculated collagen values for each diet for this particular DIFF, and it can be seen that, except for one point, the others are correctly estimated to within 1 or 1.5%o. 

---