Experimental Design, Evaluation Methods, Data Analysis, Publication, and Research Ethics
Yuehuei H. An, Richard J. Friedman in Animal Models in Orthopaedic Research, 2020
Nonparametric tests are statistical techniques which can be applied when there is no assumption of a Gaussion distribution within the population. Thus they are often referred to as distribution-free tests. While not as powerful or flexible as their parametric counterparts (i.e. t-test and ANOVA), nonparametric tests can be applied in situations where parametric tests are not valid. There are a number of nonparametric tests. Chi-square is the most commonly used and it requires nominal data. Others, which require ordinal data, include the Mann-Whitney U test, the Wilcoxon Signed Rank test, and the Kruskal Wallis test. The Mann-Whitney U test is used to test the hypothesis that the distributions of two different sets of data are equal. It is the nonparametric equivalent of an unpaired t-test. Similarly, the Wilcoxon Signed Rank test is the nonparametric equivalent of the paired t-test. The Kruskal Wallis test is analogous to ANOVA and tests whether two or more sets of data come from the same distribution or from different distributions. Further discussion of their uses may be found in many statistical texts such as those by Abacus Concepts, Inc.,33 Munro et al.,12 and Forthofer and Lee.18
Inferential statistics
Louis Cohen, Lawrence Manion, Keith Morrison in Research Methods in Education, 2017
The important figure to note here is the 0.009 (‘Asymp.Sig.) in Table 41.25: the significance level. Because this is less than 0.05 we can conclude that the null hypothesis (‘there is no statistically significant difference between the voting by the different groups of years in teaching’) is not supported, i.e. that the difference in the voting according to the number of years in teaching by the voters is not simply by chance. As with the Mann-Whitney test, the Kruskal-Wallis test tells us only that there is or is not a statistically significant difference, not where the difference lies. To find out where the difference lies, one has to return to the cross-tabulation (Table 41.23) and examine it. In the example here it appears that those teachers in the group which had been teaching for 16–18 years are the most positive about the aspect of the course in question.
Nonparametrics
Shein-Chung Chow, Jun Shao, Hansheng Wang, Yuliya Lokhnygina in Sample Size Calculations in Clinical Research: Third Edition, 2017
To test the above hypotheses, the following Kruskal–Wallis test is useful (Kruskal and Wallis, 1952). We first rank all observations jointly from least to greatest. Let Rij denote the rank of xij in this joint ranking, , and . Note that Rj is the sum of the ranks received by treatment j and R.j is the average rank obtained by treatment j. Based on Rj, R.j, and R.., the Kruskal–Wallis test statistic for the above hypotheses can be obtained as
Analysis of elements secreted by CHO-K1 cells exposed to gamma radiation under different treatments
Published in International Journal of Radiation Biology, 2020
Joanna Czub, Janusz Braziewicz, Aldona Kubala-Kukuś, Andrzej Wójcik
A statistical analysis was performed using three statistical tools: a Kruskal–Wallis test, a Mann–Whitney test, and PCA. All statistical methods used here are widely described in the literature (Gibbons and Gibbons 1993; Jolliffe 2013), and hence we give only a brief description of them here. The Kruskal–Wallis test is a non-parametric test that allows statistically significant differences to be identified in more than two groups of independent data (Gibbons and Gibbons 1993). The Mann–Whitney test is a non-parametric test for determining statistically significant differences between two groups of independent data (Gibbons and Gibbons 1993). PCA is a non-parametric method that focuses on reducing the dimensionality of the original data set (Jolliffe 2013). In this method, the original data set is presented in terms of new coordinates called the principal components (PC) (Jolliffe 2013). The number of PC to be considered is determined on the basis of the percentage cumulative variability of the original data which is calculated on the basis of the eigenvalue of the correlation matrix determined from the original data (Jolliffe 2013). In addition, this method determines the eigenvectors of the correlation matrix, which in linear combination with the original data determines the value of the PC (Jolliffe 2013). The Mann–Whitney test was carried out using the statistical calculator available in Calculator (2019). The Kruskal–Wallis test and PCA were carried out using codes written by the authors in Excel 2007 (Microsoft, USA) and Matlab R2010a (MathWorks, USA) software, respectively.
Assessment of plasminogen activator inhibitor-1(PAI1) and thrombin activitable fibrinolysis inhibitor (TAFI) in Egyptian children with hemophilia A
Published in Pediatric Hematology and Oncology, 2022
Mohamed Soliman, Nahla Osman, Somyya Hefnawy, Mahmoud Ahmed El Hawy
Data were fed to the computer and analyzed using IBM SPSS software package version 20.0. (Armonk, NY: IBM Corp) Qualitative data were described using number and percent. The Kolmogorov-Smirnov test was used to verify the normality of distribution. Quantitative data were described using range (minimum and maximum), mean, standard deviation, median and interquartile range (IQR). Significance of the obtained results was judged at the 5% level. Chi-square test is used for categorical variables, to compare between different groups. Fisher’s Exact is used for correction for chi-square when more than 20% of the cells have expected count less than 5 .Student t-test is used for normally distributed quantitative variables, to compare between two studied groups. Mann Whitney test is used for non-normally distributed quantitative variables, to compare between two studied groups. F-test (ANOVA) is used for normally distributed quantitative variables, to compare between more than two groups. Spearman coefficient is used to correlate between two distributed non-normally quantitative variables. Kruskal Wallis test: is used for non-normally distributed quantitative variables, to compare between more than two studied groups.
Alcohol and substance misuse in the construction industry
Published in International Journal of Occupational Safety and Ergonomics, 2021
Joseph Flannery, Saheed O. Ajayi, Adekunle S. Oyegoke
The Kruskal–Wallis test is a non-parametric test which assesses the variances among three or more individually tested groups on a single and continuous variable [54]. Gupta [55] states that this is done to gauge the different responses from different respondents about a particular hypothesis. In this study, the Kruskal–Wallis test, illustrated in Tables 6 and 7, was used to evaluate how perceptions differ by occupation. Field [51] found that a p value (Asymp. Sig.) below 0.05 reveals a noteworthy difference between the respondents about a variable; any value above this shows no considerable difference of perception. The findings reveal that the respondents differed significantly on two of the contributing factors: ASM to deal with pain from manual labour and the working-class ethic within construction. They also differed on eight of the mitigating strategies, most significantly on ASM screening and harsh consequences for offenders. The results of the reliability and Kruskal–Wallis tests are presented for both causes and mitigating strategies in Tables 6 and 7 respectively.
Related Knowledge Centers
- Bonferroni Correction
- Friedman Test
- NONparametric Statistics
- Mann–Whitney U Test
- Statistical Significance
- Multiple Comparisons Problem