ANOVA tests

Do the simple ANOVA test (Section 1.5.6) to detect variability between the group means in excess of what is expected due to chance alone. 

Analysis of variance (ANOVA) tests whether one group of subjects (e.g., batch, method, laboratory, etc.) differs from the population of subjects investigated (several batches of one product different methods for the same parameter several laboratories participating in a round-robin test to validate a method, for examples see Refs. 5, 9, 21, 30. Multiple measurements are necessary to establish a benchmark variability ( within-group ) typical for the type of subject. Whenever a difference significantly exceeds this benchmark, at least two populations of subjects are involved. A graphical analogue is the Youden plot (see Fig. 2.1). An additive model is assumed for ANOVA. 

Table 1.15. Raw Data and Intermediate Results of an ANOVA Test for Simulated Data. (Eq. 1.30)...

Because of the observed homoscedacity, a simple ANOVA-test (see Table 4.8) can be applied to determine whether the means all belong to the same population. If there was any indication of differences among the means, this would mean that the conditioner worked in a position-sensitive mode and would have to be mechanically modified. 

Table 4.38. Effect of Raw Data Rounding on Bartlett and ANOVA Tests...

The standard deviations are not distinguishable (Bartlett test). Conclusions are valid for all three data sets. All means belong to the same population (ANOVA test). Overall result 97.5 3.2 (compound assay). 

ANOVA) if the standard deviations are indistinguishable, an ANOVA test can be carried out (simple ANOVA, one parameter additivity model) to detect the presence of significant differences in data set means. The interpretation of the F-test is given (the critical F-value for p = 0.05, one-sided test, is calculated using the algorithm from Section 5.1.3). 

ANOVA TEST COMPARISONS FOR LABORATORIES AND METHODS (ANOVA s4 WORKSHEET)... 

ANOVA test comparisons (using ANOVA s2 worksheet)... 

This set of articles presents the computational details and actual values for each of the statistical methods shown for collaborative tests. These methods include the use of precision and estimated accuracy comparisons, ANOVA tests, Student s t-testing, The Rank Test for Method Comparison, and the Efficient Comparison of Methods tests. From using these statistical tests the following conclusions can be derived ... 

This Worksheet demonstrates using Mathcad s F distribution function and programming operators to conduct an analysis of variance (ANOVA) test. 

Sections on matrix algebra, analytic geometry, experimental design, instrument and system calibration, noise, derivatives and their use in data analysis, linearity and nonlinearity are described. Collaborative laboratory studies, using ANOVA, testing for systematic error, ranking tests for collaborative studies, and efficient comparison of two analytical methods are included. Discussion on topics such as the limitations in analytical accuracy and brief introductions to the statistics of spectral searches and the chemometrics of imaging spectroscopy are included. 

The One Way ANOVA test was used to determine statistical significance. Input concentrations between summer and the fall winter season were not significant however, for dissolved As and Zn, total As and Zn differences were significant at p < 0.01. 

One-way-ANOVA tests were made to control the quality of the data. To achieve the proposed objectives, multiple comparison of means of the four groups was made by Tukey (p<0,05) test. The Dunnett (p<0,05) test was used to compare the means of three groups of mining sites with the control group (Seaman et al. 1991). Pearson correlation coefficients were also obtained to confirm the tests results. 

The ANOVA test, which is also recommended by the Analytical Methods Committee of The Royal Society of Chemistry (UK), can be generalized to other regression models, and it can be extended to handle heteroscedasticity. For a more detailed prescription and the extension of the test see further reading. 

Prior to cluster analysis, these re-scaled travel experience variables were initially evaluated to determine which ones were relevant in differentiating travel experience levels. Using self-perception of travel experience level as the independent variable, the other 7 travel experience variables were subject to Kruskal-Wallis analysis. This procedure attempted to establish a face validity for using the specified variables to describe travel experience by relating them to the respondents own perception of their travel experience. Kruskal-Wallis analysis, which is the non-parametric equivalent of one-way ANOVA, tests whether several independent samples are from the same population (SPSS Inc., 1999). This test was selected as the correct procedure since heavily skewed data were involved and the Kruskal-Wallis is suitable for this situation (Diekhoff, 1992). The results are presented in Table 3.7. 

If you wish to compare the variances of two sets of data that are normally distributed, use the F-test. For comparing more than two samples, it may be sufficient to use the F max-test, on the highest and lowest variances. The Scheff Box (log-ANOVA) test is recommended for testing the significance of differences between several variances. Non-parametric tests exist but are not widely available you may need to transform the data and use a test based on the normal distribution. 

Statistical analysis. All data are presented as mean SEM. Statistical analysis was performed using the Mann-Whimey and repeated ANOVA tests. Values corresponding to p < 0.05 were considered significant. 

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... 

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