R-test

Gillis, J. R., Testing for Explosiveness of Dusts, Loss Prevention, Vol. 2, Amer. Inst. Chem. Engr., 1968, p. 34. 

Comparisons between data sets (r test, multiple range test, F test, simple ANOVA),... 

The example demonstrates that all relevant information must be used ignoring the fact that the PM and HPLC measurements for / = 1. .. 5 are paired results in a loss of information. The paired data should under all circumstances be plotted (Youden plot. Fig. 2.1, and Fig. 1.23) to avoid a pitfall it must be borne in mind that the paired r-test yields insights only for the particular (addi-... 

The situation of having more than two series of measurements to compare is frequently encountered. One possibility resides in doing a r-test as discussed above for every pairing of measurement series this not only is inefficient, but also does not answer the question of whether all series belong to the same population. The technique that needs to be employed is discussed in detail later (Section 1.5.4) and is fully integrated into program MULTI. The same howto format of questions and instructions is used as previously. 

Up to this point it was assumed that the number of determinations n was sufficient for a given statistical test. During the discussion of the r-test (case a), an issue was skirted that demands more attention Is Xmean different from... 

Program FACTORS in Section 5.2.3 lists the exact procedure, which is only. sketched here. Table 3.2, for each factor and interaction, lists the observed effect, and the specific effect, the latter being a slope or slopes that make(s) the connection between any factor(s) and the corresponding effect. A r-test is conducted on the specific effects, i.e., t = Ej/(Ax se), where Ej is the observed effect y, - yi, se its (estimated) standard deviation, and Ax the change in the factor(s) that produced the effect. If t is larger than the... 

Results The uncertainties associated with the slopes are very different and n = H2, so that the pooled variance is roughly estimated as (V + V2)/2, see case c in Table 1.10 this gives a pooled standard deviation of 0.020 a simple r-test is performed to determine whether the slopes can be distinguished. (0.831 - 0.673)/0.020 = 7.9 is definitely larger than the critical /-value for p - 0.05 and / = 3 (3.182). Only a test for H[ t > tc makes sense, so a one-sided test must be used to estimate the probability of error, most likely of the order p = 0.001 or smaller. 

Equations) gives these equations in a common format because not all r-test procedures return tbe same number of degrees of freedom or the same r-value, the interpretations can slightly differ. For each of the four combinations of N] (=, 7 ) Nj and Vi (=, 7 ) V2 all equations that apply are used and the corresponding results and interpretations are displayed. 

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. 

If P and P are free and contain at most r tests, a path with at most nm + 1 assignment statements is altogether of length at most r(nm + 2). Thus we need only test paths of length up to r(nm +2) and they are finite in number. Hence ... 

To give a uniform definition, let us represent TRUE by 1 and FALSE by 0 and define the interpreted value language L (S) of a monadic recursion scheme S with r tests T-, ...,T as the set of all words of the farm ... 

Z = F or Z = f for a basis function f ), causes the machine to collect in its finite state control the outcomes of the r tests under the interpretation described by the input word. 

THEOREM 8.4 The reversal of the interpreted value language of a monadic recursion scheme with r tests is an (r+1)-definite deterministic context-free language. 

Murray J.N., Yaffe M.R., Testing aqueous caustic electrolyzers at high temperatures, Int. ]. Hydrogen Energ., 4,193-204,1979. 

Gray, H.R., Testing for hydrogen environment embrittlement experimental variables, in Hydrogen Embrittlement Testing, American Society for Testing and Materials, Special Technical Publication ASTM STP-543, Philadelphia, PA, 1974, p. 133. 

Source Data from Jaklin, J., Krenmayr, P., and Varmuza, K., Fresenius Z. Anal. Chem., 331,479, 1988. Note The concentrations, in percent of all 14 PAHs, are used as variables in exploratory data analysis. The mean concentrations for the samples in Vienna and Linz are given, as well as the p-values for the r-test and the [/-test. 

Klopffer, W., Haag, F., Kohl, E.G., and Frank, R. Testing of the abiotic degradation of chemicals in the atmosphere the smog chamber approach, Ecotoxicol. Environ. Saf., 15(3) 298-319,1988. 

Traditionally, the determination of a difference in costs between groups has been made using the Student s r-test or analysis of variance (ANOVA) (univariate analysis) and ordinary least-squares regression (multivariable analysis). The recent proposal of the generalized linear model promises to improve the predictive power of multivariable analyses. 

A basic assumption underlying r-tests and ANOVA (which are parametric tests) is that cost data are normally distributed. Given that the distribution of these data often violates this assumption, a number of analysts have begun using nonparametric tests, such as the Wilcoxon rank-sum test (a test of median costs) and the Kolmogorov-Smirnov test (a test for differences in cost distributions), which make no assumptions about the underlying distribution of costs. The principal problem with these nonparametric approaches is that statistical conclusions about the mean need not translate into statistical conclusions about the median (e.g., the means could differ yet the medians could be identical), nor do conclusions about the median necessarily translate into conclusions about the mean. Similar difficulties arise when - to avoid the problems of nonnormal distribution - one analyzes cost data that have been transformed to be more normal in their distribution (e.g., the log transformation of the square root of costs). The sample mean remains the estimator of choice for the analysis of cost data in economic evaluation. If one is concerned about nonnormal distribution, one should use statistical procedures that do not depend on the assumption of normal distribution of costs (e.g., nonparametric tests of means). 

Jeanmougin M et al (2010) Should we abandon the r-test in the analysis of gene expression microarray data a comparison of variance modeling strategies. PLoS One 5 el2336. doi 10.1371/journal.pone.0012336... 

In the U.S.S.R., tests to authorize permitted explosives for use in dangerous mines are carried out according to the standard specification—GOST 7140-54. 

Values not included. Outliers were tested as follows. For copper, each extreme value was tested. The test used to decide if the extreme value were in error was the r test as applied by Massey 20), Dixon 21), and Proschan 22). The test was applied at the 0.5 level of significance thus, a true value would be rejected 5% of the time. Formulas used were as follows ... 

Comp. Reg. % of rechallenge tumor regressed mice completely at 14 days after the tumor inoculation was calculated as (number of mice without a rechallenge tumor / number of used mice) x 100. significantly different from PBS group in each experiment by students r-test. 

Perez Ara (Ref 26, p65) describes another bomb, called "Burlot-Malsallez . The bomb represented here in Fig may also be used for calor-imerri r tests... 

Consistency of NC Test, Same as Viscosity Test of Nitrocellulose (See Vol 2 of this Encycl, p C122-R, test h)... 

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