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Statistical Inference II
Published in Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos, Statistical and Econometric Methods for Transportation Data Analysis, 2020
Simon Washington, Matthew Karlaftis, Fred Mannering, Panagiotis Anastasopoulos
The median test is used to conduct hypothesis tests about a population median. Recall that the median splits a population in such a way that 50% of the values are at the median or above and 50% are at the median or below. To test for the median, the sign test is applied by simply assigning a plus sign whenever the data in the sample are above the hypothesized value of the median and a minus sign whenever the data in the sample are below the hypothesized value of the median. Any data exactly equal to the hypothesized value of the median should be discarded. The computations for the sign test are done in exactly the same way as was described in the previous section.
An investigation of following behavior and associated safety of MTWs in heterogeneous traffic
Published in Transportation Letters, 2023
Jaikishan Damani, Perumal Vedagiri
It is important to investigate if there is a statistically significant difference in the following behavior based on the type of leader vehicle. The tests are conducted on Distance Gap, Clear Lateral Gap, and Time Gap. Non-parametric tests such as Kruskal Wallis Test, Median Test, Jonckheere-Terpstra Test, Mann Whitney U Test, and KS Test were used for the analysis, since they do not make any assumptions about the underlying distribution and variance of data, and also require lesser sample size for accurate results. Since all the asymptotic significance values mentioned in Table 3 are significant at 5% level of significance, the type of leader vehicle is indeed a statistically significant parameter in affecting the following behavior of MTWs.
An alternative approach to pupils’acquiring a concept parameter in solving inequalities in school mathematics
Published in International Journal of Mathematical Education in Science and Technology, 2021
From Table 1 and from graph (Figure 1), we can see that there are differences between the three groups of students in the mathematical pre-test results. We wanted to find out if these differences are also statistically significant. We used the median k-sample test to verify the statistical significance of the differences. The median test is a non-parametric test to compare two or more independent samples. It is an alternative method to ANOVA. However, unlike ANOVA, it does not assume normality in the samples, and so is useful when comparing medians where normality is questionable.
Two-stage hybrid flow shop batching and lot streaming with variable sublots and sequence-dependent setups
Published in International Journal of Production Research, 2019
Shasha Wang, Mary Kurz, Scott Jennings Mason, Eghbal Rashidi
We compute the objective value and running time for 30 test runs of each instance. Let denote the average objective value achieved by applying each heuristic listed in Table 1. The gap, , is computed to assess heuristics solution quality. Table 6 list the minimum, mean, and maximum objective value, the , and the computational time of all 40 instances for each heuristic. For Instances 1-10, heuristics C1R, C1W , and C1J found optimal solutions while other methods found near-optimal solutions. For Instances 11-40 except Instance 15, the heuristics provided better objective values than Gurobi (1-hour time limit). All proposed heuristics found feasible solutions for Instance 32 within 24 seconds. The Mood's median test, a non-parametric method for testing whether two or more populations are from the same distribution based on their medians, is used. It provides 95% confidence intervals (CIs) for medians to compare the heuristics testing the following null hypothesis: all medians of all are equal. The p-value of ∼0.0001 indicates that we can reject the null hypothesis. The CIs of for all heuristics, shown in Figure 4, show that product-splitting method C1 is better than the other two methods C2 and R. For the 40 instances, sequencing methods RK and WSPT perform almost the same, but are better than JR. These 40 instances are small- and medium-size problems in terms of the maximum number of products considered (six). The permutation of products is less than the number of iteration (1000) used by each heuristic method. RK has a high probability of performing well by enumerating all products sequences.