Comparison tests

MohsAn early (1822) hardness comparison test involved assigning a relative number to aH known materials (usuaHy minerals and pure metals) by virtue of their relative abHity to scratch one another. The results of this classification are not relatable to other properties of materials or to other measures of hardness. As a result of this limited useflilness, the Mohs hardness test is primarily used for mineral identification. Some examples of the Mohs hardness scale, which ranks materials from 1 to 10, are Hsted in Table 6. 

The convergence or divergence of an infinite series is unaffected by the removal of a finite number of finite terms. This is a trivial theorem but useful to remember, especially when using the comparison test to be described in the subsection Tests for Convergence and Divergence. ... 

Comparison Test. A series will converge if the absolute value of each term (with or without a finite number of terms) is less than the corresponding term of a known convergent series. Similarly, a positive series is divergent if it is termwise larger than a known divergent series of positive terms. 

With unprotected comparison test pieces, the corrosion rate was 4 mm a , which from cell current measurements indicated that the self-corrosion was 50%. 

Kister discusses his comparison tests in great detail and presents Figures 20 and 21 for comparison of capacity and efficiency. We quote from his summary as follows (Reproduced with permission of the American Institute of Chemical Engineers, copyright 1994 AlChE, all rights reserved) ... 

Comparison of Sweetness between Trehalose Derivatives and the Corresponding Monosaccharide Analogs by Paired Comparison Test d... 

If the 3- and 4-hydroxyl groups constitute the Shallenberger AH,B unit, it is possible that a disaccharide (such as a,a-trehalose) and methyl a-D-glucopyranoside may possess the same molar sweetness. By a ranking procedure, and using trained panelists in a Paired Comparison Test, it was, indeed, found that isomolar solutions of these two sugars are equi-... 

Comparison of Sweetness between Reducing Disaccharides and Monosaccharides" by Paired Comparison Test on Sugar Solutions... 

In the first set of comparison test runs, a 0. lOg of each sulfated sample was examined by TPR in a soak (300°C)-ramp (up to 850°C at 20°C/min.) mode, using propane at 14.2 ml/min as the reactant. In the second set of propane-TPR comparison test mns, another 0. lOg of each sulfated sample was examined by a soak (300°C)-ramp (30°C/min.)-soak (up to 530°C) mode. The reaction products such as SO and HjS released during the course of a TPR run were determined by means of mass spectrometry (Hiden Analytical, HAL-2) in MID mode, monitoring mass numbers 48 for SO fragment from SOj, and 34 for H S. 

In paired comparison tests two different samples are presented and one asks which of the two samples has most of the sensory property of interest, e.g. which of two products has the sweetest taste (Fig. 38.3). The pairs are presented in random order to each assessor and preferably tested twice, reversing the presentation order on the second tasting session. Fairly large numbers (>30) of test subjects are required. If there are more than two samples to be tested, one may compare all possible pairs ( round robin ). Since the number of possible pairs grows rapidly with the number of different products this is only practical for sets of three to six products. By combining the information of all paired comparisons for all panellists one may determine a rank order of the products and determine significant differences. For example, in a paired comparison one compares three food products (A) the usual freeze-dried form, (B) a new freeze-dried product, (C) the new product, not freeze-dried. Each of the three pairs are tested twice by 13 panellists in two different presentation orders, A-B, B-A, A-C, C-A, B-C, C-B. The results are given in Table 38.3. 

The results of such multiple paired comparison tests are usually analyzed with Friedman s rank sum test [4] or with more sophisticated methods, e.g. the one using the Bradley-Terry model [5]. A good introduction to the theory and applications of paired comparison tests is David [6]. Since Friedman s rank sum test is based on less restrictive, ordering assumptions it is a robust alternative to two-way analysis of variance which rests upon the normality assumption. For each panellist (and presentation) the three products are scored, i.e. a product gets a score 1,2 or 3, when it is preferred twice, once or not at all, respectively. The rank scores are summed for each product i. One then tests the hypothesis that this result could be obtained under the null hypothesis that there is no difference between the three products and that the ranks were assigned randomly. Friedman s test statistic for this reads... 

Fig. 38.3. Paired comparison test two different products are presented and the assessor has to indicated the one that has most of a specified attribute.

METH-induced changes in neuropeptide levels, selective Dj (SCH 23390) and D2 (sulpiride) dopaminergic receptor antagonists were coadministered. The results are expressed as percent of control to facilitate comparisons each value represents the mean SEM of five to seven animals. Data were subjeeted to either a Student s r-test (figures 4 and 5) or ANOVA analysis followed by a multiple comparisons test (figures 1, 2, and 3). Signifieanee was set at the. 05 level. 

Part 3 Testing for systematic error in each method by performing a comparison test for a set of measurements versus the known True Value ... 

TESTING FOR SYSTEMATIC ERROR IN A METHOD COMPARISON TEST FOR A SET OF MEASUREMENTS VERSUS TRUE VALUE - SPIKED RECOVERY METHOD (COMPARE 71 WORKSHEET)... 

COMPARISON TEST FOR A SINGLE SET OF MEASUREMENTS VERSUS A TRUE ANALYTICAL RESULT... 

Paint technologies, 18 54-55, 56 Paint viscosity, measuring, 18 69 Paired comparison test, 11 512 Paired synthesis, of phthalide and 4.4-butylbenzaldehyde, 9 680-681 PAI resins, properties of, 10 215t Pair production process, 21 313 Palatinit, 12 44... 

Analysis of variance was the statistical model used with preplanned comparison testing for significant differences by the least square means method. 

Group comparison tests for proportions notoriously lack power. Trend tests, because of their use of prior information (dose levels) are much more powerful. Also, it is generally believed that the nature of true carcinogenicity (or toxicity for that matter), manifests itself as dose-response. Because of the above facts, evaluation of trend takes precedence over group comparisons. In order to achieve optimal test statistics, many people use ordinal dose levels (0,1,2..., etc.) instead of the true arithmetic dose levels to test for trend. However, such a decision should be made a priori. The following example demonstrates the weakness of homogeneity tests. 

Biologically meaningful and easier to resolve contrasts and multiple comparison tests. 

The distribution-free multiple comparison test should be used to compare three or more groups of nonparametric data. These groups are then analyzed two at a time for any significant differences (Hollander and Wolfe, 1973, pp. 124-129). The test can be used for data similar to those compared by the rank-sum test. We often employ this test for reproduction and mutagenicity studies (such as comparing survival rates of offspring of rats fed various amounts of test materials in the diet). 

For relative comparisons, tests at a controlled held site resulted in almost complete recovery of kerosene from sand after 126 pore volumes of steam flushing. An EPA SITE program reported 85 to 99% removal of chlorinated VOCs from clay... 

Further discussion of method validation can be found in Chapter 7. However, it should be noted from Table 11 that it is frequently desirable to perform validation experiments beyond ICH requirements. While ICH addresses specificity, accuracy, precision, detection limit, quantitation limit, linearity, and range, we have found it useful to additionally examine stability of solutions, reporting threshold, robustness (as detailed above), filtration, relative response factors (RRF), system suitability tests, and where applicable method comparison tests. 

One uses ANOVA when comparing differences between three or more means. For two samples, the one-way ANOVA is the equivalent of the two-sample (unpaired) t test. The basic assumptions are (a) within each sample, the values are independent and identically normally distributed (i. e., they have the same mean and variance) (b) samples are independent of each other (c) the different samples are all assumed to come from populations having the same variance, thereby allowing for a pooled estimate of the variance and (d) for a multiple comparisons test of the sample means to be meaningful, the populations are viewed as fixed, meaning that the populations in the experiment include all those of interest. 

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