Non-parametric statistical tests

The obtained results are reported in the following tables medians and non-parametric statistical tests were used because data did not approach a Gaussian distribution. 

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).

The principal measure taken is the animal s latency to cross to the dark compartment at T2. This score provides an estimate of the animal s retention of the shock received at Tl. The latencies measured at T2 have a 180 second cut-off. The scores in the control group are therefore abnormally distributed because of the presence of numerous ceiling scores. It is therefore essential to apply non-parametric statistics, for example the Mann-Whitney U-test, to analyze the data. 

Urine volume, electrolyte concentrations and osmolality are averaged for each group. The values are plotted against time to allow comparison with pretreatment values as well as with water controls and standards. The non-parametric U-test is used for statistical analysis. 

Hypothesis testing techniques should include ANOVA, regression analysis, multivariate techniques and parametric and non-parametric statistics. 

The non-parametric Eriedman test was used to evaluate the significance of differences between the three soil components for a given site, metal and extractant, as well as between sites for a given soil component. Non-parametric statistics were chosen because of the small number of samples available for the statistical analyses. Indeed, the sample numbers were not high enough to meet... 

Parametric statistics (t-test, ANOVA) are by far the most commonly used in studies of sensory-motor/psychomotor performance due, in large part, to their availability and ability to draw out interactions between dependent variables. However, there is also a strong case for the use of non-parametric statistics. For example, the Wilcoxon matched-pairs statistic maybe preferable for both between-group and within-subject comparisons due to its greater robustness over its parametric paired f-test equivalent, with only minimal loss of power. This is important due to many sensory-motor measures having very non-Gaussian skewed distributions as well as considerably different variances between normal and patient groups. 

Danish mathematician George Rasch developed the Rasch model (5). Researchers can use the Rasch model to develop tests and surveys, monitor the quality of survey or test data, improve test or survey items, and calculate an equal interval total score for both test takers and survey respondents. When researchers evaluate data using parametric statistical tests (e.g., t-test, ANOVA), they assume that score data is " equal interval. We can use the Rasch analysis software to convert non-equal interval data into equal interval data. In recent years, evaluators have used the Rasch model for large-scale, assessment projects such as the evaluation of reform in the Chicago Public Schools (6)... 

Monte Carlo Filtering (MCF) is based on dividing the output sample in two or more subsets according to some criterion and testing if the inputs associated to those subsets are different or not. The tools used are non-parametric statistics and their associated tests.The following ones have been considered in this study the two-sample Smirnov test and the Mann-Whitney test. 

In non-parametric statistics the usual measure of dispersion (replacing the standard deviation) is the interquartile range. As we have seen, the median divides the sample of measurements into two equal halves if each of these halves is further divided into two the points of division are called the upper and lower quartiles. Several different conventions are used in making this calculation, and the interested reader should again consult the bibliography. The interquartile range is not widely used in analytical work, but various statistical tests can be performed on it. 

The sign test is among the simplest of all non-parametric statistical methods, and was first discussed in the early eighteenth century. It can be used in a number of ways, the simplest of which is demonstrated by the following example. 

It is apparent from this example that the sign test will involve the frequent use of the binomial distribution with p = q =. So common is this approach to non-parametric statistics that most sets of statistical tables include the necessary data, allowing such calculations to be made instantly (see Table A.9). Moreover, in many practical situations, an analyst will always take the same number of readings or samples, and will be able to memorize easily the probabilities corresponding to the various numbers of -t or - signs. 

In the analysis stage, appropriate parametric and non-parametric statistics were employed to identify significant changes and effect sizes. Residual gain analyses for both attitude and cognitive tests identified individual teacher outcomes. Similarities between teachers were explored by cluster analysis. Pupil results for each cluster were then examined with respect to the changes shown by their teachers. 

ABSTRACT There are many properties correlated with maintenance costs. Due to minimize the maintenance costs we should recognize them and assess the level of influence and choose them of which the mitigation is the most cost effective. One of the most important property is lifetime which is assessed using statistical methods during accelerated tests. And may be improved based on real data. The parametric and non-parametric statistics could be applied to assessment the lifetime of aviation items. In the paper their advantages and disadvantages were recognized. 

In terms of summary statistics, means are less relevant because of the inevitable skewness of the original data (otherwise we would not be using non-parametric tests). This skewness frequently produces extremes, which then tend to dominate the calculation of the mean. Medians are usually a better, more stable, description of the average . 

Non-parametric methods statistical tests which make no assumptions about the distributions from which the data are obtained. These can be used to show iifferences, relationships, or association even when the characteristic observed can not be measured numerically. 

There are two main families of statistical tests parametric tests, which are based on the hypothesis that data are distributed according to a normal curve (on which the values in Student s table are based), and non-parametric tests, for more liberally distributed data (robust statistics). In analytical chemistry, large sets of data are often not available. Therefore, statistical tests must be applied with judgement and must not be abused. In chemistry, acceptable margins of precision are 10, 5 or 1%. Greater values than this can only be endorsed depending on the problem concerned. 

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. 

Two non-parametric methods for hypothesis testing with PCA and PLS are cross-validation and the jackknife estimate of variance. Both methods are described in some detail in the sections describing the PCA and PLS algorithms. Cross-validation is used to assess the predictive property of a PCA or a PLS model. The distribution function of the cross-validation test-statistic cvd-sd under the null-hypothesis is not well known. However, for PLS, the distribution of cvd-sd has been empirically determined by computer simulation technique [24] for some particular types of experimental designs. In particular, the discriminant analysis (or ANOVA-like) PLS analysis has been investigated in some detail as well as the situation with Y one-dimensional. This simulation study is referred to for detailed information. However, some tables of the critical values of cvd-sd at the 5 % level are given in Appendix C. 

The Wilcoxon s Rank-Sum Test (WRST) is a non-parametric alternative. The WRST is robust to the normal distribution assumption, but not to the assumption of equal variance. Furthermore, this test requires that the two groups of data under comparison have similarly shaped distributions. Non-parametric tests typically suffer from having less statistical power than their parametric counterparts. Similar to the /-test, the WRST will exhibit false positive rate inflation across a microarray dataset. It is possible to use the Wilcoxon test statistic as the single filtering mechanism however calculation of the false positive rate is challenging (48). 

A non-parametric test is the Reverse Arrangements Test, in which a statistic, called 2I, is calculated in order to assess the trend of a time series. The exact procedure of calculation as well as tables containing confidence intervals is described in Bendat Piersol (2000). If A is too big or too small compared to these standard values could mean there is a significant trend in the data, therefore the process should not be considered in steady state. The test is applied sequentially to data windows of a given... 

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