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Testing
Published in Richard C. Fries, Handbook of Medical Device Design, 2019
Another non-parametric test, that is, a test that does not assume a particular distribution, is the Sign Test. The Sign Test works by comparing the sample data against a standard. If the particular datum is greater than the standard, it counts as a success (a “+”). If the datum is less than the standard, it counts as a failure (a “-”). If the datum is equal to the standard, it is not counted. An example would be: “the null hypothesis is that the difference between the means of the two samples is no more than three.” The data in the two samples would be compared pair-by-pair against the value of three, and appropriate +’s and -’s assigned.
Nonparametric Statistics
Published in William M. Mendenhall, Terry L. Sincich, Statistics for Engineering and the Sciences, 2016
William M. Mendenhall, Terry L. Sincich
To conduct the test we calculate the differences (yi − 100) for the sample. Recall that the sign test depends only on the number of positive differences in the sample. The signed ranks test, on the other hand, requires that we first rank the differences, then sum the ranks of the positive differences. Thus, the Wilcoxon signed ranks test for a single sample is conducted exactly as the signed ranks procedure for matched pairs, except that the differences are calculated by subtracting the hypothesized value of the median from each observation. We summarize the procedure in the next box.
Spectral Clustering on Spherical Coordinates Under the Degree-Corrected Stochastic Blockmodel
Published in Technometrics, 2022
Francesco Sanna Passino, Nicholas A. Heard, Patrick Rubin-Delanchy
Under the same setup as the simulation in Section 5.2, p-values are calculated for the two Mardia tests applied for each community on the spherical embedding and the row-normalized embedding . Then, binomial sign tests for paired observations are calculated on the differences between the p-values obtained from , and those obtained from , separately for pS and pK, under the null hypothesis that those are sampled from the same distribution. The alternative hypothesis is that the distribution of the p-values obtained from is stochastically larger than the corresponding distribution for . The p-value of the sign test is for both skewness and kurtosis, confirming the impression in Figure 3 that the transformation (4) to tends to Gaussianize the embeddings and .
A distribution-free Shewhart-type Mann–Whitney control chart for monitoring finite horizon productions
Published in International Journal of Production Research, 2021
Giovanni Celano, Subhabrata Chakraborti
Note that the values of the actual measurement readings of carbon dioxide have been shifted by a constant value to preserve industrial confidentiality. Both the p-values for ‘level’(location) and ‘scale’ are larger than : therefore, x can be considered a stable reference sample of observations to be used to run the MW control chart. The dashed line in the upper panel of Figure 7 shows an estimate of the process mean of the shifted carbon dioxide content. Similarly, the dashed line in the lower panel of Figure 7 shows an estimate of process standard deviation of the carbon dioxide content. A sign test on the reference sample median vs. the mid-point of the specification interval does not reject the null hypothesis (p-value).
Application of mixed discrete student psychology-based optimisation for optimal placement of unity power factor distributed generation and shunt capacitor
Published in International Journal of Ambient Energy, 2022
Bikash Das, Soumyabrata Barik, Vivekananda Mukherjee, Debapriya Das
To verify the obtained results using MDSPBO, statistical analysis has been performed and reported in the current article. The statistical analysis includes the sign test, the Wilcoxon signed ranks test, and the Friedman test (Derrac et al. 2011). The statistical analysis proves that the proposed algorithm outperformed both MDPSO (Barik and Das 2019) and MDTLBO (Barik, Das, and Bansal 2020) with a high level of significance. To analyze the performance of MDSPBO and to obtain the optimum solution in lesser time, computational time analysis has been performed and presented in this paper. The computational time analysis proves the capability of MDSPBO to obtain the optimum solution with faster convergence mobility compared to MDPSO and MDTLBO.