Test for Variance Homogeneity

The measured results are tested for variance homogeneity by means of the multiple variance comparison according to COCHRAN [KRAUSE and METZLER, 1983]  

For potassium and sodium the variance homogeneity can be assumed with a critical probability of an error of the first kind error of a = 0.01. 

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Precision control. A prerequisite for the use of the Shewhart control card is the constancy of the standard deviations. The span control card allows the disclosure of significant differences between the standard deviations of the subgroups and thus represents a test for variance homogeneity. 

There are two methods commonly used for testing the homogeneity the Cochran and the Bartlett tests. The first is an outlier test for variances and the second tests more for the scattering of variances. In the laboratory of the authors the Bartlett criterium (Pearson and Hartley, 1962) is preferred. 

There are several statistical tests to check for variance homogeneity, some of them reviewed by Sayago and Asuero. Most of them are also detailed in many general textbooks and only minor details will be given here. Be careful, because these tests (like almost all statistical tests) are of low power with the small number of replicates we usually perform in laboratories, and are very sensitive to the lack of normality. 

Bartlett s test does not test for normality, but rather homogeneity of variance (also called equality of variances or homoscedasticity). 

Snedecor GW, Cochran WG (1967) Variance test for homogeneity of binormal distribution. Statistical methods, 6th edn. Iowa State University Press, Ames, pp 240-241... 

If a sample has been analyzed by k laboratories n times each, the sample variances of the n results from each laboratory can be tested for homogeneity —that is, any variance outliers among the laboratories can be detected. The ISO-recommended test is the Cochran test. The statistic that is tested is... 

Spreadsheet 2.3. Cochran test for homogeneity of variances in the soil analysis example given in the text. 

The above analysis assumes that the results are normally distributed and without outliers. A Cochran test for homogeneity of variance and Grubbs s tests for single and paired outliers is recommended (see chapter 2). Data from... 

C test standard statistical test for homogeneity of variance. 

The condition of variance homogeneity can be proven with the help of statistical tests (/- -test for quotient of variances at the lower and upper end of the calibration range, or better, in the case of rij>5 by using the Bartlett-test, which includes all of the variances in the calibration range). If variance homogeneity is violated, a weighted least squares regression (WLS) should be used. 

Bartlett s test for homogeneity of variances at 0.5, 1 and 1.5 times the OSHA standard showed that the variances may be pooled. Therefore, the coefficient of variation was calculated from the pooled variances ... 

In case that both data sets to be compared are normally distributed the F-test is applied. The hypothesis of homogeneity of variance of both test series is eliminated when the significance level for homogeneity of variance is 5 %. The t-test for paired and non-paired data is performed when homogeneity of variance is present. In any case, a paired difference test (for paired data) or the U-test (for non-paired data) is likewise carried out (paired of difference test = Wilcoxon test U-test = Wilcoxon-Mann-Whitney or Mann-Whitney test, respectively). 

Homogeneity test of variance (Levene s test) for each dependent variable. 

The wide availability of tests based on the normal distribution and their relative simplicity means you may wish to transform your data to make them more like a normal distribution. Table 41.1 provides transformations that can be applied. The transformed data should be tested for normality as described above before proceeding - don t forget that you may need to check that transformed variances are homogeneous for certain tests (see below). 

If you can assume that your data are normally distributed, the main test for comparing two means from independent samples is Student s f-test (see Boxes 41.1 and 41.2, and Table 41.2). This assumes that the variances of the data sets are homogeneous. Tests based on the t-distribution are also available for comparing paired data or for comparing a sample mean with a chosen value. 

BARTLETT-test for homogeneity of variances (99%J Critical value 11.300 ... 

In terms of the statistical methods of the partial life cycle whole-effluent tests, survival, growth, and reproduction data from the 7 day cladoceran or fish exposure are often analyzed using hypothesis testing to determine acceptable concentrations. In order to determine the appropriateness of using parametric statistical methods, the data are first tested for normality of distribution and homogeneity of variance, for which the US EPA recommends the use of Shapiro-Wilk s test and Bartlett s test, respectively. Kolmogorov test for normality and Levine s test for homogeneity can be also used for these purposes. Dunnett s anova test is typically used for a... 

The linearity test based on the XPT 90-210 (French Standard, 1999) was checked by performing a homogeneity test of variances based on the analysis of 5 standard solutions (ranging from 25 to 122 pg/L) using five different electrodes for each metal Cu, Pb and Cd. The application of the linearity test which has taken into account the five calibration curves gave correct results and revealed no problem of linearity. 

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