Bartlett’s Test

Provided that the m variances Vj - sj are roughly equal (Bartlett s test, see Section 1.7.3), the m means are ordered (cf. subroutine SORT, Table 5.17). The smallest mean has index 1, the largest has index m. A triangular matrix (see Tables 4.9, 4.10) is then printed that gives the m (m- l)/2 differences AXmean.wi = Xmean.M Xmean.i for all possible pairings. Every element of the... 

Once the new experiment has been conducted, all models are tested for adequacy. Depending on our knowledge of o2 we may perform a y2-test, an F-test or Bartlett s % -test (when is completely unknown). The first two tests have been... 

The above two objectives, data examination and preparation, are the primary focus of this section. For data examination, two major techniques are presented the scattergram and Bartlett s test. Likewise, for data preparation (with the issues of rounding and outliers having been addressed in a previous chapter) two techniques are presented randomization (including a test for randomness in a sample of data) and transformation. Exploratory data analysis (EDA) is presented and briefly reviewed later. This is a broad collection of techniques and approaches to probe data, that is, to both examine and to perform some initial, flexible analysis of the data. 

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

This test could be considered as a two group equivalent of the Bartlett s test. 

ANOVA is robust for moderate departures from equality of variances (as determined by Bartlett s test) if the sample sizes are approximately equal. 

BARTLETT S TEST for homogeneity of CV s is applied in order to test the feasibility of "pooling the coefficients of variation" for any set of 18 generated samples (i.e., 6 at each of the 0.5, 1, and 2X OSHA standard levels). The following equation for the Chi-square, with 2 degrees of freedom, was used ... 

In order to pass Bartlett s test at the 1% significance level, chi-square must be less than or equal to 9.21 (chi-square has 2 degrees of freedom). 

In an experiment to determine the effects of sample size and amount ofliquid phase on the height equivalent to a theoretical plate (HETP) in gas chromatography, it was necessary to utilize solid support material from different batches. It was therefore imperative that the resulting data be checked for homogeneity prior to attempting to develop any quantitative expressions regarding the effects of these variables on HETP. Several sets of data points were selected at random and examined using Bartlett s test. 

In order to test the feasibility of pooling the coefficients of variation, Bartlett s test for homogeneity of CV s was applied. The CV jp may be pooled at the 1% significance level for "n" sets of data, if x 2.91, where... 

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 ... 

A more general form of Bartlett s test, for the case where the several variances being compared have different degrees of freedom, is available, but will not be discussed here. 

The use of Bartlett s Test thus leads to the same conclusion as the control chart for ranges. It requires more calculation, but on the other hand has the advantages of being more sensitive and precise. 

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... 

Table 12.8 Chemostat Kinetics Results from Model Adequacy Tests Assuming a, is Unknown (Bartlett s -test) Performed at a=0.0l Level of Significance...

The test of significance for several variances, whereby an analytical method is applied to several samples or where several methods are to be compared after analyzing the same sample, is generally known as Bartlett s test. Specifically we wish to know whether the several variances could reasonably exist in the same population. 

Bartlett s test, p < 0.01). The variation in urinary iodine is even wider than the variation in thyroid-stimulating hormone (TSH), renowned for its huge variation compared with other biochemical analytes (Andersen et al., 2002b, 2003). 

KMO and Bartlett s tests of the questionnaire show that the value of KMO of the questionnaire is 0.701, more than 0.70, and the Bartlett sphere test shows the value of 2 is 4601.317, degree of freedom is 1770, the significance probability P equals to 0.00, less than 0.05, rejecting null hypothesis, suggesting the existence of a common factor in overall correlation matrix. Factor analysis is suitable. 

An appropriate test of consistency is Bartlett s (1937) (see also Snedecor, 1948) of homogeneity of variances which, in this case, would be applied to the error variances in Table XII. Bartlett s test is made by comparing an adjusted value with the value for an appropriate number of degrees of freedom where ... 

The results of the analysis are given in Table V. One result at 0.5 times the TWA PEL target concentration was an outlier and was excluded from statistical analysis. Experimental justification for rejecting it is that the outlier value was probably due to a spiking error. The coefficients of variation for the three test levels at 0.5 to 2.0 times the TWA PEL target concentration passed the Bartlett s test and were pooled. 

Similar to the PCA, only the significantly different sensory descriptors were used in the CVA. As CVA is a classification technique, an a priori grouping is needed. We chose the most basic model, and used a MANOVA model with only the sample effect. Bartlett s test for the determination of significant canonical dimensions revealed that only the first CV was significantly different (P<0.05). However, a knee in the scree plot was observed after the first two CVs, thus, the first two dimensions were kept for interpretation (data not shown). 

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