Some Observations on the Wilcoxon Rank Sum Test

This manuscript presents some general comments about the Wilcoxon rank sum test. Even the most casual reader will gather that I am not too impressed with the scientific usefulness of the Wilcoxon test. However, the actual motivation is more to illustrate differences between parametric, semiparametric, and nonparametric (distribution-free) inference, and to use this example to illustrate how many misconceptions have been propagated through a focus on (semi)parametric probability models as the basis for evaluating commonly used statistical analysis models. The document itself arose as a teaching tool for courses aimed at graduate students in biostatistics and statistics, with parts of the document originally written for applied biostatistics classes and parts written for a course in mathematical statistics. Hence, some of the material is also meant to provide an illustration of common methods of deriving moments of distributions, etc

Misconceptions Leading to Choosing the t Test Over the Wilcoxon Mann-Whitney Test for Shift in Location Parameter

There exist many misconceptions in choosing the t over the Wilcoxon Rank-Sum test when testing for shift. Examples are given in the following three groups: (1) false statement, (2) true premise, but false conclusion, and (3) true statement irrelevant in choosing between the t test and the Wilcoxon Rank Sum test

An extension of the Wilcoxon rank sum test for complex sample survey data: Extension of Wilcoxon Rank Sum Test

In complex survey sampling, a fraction of a finite population is sampled. Often, the survey is conducted so that each subject in the population has a different probability of being selected into the sample. Further, many complex surveys involve stratification and clustering. For generalizability of the sample to the finite population, these features of the design are usually incorporated in the analysis. While the Wilcoxon rank sum test is commonly used to compare an ordinal variable in bivariate analyses, no simple extension of the Wilcoxon rank sum test has been proposed for complex survey data. With multinomial sampling of independent subjects, the Wilcoxon rank-sum test statistic equals the score test statistic for the group effect from a proportional odds cumulative logistic regression model for an ordinal outcome. Using this regression framework, for complex survey data, we formulate a similar proportional odds cumulative logistic regression model for the ordinal variable, and use an estimating equations score statistic for no group effect as an extension of the Wilcoxon test. The proposed method is applied to a complex survey designed to produce national estimates of the health care use, expenditures, sources of payment, and insurance coverage

Punctuated chromatin states regulate Plasmodium falciparum antigenic variation at the intron and 2 kb upstream regions

2 kb upstream region FAIRE-Seq signal comparison between var genes and different gene families (P-value is calculated based on Wilcoxon-Rank-Sum test, FDR indicates false discovery rate). (XLSX 53 kb

Vastasyntyneiden SCID-seulonta TREC-analyysin avulla

Tarkoitus: SCIDiä (severe combined immunodeficiency) voidaan seuloa mittaamalla vastasyntyneiden verinäytteestä TREC-kopioiden määrä. Alhaiseen TREC-arvoon perustuva seulonta on jo käytössä monessa eri maassa, mutta ei vielä Suomessa. Tutkimme EnLite Neonatal TREC -kitin sopivuutta SCID-seulonnan metodiksi ja erityisesti TREC-kopioiden seulontarajan asettamista. Aineisto: Tutkimuksen aineisto koostui 6000 vauvasta, jotka olivat osallistuneet NeoPilot-tutkimukseen Turussa vuosina 2011-2012. Tapauksiksi katsoimme ne vauvat, joiden TREC-arvo oli alle 30 kopiota/µl ja valitsimme heille kaksi kontrollia, joilla oli normaali TREC-arvo. Potilaita oli seurattu pseudoanonymisoidusti vähintään kuuden vuoden ajan. Menetelmät: TREC-arvoja verrattiin tapauksien ja kontrollien välillä Wilcoxon rank sum 2-sample T testillä. Diagnoosien lukumääriä ryhmien välillä tarkastelimme Wilcoxon rank sum 1-Way testillä. Laskimme myös erikseen yhteen kunkin potilaan välikorva- ja hengitystietulehdukset ja vertasimme niitä ryhmien välillä Pearsonin testillä. Osastohoitovuorokausien ja hoitokäyntien lukumääriä sekä veren lymfosyyttimääriäryhmien välillä vertailimme Wilcoxon rank sum 1-Way testillä. Tulokset: Tapauksien TREC-arvojen mediaani oli 26,2 kopiota/µl ja kontrollien 93 kopiota/µl (p 0,05). Osastovuorokausien lukumäärien mediaani oli molemmilla ryhmillä 5, eikä ero ollut tilastollisesti merkitsevä (Wilcoxon Rank Sum, 1-Way Test, ChiSquare Approximation, p = 0,5628). Hoitokäyntien lukumäärien mediaani oli tapauksilla 11 ja kontrolleilla 8, eikä ero ollut tilastollisesti merkitsevä (Wilcoxon Rank Sum, 1-Way Test, ChiSquare Approximation, p = 0,4397). Lymfosyyttien lukumäärän mediaani tapauksilla oli 2,904 ja kontrolleilla 4,719 ja ero ryhmien välillä oli lähes tilastollisesti merkitsevä (Wilcoxon Rank Sum, 1-Way Test, ChiSquare Approximation, p = 0,0523). Kuudella lapsella oli yli sata eri diagnoosikoodia. Heistä kolme oli pikkukeskosia ja kolmella muu perussairaus. Lymfosyyttien määrä heillä oli 1,8 – 7,6 x 10e9 (24-70% kokonaisleukosyyteistä). Päätelmät: Tutkimuksen tulosten perusteella hälytysraja 30 kopiota/ul näyttää olevan kansallisen seulonnan aloittamisessa liian korkea. Jopa 0,5% näytteistä jäisi tämän rajan alle ja hälytyksiä tulisi 250 vuodessa koko Suomessa, vaikka todellisia tapauksia lienee vain muutama. Kuitenkin vasta riittävän pitkä kansallinen seulonta osoittaa todellisuudessa sopivan hälytysrajan

THE CURRENT STATE OF ARTIFICIAL REEFS IN LEBAH COASTAL WATERS, KARANGASEM, BALI: AN EVALUATION ON THE COASTAL RESOURCE REHABILITATION PROJECT

The study was conducted in May 2001 wlth aims to identifl and examine changes the biotic condition of coastal resources. The study used dual approaches of old and new data collections followed by statistical test of Wilcoxon Rank Sum Test

On a one-sample distribution-free test statistic V

SUMMARY A table of exact critical values of a one-sample distribution-free test statistic V is presented for selected significance levels and sample sizes n = 3( 1) 20. It is shown that this test is computationally similar to the well-known Wilcoxon rank sum test statisti

Uniform Approximation Is More Appropriate for Wilcoxon Rank-Sum Test in Gene Set Analysis

Gene set analysis is widely used to facilitate biological interpretations in the analyses of differential expression from high throughput profiling data. Wilcoxon Rank-Sum (WRS) test is one of the commonly used methods in gene set enrichment analysis. It compares the ranks of genes in a gene set against those of genes outside the gene set. This method is easy to implement and it eliminates the dichotomization of genes into significant and non-significant in a competitive hypothesis testing. Due to the large number of genes being examined, it is impractical to calculate the exact null distribution for the WRS test. Therefore, the normal distribution is commonly used as an approximation. However, as we demonstrate in this paper, the normal approximation is problematic when a gene set with relative small number of genes is tested against the large number of genes in the complementary set. In this situation, a uniform approximation is substantially more powerful, more accurate, and less intensive in computation. We demonstrate the advantage of the uniform approximations in Gene Ontology (GO) term analysis using simulations and real data sets