Welch test

If the variances sf and sf, differ significantly, a generalized (-lest (tw test) according to Welch [1937] can be applied ... 

Statistical analysis For statistical analysis of the behavioral tests an analysis of variance (two-way ANOVA) was used. For the symptomatology a Fisher exact probability test or an unpaired t-test with Welch s correction was used. In all tests p values <0.05 were considered significant. 

Blood AChE-inhibition The mean blood AChE-inhibition after pretreatment, measured as a percentage of the baseline value, was 20-35 % (see Table 2). The AChE-inhibition measured one hour after soman followed by a post-intoxication therapy, was significantly lower in all groups (t-test with Welch s correction, p < 0.05). The inhibition of AChE after soman was less in animals pretreated with PYR or with PHY combined with PC (resp. 85.5 1 % and 89.4 2 %). 

The treatment means will be compared using the unpaired t-test. If, however, the group standard deviations are significantly different according to the F-test, then the comparison of the means will be based on Welch s form of the unpaired t-test. ... 

Gamer, R.C., Welch A. Pickering. C. (1981) Mutagenic activity of 42 coded compounds in the /7wone//6z/microsome assay. In de Serres. F.J. Ashby, J., eds, Evaluation of Short-Term Tests for Carcinogens. Report of the International Collaborative Program (Progress in Mutation Research, Vol. 1). Amsterdam Elsevier, pp. 280-284... 

Where the problem is solely one of unequal SDs, there is a minor variant of the test, Welch s approximate t that does not have this requirement. In fact, in Minitab, this is the default test, and if you want the classical f-test, you will have to select it (see the web site for details). 

To test the differences among sites and among seasons, analysis of variance (ANOVA) techniques were utilized. For the one-way ANOVA the standard F-test was augmented by the Welch and Browne-Forsythe tests (12), in order to account for the unequal variances of the compared groups (sites or seasons). Throughout this study a significance level of 0.05 was utilized. All the tests were performed with the BMDP statistical routines (13). 

Kidwell, D. A. and Blank, D. L., Mechanisms of incorporation of drugs into hair and the interpretation of hair analysis data, in NIDA Research Monograph, Cone, E. J. and Welch, M., Eds., 1994. Su, T. P, Tsai, W. J., Joseph, R., Tsao, L. L, and Cone, E. J., Cocaine binds in a sterospecific, saturable manner to hair a precaution on hair testing for forensic purposes, presented at College on Problems of Drug Dependence, Palm Beach, June 18-23,1994. 

Welch et al. evaluated analytical procedures and environmental issues. They investigated methods for the extraction and detection of cocaine, some of its metabolites, morphine, and codeine from hair. They concluded from a round-robin study that extractions with 0.1 ATHCL are as efficient to remove the target compounds from hair as enzymatic digestion that dissolve the hair. GC/MS with either El or Cl provides accurate determinations of the targeted compounds. External contamination by powdered or vapor-deposited cocaine was incompletely removed by all approaches tested, making it difficult to differentiate incorporated drug from external contamination. This was also proved in extensive laboratory experiments by Wang and Cone. ... 

There have been a few reports in the literature where hair has been analyzed directly for cocaine analytes, without analyte isolation. The earliest report was by Valente et al., who compared direct incubation of hair with the antiserum in an RIA test with acid, base, and methanol isolation. Although cocaine analytes were detected using this method, only 31% were recovered. In 1993, Kid well and Welch etal. noted that cocaine analytes could be observed in hair using tandem mass spectrometry (MS/MS) with no prior isolation. The washed samples were rapidly heated and the vaporized material analyzed. However, Welch et al. report that unambiguous results were only obtained when the hair samples were cryogenically powdered, which required more effort than preisolation of the analytes. 

Welch SP, Dewey WL (1990) The activity of several peptide fragments of parathyroid hormone, alone and in combination with salmon caldtonin and morphine, in antinociceptive tests in the mouse. J Pharmacol Exp Ther 252 140-146... 

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