Statistical analyses Kruskal-Wallis test

Fig. 6 Effect of methylphenidate on Acquisition of the PAR in juvenile rat pups. Juvenile rat pups (day 15-16) were tested for acquisition of a multi-trial PAR. Littermates were equally divided into vehide or drug treatment groups. Methylphenidate salt was given ip at a dose of 3 mg/kg (base), 30 mins prior to training. Animals were returned to their home cage with their littermates for the intertrial time period. indicates statistically significant differences between drug-treatment group and vehide-treatment group at the specific trial. Non-parametric statistical analysis (Kruskal-Wallis test) was conducted on median latencies (sec). Mean + SEM entry latendes (sec) are presented (n = 12-18/group).

For statistical analysis, fetal abnormality values belong to two types those where at least 50% of litters have one or more fetuses affected, and those where most litters have no affected fetuses. For the first type, the incidences (percentage of affected fetuses within that litter) are analyzed by the Kruskal-Wallis test (13) for the second type, the number of litters with affected fetuses is compared with the number with no affected fetuses by Fisher s Exact test (14). 

With the one-way ANOVA, most statistical packages implement a series of followup tests to determine exactly where any differences lie. Similar procedures exist to allow follow-up after a significant Kruskal-Wallis test, but unfortunately they are not widely implemented in statistical packages. There would be no point in doing so in the present case, but if another data set proves significant and you want to perform follow-up tests, you will either have to resort to a very powerful (and probably not very friendly) statistical package, or do the calculation manually. The latter is tedious, but recipes are available. (A clear account is available in Zar J.H., 1999, Biostatistical Analysis, Prentice Hall, NJ pp. 223-226.)... 

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. 

General guidelines for statistical analysis were presented previously (see section 5.1.3). Where continuous variables, such as consumption, are measured, means are compared using parametric tests (e.g., -test, ANOVA) or nonparamet-ric tests (e.g., Wilcoxon two-sample test or the Kruskal-Wallis test) as appropriate. For simple choice tests, the G-test or Fisher s exact test (Sokal Rohlf 1995) are often used to test for deviations of the observed pattern of choices from a random pattern. 

The analysis of rank data, what is generally called nonparametric statistical analysis, is an exact parallel of the more traditional (and familiar) parametric methods. There are methods for the single comparison case (just as Student s t-test is used) and for the multiple comparison case (just as analysis of variance is used) with appropriate post hoc tests for exact identification of the significance with a set of groups. Four tests are presented for evaluating statistical significance in rank data the Wilcoxon Rank Sum Test, distribution-free multiple comparisons, Mann-Whitney U Test, and the Kruskall-Wallis nonparametric analysis of variance. For each of these tests, tables of distribution values for the evaluations of results can be found in any of a number of reference volumes (Gad, 1998). 

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. 

Fig. 45 A Statistical analysis of the density of BrdU+ cells in SVZa on postischemic day 9. p < 0.001 versus anterior, caudate, and dorsal SVZa p < 0.05 versus caudate and dorsal SVZa one-way ANOVA followed by Tukey-Kramer post hoc. B Proportions of BrdU+ cells retaining presence in SVZa. Densities of BrdU+ cells on day 44 after sham/ischemia were calculated as a percentage of the densities of day 9 after sham/ischemia. p < 0.05 versus respective sham-operated control Kruskal-Wallis or Mann-Whitney tests...

Statistical Analysis. T-tests, Kruskall-Wallis and analyses of variances were performed using SAS, a statistical computer software program developed by Statistical Analysis Systems, Inc. 

All data are presented as means S.E. A statistical analysis was performed using the Kruskal-Wallis and Steel test. A probability value of less than 0.05 was considered significant. 

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