ANOVA report

The ANOVA report as shown in Figure 2.2 is generated. The comparison between the F-test result (F) and the critical value (Fcrit) provide a decision concerning the similarity/difference of the groups. 

We will use ANOVA to evaluate potential bias in reported results inherent in the analytical methods themselves, or due to the operators (i.e., location of laboratory) performing the methods. For the next series of articles all computations were completed using MathCad Worksheets [4] written by the authors. The objectives of this next set of articles is to determine the precision, accuracy, and bias due to choice of analytical... 

Table 35-1 illustrates the ANOVA results for each individual sample in our hypothetical study. This test indicates whether any of the reported results from the analytical methods or locations is significantly different from the others. From the table it can be observed that statistically significant variation in the reported analytical results is to be expected based on these data. However, there is no apparent pattern in the method or location most often varying from the others. Thus, this statistical test is inconclusive and further investigation is warranted. 

Table 35-3 illustrates the ANOVA results comparing laboratories (i.e., different locations) performing the same METHOD A for analysis. This statistical test indicates that for the mid-level concentration spiked samples (i.e. 4 and 4 at 3.40 and 3.61% levels, respectively) difference in reported average values occurred. However, this trend did not continue for the highest concentration sample (i.e., Sample No. 6) with a concentration of 3.80%. The Lab 1 was slightly lower in reported value for Samples 4 and 5. There is no significant systematic error observed between laboratories using the METHOD A. 

Table 35-4 reports ANOVA comparing the METHOD B procedure to the METHOD A procedure for combined laboratories. Thus the combined METHOD B analyses for each sample were compared to the combined METHOD A analyses for the same sample. This statistical test indicates whether there is a significant bias in the reported results for each method, irrespective of operator or location. An apparent trend is indicated using this statistical analysis, that trend being a positive bias for METHOD B as compared to... 

The MathCad worksheets used for this Chemometrics in Spectroscopy collaborative study series are given below in hard copy format. Unless otherwise noted, the worksheets have been written by the authors. The text files for the MathCad v7.0 Worksheets used for the statistical tests in this report are attached as Collabor GM, Collabor TV, ANOVA s4, ANOVA s2, CompareT, and Comp Meth. References [1-11] are excellent sources of information of the details on these statistical methods. 

Physico-chemical characteristics of the soils were summarized in Table 1. The values were comparable to that described in the previous reports about the SERS (Doi and Sakurai 2003 Doi et al. 2004 Sakurai et al. 1998). The one-way ANOVA indicated that most of the soil variables significantly reflected the land degradation with high values of bulk density, sand content and exchangeable acidity, and low values of moisture content, pH, OM, base (K, Ca, Mg) contents, EC, CEC, base saturation rate, TN and TC contents, available phosphorus and MPN on the glucose medium with no antibiotics. These results also told that the human activities induced several soil environmental gradients. 

The practical consequence from this is that in the study type under consideration, always the dam/litter rather than the individual fetus is the basic statistical unit (see Chapters 23, 33, 34 and 35). Six malformed fetuses from six different litters in a treated group of dams is much more likely to constitute a teratogenic effect of the test substance than ten malformed fetuses all from the same litter. It is, therefore, important to report all fetal observations in this context and to select appropriate statistical tests (e.g., Fisher s exact test with Bonferroni correction) based on litter frequency. For continuous data, a procedure to calculate the mean value over the litter means (e.g., ANOVA followed by Dunnet s test) is preferred. An increase in variance (e.g., standard deviation), even without a change in the mean, may indicate that some animals were more susceptible than others, and may indicate the onset of a critical effect. 

The most commonly employed univariate statistical methods are analysis of variance (ANOVA) and Student s r-test [8]. These methods are parametric, that is, they require that the populations studied be approximately normally distributed. Some non-parametric methods are also popular, as, f r example, Kruskal-Wallis ANOVA and Mann-Whitney s U-test [9]. A key feature of univariate statistical methods is that data are analysed one variable at a rime (OVAT). This means that any information contained in the relation between the variables is not included in the OVAT analysis. Univariate methods are the most commonly used methods, irrespective of the nature of the data. Thus, in a recent issue of the European Journal of Pharmacology (Vol. 137), 20 out of 23 research reports used multivariate measurement. However, all of them were analysed by univariate methods. 

In the following ANOVA table we report rounded values, it is, therefore, not possible to reproduce the F-values exactly as ratios of the mean sums of the respective line and the residual mean sum of squares (according to Section 2.3) ... 

Data are reported as means S.E.M. and statistical analysis was performed by the Student s t-test or by ANOVA followed by Dunnett s post hoc test, as appropriate. Experimental data were elaborated by means of Prism 3 program (GraphPAD Software for Science, San Diego, CA, USA), and differences were considered statistically significant for P < 0.05. 

Fig. 4. BEO enhances p-Akt levels in the brain cortical tissue from rats subjected to permanent focal cerebral ischemia. Western blot analysis ofphospho-Akt (Ser473) (p-Akt) and total Akt performed using brain cortical homogenates from rats sacrificed 24 h after MCAo shows a trend toward a decrease of p-Akt and total Akt in the ipsilateral (I), ischemic, cortex as compared to contralateral (C), nonischemic, side intraperitoneal administration of BEO (0.5 ml/kg) 1 h before MCAo enhances p-Akt immunoreactivity in the ischemic cortex without increasing total Akt expression. Histograms show the results of the densitometric analysis of the bands corresponding to p-Akt, total Akt, and i3-actin. p-Akt and Akt levels were normalized to the values yielded by /3-actin and Akt phosphorylation was expressed by the ratio of p-Akt/total Akt data are reported as mean S.E.M. (n = 3 per group). Denote P < 0.01 versus contralateral side and denote P < 0.05 and P < 0.01 versus MCAo, ipsilateral side (ANOVA followed by Tukey-Kramer test for multiple comparisons).

Johnson, C. C. (2002). Within site and between site nested analysis of variance (ANOVA) for Geochemical Surveys using MS EXCEL. British Geological Survey, UK, Internal Report No. 

Standard statistical packages for computing models by least-squares regression typically perform an analysis of variance (ANOVA) based upon the relationship shown in Equation 5.15 and report these results in a table. An example of a table is shown in Table 5.3 for the water model computed by least squares at 1932 nm. 

The ANOVA only tested statistical significance. However, Tukey s test reports confidence intervals for the sizes of the various differences, so we can also assess whether any increase in yield that might be achieved by a change of catalyst would be big enough to be of practical significance. 

The grading of reflection reports from the three student populations is analyzed and correlated with a number of other statistics and performance indicators. All data were collected in Microsoft Excel and unported into Statgraphics Centurion XV for further analysis [7], We performed ANOVA tests, multiple range test or Kruskal-Wallis tests, and f-tests on the gathered information. 

In addition to the emission spectrographic data summary in Table tl. the cotKentrations of each of 30 elements were tabulated by core versus depth. These tables ate not included in this report because of the quantity of data. The emission spectrographic data, so tabulated, were statistically analyzed for 23 of the 30 elements listed in Table 11 by ANOVA at the 99% confidence level. The seven elements not analyzed were detected in less than eight samples, and their data precluded the use of analysis of variance. 

Tables with values of F for several distributions are used to determine the significance of this result, or the critical values can be obtained from statistical software. We have provided a table in Appendix 4. For a test of size a = 0.05, the critical value associated with 2 numerator df and 12 denominator df that cuts off the upper 5% of the distribution is 3.89. Although tabled values are helpful at identifying nominal p values (for example, s 0.01) statistical software is required to report the specific p value. Using statistical software, you will find that the actual p value is 0.002. Table 11.4 shows the completed ANOVA table for this example. You will see that the p value is commonly included in a complete ANOVA table.

The data should be reported as specified in the protocol with the requested significant figures. Valid data (those free of gross errors and produced following the protocol) should be submitted to various statistical treatment for outlier detection of mean and variance, and an ANOVA treatment to establish the repeatability and reproducibility figures. All these treatments and their sequence are specified in the lUPAC protocol [2]. The final report should contain all individual and statistical data additional graphical representation e.g. Youden-plots, bar-graphs etc may also be added. 

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