Variance ratio

Example 12 Suppose Analyst A made five observations and obtained a standard deviation of 0.06, where Analyst B with six observations obtained 5-3 = 0.03. The experimental variance ratio is ... 

Stegun (1964) to give equation 2.6-26, where F (equation 2.6-27) is the variance ratio distribution function and Q is the cumulative integral over F. This is similar to the classical result (equation 2 5 73) which means that pseudo-failures, a-1, are added to the failures, M, and pseudo-tests, p-a, are added to the tests, N. 

Line number Source Degrees of freedom Sum of squares Mean square Variance Ratio, F Calculation of sum of squares ... 

Variance ratio, 239 Venn diagram, 177, 192f Viral coat protein, 44, 53 Volume of distribution, 165, 168... 

There are two common methods for comparing results (a) Student s -test and (b) the variance ratio test (F-test). 

Is there any significant difference between the precision of these two sets of results Applying the variance-ratio or F-Test from Eq. (zz) we have ... 

Procedure 1.2 Statistical comparison of the relative precision of two methods using the variance ratio or iFt test... 

These factors are used in the equations given in Table I. The computation requires only that the variance ratios be accurately known. The absolute precision of the method may change from day to day without affecting the validity of either the least-squares curve-of-best fit procedure or the confidence band calculations. (It is not practical to regularly monitor local variances, and errors may develop in variance ratios. Eowever, the error due to incorrect ratios will almost always be much less than the error due to assuming constant variance. Even guessed values of, say, S a concentration are likely to yield more precise data.)... 

The test of this hypothesis makes use of the calculated Fisher variance ratio, F. 

Figure 9.4 Relationships among SS, SS and SS for calculating both the coefficient of multiple determination, R, and the variance-ratio for the significance of the factor effects,...

A statistically valid measure of the effectiveness of the factors in fitting a model to the data is given by the Fisher variance ratio... 

When feature selection is used to simplify, because of the large number of variables, methods must be simple. The univariate criterion of interclass variance/intraclass variance ratio (in the different variants called Fisher weights variance weights or Coomans weights is simple, but can lead to the elimination of variables with some discriminant power, either separately or, more important, in connection with other variables (Fig. 36). 

If we are interested in comparing variance A with variance B, and would like to know whether A is larger than B, and also whethej A is smaller than B, we use a two-tailed test on the variance ratio. F% will be the ratio of variance A to variance B. Fz will be the ratio of variance B to variance A. Both these ratios are then... 

In evaluating two testraethods for repeatability or reproducibility, the variances (standard deviation squared) of the two can be com pared by means of the variance ratio or F test. This is a tried and true statistical technique which has many other uses, as well as being a critical part of analysis of variance. 

F-tost (The Variance Ratio Test) a method for determining, with a given degree of probability, whether the variances of two populations differ significantly from one another ... 

Variance ratio test a test used to determine the difference in variability between two sets of deta. Used in the analysis of variance to compare variation due to a perticular factor with the experimental error. 

The variance ratio (F value) is not readily calculated because replicated data are not available to allow the residual error term to be evaluated. However, it is usual practice to use the interaction data in such instances if the normal probability plot has shown them to be on the linear portion of the graph. By grouping the interaction terms from Table 7 as an estimate of the residual error,... 

If it is assumed that the pooled run variance is a reasonable estimate for the residual variance. Table 7 can be reworked and the variance ratios (F values) calculated for each of the effects. The results of this rework are shown in Table 10. This approach confirms that the methanol effect is the largest by a very long way. The F value (1,8 df) is 5.32. Whilst this confirms that A is not significant. 

The test of this hypothesis makes use of the calculated Fisher variance ratio, F. DF ,DFd = S lof/Spe (6-27)... 

Figure 9.5. Relationship between. SS]of and SSpc for calculating the variance-ratio for the significance of the lack of fit, F p n fy...

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