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Engineering: Making Hard Decisions Under Uncertainty
Published in John X. Wang, Decision Making Under Uncertainty, 2002
Engineers frequently collect paired data in order to understand the characteristics of an object or the behavior of a system. The data may indicate a spatial profile (snowfall in different cities and states) or a time history (vibration acceleration versus time). Or the data may indicate cause-and-effect relationships (for example, force exerted by a spring versus its displacement from its equilibrium position) or system output as a function of input (yield of manufacturing process as a function of its process capability). Such relationships are often developed graphically, by plotting the data in a particular way. Mathematical expressions that capture the relationships shown in the data can then be developed.
Micro-Scale Field Laboratory Methods for the Chemical Analysis of Samples for Use in Site Investigations and Remediation
Published in Donald L. Wise, Debra J. Trantolo, Remediation of Hazardous Waste Contaminated Soils, 2018
Daniel M. Twomey, Stephen A. Turner
Statistical comparisons of the field and laboratory DDT results showed that the data were not normally distributed. Therefore, a nonparametric approach was selected. The Wilcoxan signed rank test was used, since the field and laboratory results represented paired data points. The test resulted in a z-value of −0.936 (with an approximate probability of 0.349), which indicated there was no statistically significant difference between the field and laboratory DDT results.
Chapter 13 Mathematical and statistical techniques
Published in B H Brown, R H Smallwood, D C Barber, P V Lawford, D R Hose, Medical Physics and Biomedical Engineering, 2017
A non-parametric equivalent of the ‘t’ statistic can be applied to small groups of data. The Mann-Whitney U statistic only relies on ranking the data and makes no assumption about the underlying population from which the sample was drawn. When the data are ‘paired’ and statistical independence is lost, as in ‘before’ and ‘after’ studies, a different approach must be adopted. The Wilcoxon matched-pairs signed-ranks statistic is used to assess the ‘paired’ data.
Solving the flexible job shop scheduling and lot streaming problem with setup and transport resource constraints
Published in International Journal of Systems Science: Operations & Logistics, 2023
Pinar Yunusoglu, Seyda Topaloglu Yildiz
The paired t-test is a parametric test used to determine whether the mean of the differences between the paired data is zero or not. Note that to apply this test, the differences in the paired data should approximate the normal distribution. The null and alternative hypotheses are given in Equations (31) and (32), where represents the mean of the paired differences between the objective values obtained by the proposed solution approach and those obtained by the existing solution approach in the literature.
Optimized feature fusion-based modified cascaded kernel extreme learning machine for heart disease prediction in E-healthcare
Published in Computer Methods in Biomechanics and Biomedical Engineering, 2023
Sumit Kumar, Kamal Kumar Gola, Narayan Jee, Brij Mohan Singh
The Wilcoxon signed rank test could be utilized to test both one and two-sample paired data. It is one of the nonparametric statistical tests that are highly powerful as it makes use of difference magnitude instead of its signs. The fundamental idea behind the Wilcoxon signed rank test is the formation of null and alternative hypotheses with the selection of the degree of confidence. Next, the test statistics need to be computed, and it is compared with the critical value. This test is carried out to check whether one or numerous paring sets are statistically different. The steps involved in this test are given as follows.
An Efficient Extraction Method of Persistent Organic Pesticides in Soil Samples for Their Chromatographic Determination
Published in Soil and Sediment Contamination: An International Journal, 2018
Mara C. Avendaño, Pablo Roqué, Miriam E. Palomeque
The differences between the paired data are considered, and the mean values should not differ statistically from “0”. A value tcalculated = 0.195 was obtained and compared with a tabulated value t(11,0.05) = 2.228. The test indicates that as tcalculated is lower than the tabulated value, the null hypothesis (H0: δ0 = 0, δ0 is the ideal difference) cannot be rejected at 0.05 significant levels. Therefore, it is concluded that there is no significant differences between both methods for the quantification of determined pesticides in soil sample.