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Experimental Design and Analysis in Aquaculture
Published in Hillary S. Egna, Claude E. Boyd, Dynamics of POND Aquaculture, 2017
Most statistical software packages are capable of doing a variety of nonparametric tests. The following is a representative list and description of several tests, with the analogous parametric analysis given in parentheses. The Kolmogorov-Smirnov One-Sample Test is a goodness-of-fit test that examines the null hypothesis that the distribution of your data is not significantly different from a specified parametric distribution (e.g., normal, Poisson, binomial, etc.). The Kolmogorov-Smirnov Two-Sample Test tests the null hypothesis that two independent samples have the same underlying population distribution. Wilcoxon’s Signed Rank Test (paired sample t-test) is used for detecting differences with paired treatments (i.e., changes due to treatment within experimental units). The Mann-Whitney Test (t-test) compares two sample means based on ranks. The Kruskel-Wallis Test (ANOVA) compares three or more sample means based on ranks. Spearman’s Rank Correlation (correlation) measures the association of two variables based on ranked observations of each variable. The calculated Spearman’s rank correlation coefficient (rs) only gives a probability of association and says nothing about the nature of the tested association.
Nonparametric Statistics
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
Spearman’s rank correlation coefficient is found by first ranking the values of each variable separately. (Ties are treated by averaging the tied ranks.) Then rs is computed in exactly the same way as the Pearson correlation coefficient r—the only difference is that the values of x and y that appear in the formula for r are replaced by their ranks. That is, the ranks of the raw data are used to compute rs rather than the raw data themselves. When there are no (or few) ties in the ranks, this formula reduces to the simple expression rs=1-6∑di2n(n2-1)
Statistical learning and predictive analytics
Published in Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton, Texts in Statistical Science, 2017
Benjamin S. Baumer, Daniel T. Kaplan, Nicholas J. Horton
In addition to the usual Pearson product-moment correlation, measures of rank correlation are also occasionally useful. That is, instead of trying to minimize y−y^, it might be enough to make sure that the y^i ’s are in the same relative order as the yi’s. Popular measures of rank correlation include Spearman’s ρ and Kendall’s τ .
Probabilistic model-checking based reliability analysis for failure correlation of multi-state systems
Published in Quality Engineering, 2020
Rongxi Wang, Zezhou Tang, Jianmin Gao, Zhiyong Gao, Zhen Wang
The rank correlation measure based on the Copula function reflects the monotonic dependence between variables. This measure is a nonlinear measure of multiple random variables, and it remains constant under nonlinear monotonic transformation. Furthermore, it has good statistical properties and is more widely used than linear correlation coefficients. The most well-known of the rank correlation coefficients is the Kendall rank correlation coefficient which is a consistency-based correlation measure. In data sample processing, indicates the difference between the probabilities that two randomly selected test values are the same or different from
Nursing shortage in the public healthcare system: an exploratory study of Hong Kong
Published in Enterprise Information Systems, 2020
Polly P. L. Leung, C. H. Wu, C. K. Kwong, W. K. Ching
Using the samples and questionnaires collected, correlation analysis was conducted to determine whether there was a real statistical significant association between the seven factors of job dissatisfaction identified from literature, i.e. workload, stress and burnout; pay; work schedule; opportunities for advancement/promotion; organisational commitment; empowerment and autonomy; and management style/supervisor, and Hong Kong nursing staff’ intention to leave. Only those factors demonstrating a real statistical significant association (P value <0.05) with Hong Kong nursing staff’ intention to leave will be considered as relevant to Hong Kong. Spearman’s rank correlation coefficient, rs, can take a range of values from −1 to +1. The magnitude of the correlation coefficient indicates the strength of the association while the sign (±) indicates the direction of the association. The stronger the association of the two variables, the closer the rs will be having absolute value 1 (Portney and Watkins 2009, 531).
Evaluation of the safety performance of highway alignments based on fault tree analysis and safety boundaries
Published in Traffic Injury Prevention, 2018
Yikai Chen, Kai Wang, Chengcheng Xu, Qin Shi, Jie He, Peiqing Li, Ting Shi
Through investigation, the exposure to crash risk—that is, the average annual daily traffic of the road sections—is very similar and can thus be neglected in the validation process. Because the main objectives of the procedure are to rank road sections precisely in terms of safety performance and identify most hazardous road sections, Spearman's rank correlation was used to examine the level of agreement between the rankings of the average crash probability predicted by the proposed method and the rankings of the observed crash frequency per kilometer. Spearman's rank correlation coefficient is a measure of the association between the rankings of 2 variables and is often used as a nonparametric alternative to a traditional coefficient of correlation. One advantage of the method is that when testing for the correlation between 2 data sets, it is not necessary to make assumptions about the nature of the sampled population distributions (Cafiso and Cava 2007). As shown in Table 2, the Spearman's rank correlation coefficients were 0.781, 0.795, and 0.860 for road sections with lengths of 2, 5, and 10 km, respectively.