Fisher variance ratio

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

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

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

The Fisher variance ratio test will compare two variances, but not more than two. Suppose we have a group of ten machines turning out batches of Some product, and we measure some quality x on each batch. Suppose we suspect that some machines manufacture the product more regularly than others, i.e. that... 

Accordingly, we wish to test whether the Between Column Mean Square is significantly greater than the Within Column Mean Square. This can be done with the Fisher variance ratio test, discussed earlier in Chapter IV (a). 

In Section 6.4, it was shown for replicate experiments at one factor level that the sum of squares of residuals, SS can be partitioned into a sum of squares due to purely experimental uncertainty, SS, and a sum of squares due to lack of fit, SSi f. Each sum of squares divided by its associated degrees of freedom gives an estimated variance. Two of these variances, and were used to calculate a Fisher F-ratio from which the significance of the lack of fit could be estimated. 

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). 

The test of significance for this type of problem is due to Fisher (Fisher actually dealt with the natural logarithm of the ratio of the square roots of the variances, which he called z, but here we will use the simple variance ratio which is denoted by F). 

The various mean squares are tested for significance with Fisher s variance ratio test. Here we are principally interested in the Row and Column effects,... 

A more powerful criterion of goodness of fit is the F-test, pioneered by Fisher (1925), of the variance ratio... 

The F test In contrast to the t test, which is a comparison of means, the F test is a comparison of variances. The ratio between the two variances to be compared is the variance ratio F (for R. A. Fisher), defined by... 

Fischer-Formel/ Fischer-Projektionsformel Fischer projection, Fischer formula, Fischer projection formula Fisher-Verteilung/F-Verteilung/ Varianzquotientenverteilung variance ratio distribution, F-distribution, Fisher distribution fixieren (mit Fixativ harten) fix (befestigen/fest machen) affix, attach... 

Fisher statistic, Fisher value ratio of variances for two models to be compared. It can be overall or partial F value. The overall Fisher statistic tests the entire equation, whether all coefficients are significant in the model. The partial F value is used to test whether the incriminated variable is significant in the model. 

The variance ratios in the last column are compared with those found by entering the variance ratio tables (Fisher and Yates ) with the appropriate d.f. and indicate that the doses have had a highly significant effect, but that there is little variation due to runs. 

Mendal et al. (1993) compared eight tests of normality to detect a mixture consisting of two normally distributed components with different means but equal variances. Fisher s skewness statistic was preferable when one component comprised less than 15% of the total distribution. When the two components comprised more nearly equal proportions (35-65%) of the total distribution, the Engelman and Hartigan test (1969) was preferable. For other mixing proportions, the maximum likelihood ratio test was best. Thus, the maximum likelihood ratio test appears to perform very well, with only small loss from optimality, even when it is not the best procedure. 

The null hypothesis (statistical terminology), states that if there are no significant differences in the variances, then the ratio must be close to 1. Reference should therefore be made to the Fisher-Snedecor values of F, established for a variable number of observations (Table 22.3). If the calculated value for F exceeds that found in the table, the means are considered to be significantly different. Since the variability is greater than si, then the second series of measurements is therefore the more precise one. 

Fisher s test (F = MSuop IMS Kg) allows the two estimates of the variance, s/ and to be compared. A ratio much larger than 1 would indicate to us that the estimation j/ is too high and that therefore the model is inadequate, certain necessary terms having been omitted. In Fisher s tables, a value F, = 6.60 corresponds to a significance level of 0.05 (5%). Two cases may be envisaged ... 

Z. (1) The symbol for a standardized value of a Normal variable. (2) The symbol for the test statistic in Whitehead s boundary approach to sequential clinical trials (see Chapter 19). (3) The symbol which R.A. Fisher used to designate half the difference of the natural logarithms of two independent estimates of variances when comparing them. (Nowadays we tend to use the ratio instead, which we compare to the F-distribution.) (4) The last entry in this glossary. 

The discriminant power of the variables has been evaluated using Wilk s A, F (Fisher statistics), andp-level parameters. The Wilk s A is computed as the ratio of the determinant of the within-group variance/covariance matrix to the determinant of the total variance/covariance matrix Its values ranges from 1 (no discriminatory power) to 0 (perfect discriminatory power). 

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