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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)
Data analysis
Published in Fernando Olavo Franciss, Hard Rock Hydraulics, 2021
The Spearman rank correlation coefficient test is a nonparametric hypothesis testing. It is a variant of Pearson’s rank correlation coefficient, and instead of applying the Pearson’s formula to the original data, it applies to the ranks of the data. Some commercial mathematical software13 includes a Spearman subroutine to allow rapid comparisons of pairs of WT time series. The reader is encouraged to know more about these specialized software packages.
Measures of Linearity, Dependence and Correlation
Published in Alan R. Jones, Probability, Statistics and Other Frightening Stuff, 2018
Spearman’s Rank Correlation Coefficient can take any value in the range –1 to +1 (or –100% to 100% if you prefer the percentage approach). Just as we did for Pearson’s Linear Correlation we need to interpret it appropriately. Tables 5.15 to 5.18 attempt to summarise what the Spearman’s Rank Correlation Coefficient might be trying to tell us.
Predicting the effectiveness of supplement time on delay recoveries: a support vector regression approach
Published in International Journal of Rail Transportation, 2022
Yuexin Wang, Chao Wen, Ping Huang
Spearman correlation analysis is performed by calculating the Spearman rank correlation coefficient. Spearman rank correlation coefficient is a non-parametric test method used to measure the strength of the relationship between variables. In the absence of repeated data, if one variable is a strictly monotonic function of another variable, the Spearman rank correlation coefficient is +1 or −1. Compared with the Pearson coefficient, the Spearman rank correlation coefficient has a wider application range. The conditions for using Pearson correlation coefficient include that the data must meet normal distribution and the variables are linearly correlated. However, the data sets for correlation analysis in this paper do not conform to normal distribution. Therefore, the Pearson correlation coefficient cannot be used. Applicable conditions and advantages of Spearman rank correlation coefficient are:
Region-specific biomass feedstock selection for gasification using multi-attribute decision-making techniques
Published in International Journal of Sustainable Engineering, 2021
Joel George, P. Arun, C. Muraleedharan
Ranking results obtained by implementing AHP-TOPSIS hybrid model are validated by comparing with some existing MADM approaches – Euclidean distance-based approximation (EDBA) method and Simple Additive Weighting (SAW). These methods were implemented to assess the biomass gasification feasibility of already selected biomasses following the standard procedures presented in the literatures cited in Section 2.4. Comparison among ranks obtained for different methods is displayed in Table 10. The strength and direction of the relationship between two ranked variables can be measured using Spearman’s rank correlation coefficient. It is a non-parametric measure of rank correlation and evaluates how well the relationship between two variables be defined using a monotonic function (function which is either entirely non-decreasing or non-increasing). The Spearman rank correlation coefficient between two variables will be high (+1) when observations have a similar rank between the two variables, and low (−1) when observations have a dissimilar rank between the two variables. The sign of the correlation indicates the direction of the association between two variables. Spearman’s rank correlation coefficient (ρ) is measured using the following relation:
Identification of black spots on highways using fault tree analysis and vehicle safety boundaries
Published in Journal of Transportation Safety & Security, 2021
Yikai Chen, Kai Wang, Yu Zhang, Qin Shi
Spearman’s rank correlation was used to determine the level of agreement between the average probability of crash occurrence of each section and the number of crashes per kilometer. Spearman’s rank correlation coefficient is a measure of the association between the rankings of two variables measured on N individuals 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 two data sets, it is not necessary to make assumptions about the nature of the sampled populations (Cafiso & Cava, 2009; Cafiso et al., 2007). At a 99.9% significance level, the Spearman’s rank correlation coefficients were 0.781, 0.797, and 0.860 for road sections with lengths of 2 km, 5 km, and 10 km, respectively.