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Published in Stuart H Rubin, Lydia Bouzar-Benlabiod, Reuse in Intelligent Systems, 2020
Ahmad Abu Shanab, Taghi M Khoshgoftaar
We also performed a set of two-tailed z-tests for each paired comparison to find statistically significant patterns. The tests performed were across all datasets and factors, and for each level of data quality. The z-test method tests the null hypothesis that the population means related to two independent group samples are equal against the alternative hypothesis that the population means are different. p-values are provided for each pair of comparisons in the table. The significance level is set to 0.05; when the p-value is less than 0.05, the two group means are significantly different from one another.
Tails of the unexpected (1): Hypothesis Testing
Published in Alan R. Jones, Probability, Statistics and Other Frightening Stuff, 2018
The Z-Test is one which evaluates whether the value of any Normally Distributed sample statistic is significantly different from a known or assumed value of that statistic for the population overall. To do this it measures the deviation of the observed sample value from the assumed population value, expressed in terms of the statistic’s Standard Error.
Effectiveness of the red-edge band of RapidEye in land cover classification
Published in Journal of the Chinese Institute of Engineers, 2023
Tzu-Ying Chen, Hui-Hsin Chen, Tee-Ann Teo, Peter Tian-Yuan Shih
In this study, the OA and Kappa coefficients were included in the accuracy assessment. Moreover, a Kappa analysis and a pairwise Z-test were conducted to determine whether the two classifications were significantly different (Weih and Riggan 2010). The Z-test was used to test for statistical significance. We performed this test to evaluate whether the classifications, with and without the red-edge band, were significantly different from each other. The critical Z-score values in the 95% confidence level were −1.96 and +1.96 standard deviations. If the value of Z-score was larger or less than 1.96, the null hypothesis was rejected and the alternative hypothesis was accepted. Thus, the p-value associated with a 95% confidence level was 0.05. The pairwise Z-scores and probabilities (p-values, α) were calculated for each combination of the two classifications (Equation 4). This study applied the Z-test by testing a hypothesis (p-values α = 0.05 and Z0.05 = 1.96): If the p-value was < 0.05, the null hypothesis was rejected, meaning that the two classifications were considered to be statistically significantly different.
Competitive bi-agent flowshop scheduling to minimise the weighted combination of makespans
Published in International Journal of Production Research, 2022
Danyu Bai, Ali Diabat, Xinyue Wang, Dandan Yang, Yao Fu, Zhi-Hai Zhang, Chin-Chia Wu
The DA-based heuristics are tested with the processor-task combinations m × n = 5 × 100, 10 × 100, 20 × 100, 20 × 200, and 20 × 500 selected from Taillard (1993), where the averages are reported in Table 3. Ratios α3 and α4 are the MRG values obtained by the DAF or DAA heuristics, respectively, where . The MRG values show the identical tendency as presented in Section 6.1. For the 20-processor instances, ratio α3 (α4) decreases from 43.3295% (49.8227%) to 21.5210% (21.7510%) as the number of tasks increases from 100 to 500. These results indicate that the asymptotic optimality of the DA-based heuristics holds without assumptions A1 and A2. Ratio β3 in Table 3 is the MRD values obtained by the DA-based heuristics, where G1=DAF and G2=DAA. The results of Example 1 and Theorem 3 indicate that the worst-case performance of DAA heuristic dominates that of DAF heuristic for certain extreme case. For the 100-task instances, a hypothesis test is executed on ratio β3 to reveal the dominance of the two heuristics under the benchmark data. With the MRD values in Table 3, therefore, the null and alternative hypothesises are set as β3 ≥ 100% and β3 < 100% (claim). The z-test is introduced, where the significance level is 0.05. The standardised test statistic and critical value are determined as z = −3.346 and z0.05 = −1.645, respectively. Given that z = −3.346 < −1.645, it decides to reject the null hypothesis. This phenomenon might cause by the structure of benchmark data for medium-scale instances. As problem scale keeps on enlarging, the MRD value trend to 100% as shown in Section 6.1.