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Significance testing
Published in John Bird, Bird's Higher Engineering Mathematics, 2021
When critical regions occur on both sides of the mean of a normal distribution, as shown in Fig. 75.1, they are as a result of two-tailed or two-sided tests. In such tests, consideration has to be given to values on both sides of the mean. For example, if it is required to show that the percentage of metal, p, in a particular alloy is x%, then a two-tailed test is used, since the null hypothesis is incorrect if the percentage of metal is either less than x or more than x. The hypothesis is then of the form: H0:p=x%H1:p≠x%
Ideation
Published in Walter R. Paczkowski, Deep Data Analytics for New Product Development, 2020
Another level of analysis could be done, data permitting. For each attribute, the difference between the mean performance of your product and the mean of each of the competitors’ mean performance can be determined for each attribute. The difference should, of course, be statistically tested. The recommended test is Dunnett’s multiple comparison test. In multiple comparison tests in general, there is an issue of performing more than one statistical test on the same data. The standard level of significance, which is the probability of falsely rejecting the Null Hypothesis, used in, say, a t-test is α = 0.05.18 This is sufficient when one test is performed to determine a difference. When more than one test is performed, however, it can be shown that the probability of falsely rejecting the Null Hypothesis, H0, is greater than 0.05. In fact, Pr(Falsely Rejecting H0) = 1 − (1 − α)k where k is the number of tests. Table 2.3 shows what happens to this probability for different values of k.
Introduction to Research
Published in Vinayak Bairagi, Mousami V. Munot, Research Methodology, 2019
Geetanjali V. Kale, J. Jayanth
If the outcome does not support the null hypothesis, we conclude with an alternate hypothesis. One can define a problem using null hypothesis as “There is no relation between the illness of children and change in season.” If the result rejects the hypothesis, an alternate hypothesis is “Illness of children occurs mainly due to change in season.” The null hypothesis is the precise statement about the parameters. Researchers either approve the hypothesis or disapprove the hypothesis. If researcher disproves the null hypothesis, all other possibilities are represented by alternative hypothesis. Null hypothesis does not provide a statistically significant relationship between variable, whereas, alternate hypothesis provides a statistically significant relationship between them.
Statistics of Atterberg limit values of some pure kaolinitic clays
Published in Geomechanics and Geoengineering, 2023
Giovanni Spagnoli, Satoru Shimobe
Hypothesis testing (i.e. a hypothesis that is testable on the basis of observed data modelled as the realised values taken by a collection of random variables) was also performed regarding the variability of data in terms of variance (do the Atterberg limits of clay samples strongly differ?), mean values (do the Atterberg limits of clay samples have a difference in their average?) or regarding the detection of the so-called and risks have been performed (Kiemele et al. 1997, Stuart et al. 1999). To answer these questions probability and confidence levels are employed (Reagan and Kiemele 2008). A null hypothesis is used in statistics to state that there is no difference between certain values of the population (or data-generating process), which opposes to the alternative hypothesis . If is true, the p-value (i.e. the probability of observing the data given the null hypothesis is true) is calculated. Alternatively, the p-value is referred as the level of significance of the test. Normally, in statistics the p-value is compared to a threshold, , which is set as 0.05 (Reagan and Kiemele 2008). That means if the p-value is larger than , then is true, otherwise we must reject the null hypothesis.
The retention of information in virtual reality based engineering simulations
Published in European Journal of Engineering Education, 2022
To answer the above research questions a non-inferiority test was used. Ordinarily, the null hypothesis sets out that the measured and expected data sets are not different from each other, whereas the alternative hypothesis is accepted in the case where the difference between the two datasets is statistically significant. In the case of non-inferiority trials, the null hypothesis sets out that the datasets are different (e.g. that the measured is inferior to the expected) and if the difference is not statistically significant the alternative hypothesis is accepted (Walker and Nowacki 2010). For this reason, the non-inferiority test was chosen because the goal of this study is to prove that the new educational approach using VR is no less effective than the equivalent approach currently being employed in the real world, whilst of course still offering the advantages of educational logistics, engagement and learning experiences that may be impossible in a real industrial environment. Non-inferiority tests use an equivalence margin (see section Quiz) to establish if the two datasets are not inferior to each other. Such a test is commonly used in medical sciences but are increasingly being employed in psychology and education research contexts (Lakens, Scheel, and Isager 2018).
Simulated-annealing-based hyper-heuristic for flexible job-shop scheduling
Published in Engineering Optimization, 2022
Kelvin Ching Wei Lim, Li-Pei Wong, Jeng Feng Chin
A null hypothesis is defined such that there is no difference between and , whereas the alternative hypothesis is that a difference exists between and . Based on the results in Table 6, there are 13 positive signs, two negative signs and a tied match. Hence, the p-value is 0.00451. Given that the p-value <0.05, the null hypothesis is rejected. The conclusion is drawn that a difference exists between the medians of the signed differences. This indicates that SA-HH significantly outperforms the SA-HH.