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Experimental Design and Analysis in Aquaculture
Published in Hillary S. Egna, Claude E. Boyd, Dynamics of POND Aquaculture, 2017
Most statistical software packages are capable of doing a variety of nonparametric tests. The following is a representative list and description of several tests, with the analogous parametric analysis given in parentheses. The Kolmogorov-Smirnov One-Sample Test is a goodness-of-fit test that examines the null hypothesis that the distribution of your data is not significantly different from a specified parametric distribution (e.g., normal, Poisson, binomial, etc.). The Kolmogorov-Smirnov Two-Sample Test tests the null hypothesis that two independent samples have the same underlying population distribution. Wilcoxon’s Signed Rank Test (paired sample t-test) is used for detecting differences with paired treatments (i.e., changes due to treatment within experimental units). The Mann-Whitney Test (t-test) compares two sample means based on ranks. The Kruskel-Wallis Test (ANOVA) compares three or more sample means based on ranks. Spearman’s Rank Correlation (correlation) measures the association of two variables based on ranked observations of each variable. The calculated Spearman’s rank correlation coefficient (rs) only gives a probability of association and says nothing about the nature of the tested association.
Determining Probabilistic Inputs for Decision Models
Published in Gerald W. Evans, Multiple Criteria Decision Analysis for Industrial Engineering, 2016
Finally, one could employ a “goodness of fit” procedure such as the chi-square goodness of fit test, the Kolmogorov–Smirnov (K–S) goodness of fit test, or the Anderson–Darling test. These tests rely on an approach called “hypothesis testing” from the field of statistics. Basically, one is testing the null hypothesis (H0) that the Xi data points are independent, identically distributed random variables corresponding to the hypothesized distribution function. A problem with hypothesis tests of this type is that failure to reject the null hypothesis should not be interpreted as accepting it as true, but only that there is not enough evidence to reject it. In addition, as noted by Law (2007, p. 340), when the amount of data are not very large, these tests are not very good at recognizing differences between the data and the hypothesized distribution, which means that H0 will not be rejected; on the other hand, if there are a lot of data, H0 will almost always be rejected since it will never be exactly true. For these reasons, it is usually a good idea to just view the hypothesized distribution function superimposed over a histogram of the data and to also look at the value of the square error in evaluating various hypothesized distributions.
A stochastic ventilation model regarding leakage and user behaviour
Published in J. Carmeliet, H. Hens, G. Vermeir, Research in Building Physics, 2020
Most of the building parameters do not have a symmetric distribution. With exception of typology, they all have more high values than normal distributions. Lognormal and Weibull distributions are more appropriate to describe the distribution of these parameters. Goodness-of-fit is determined with chi-squared tests. This test reports a measure of the deviation of the fitted distribution from the original data. The p-value shows how likely it is that a new set of samples drawn from the fitted distribution would generate a fit statistic greater than or equal to χ2 (a tabulated fit statistic). Using a significance level of 0.05, all estimated distributions seem good approximations.
Demand-predictive storage assignment mechanism for flower auction centers
Published in International Journal of Production Research, 2022
Xiang T.R. Kong, Miaohui Zhu, Kaida Qin, Pengyu Yan
In this study, we expand the problem scale and consider five scenarios with different numbers of trolleys, that is, 800, 850, 900, 950, and 1000. With respect to each scenario, 100 instances were generated, yielding a total of 500 instances. For each instance, the number of customers is generated by normal distribution . For each customer, the size of an order per transaction is determined from geometric distribution . The minimum size of an order is 1. The empirical distributions are generated by using historical data. Figure 9 depicts the number of customers per day and the demand sizes per transaction. We use chi-square test to measure the goodness of fit. The results are presented in Table 7, which indicates that the null hypothesis is not rejected at the 1% significance level, and therefore the empirical distributions have good fitness. The simulation results are displayed in Table 8, which indicates that the DSA mechanism significantly outperforms the COL strategy under all scenarios.
Production of Pottery from Esfandaghe and Jiroft, Iran, late 7th - early 3rd Millennium BC
Published in Materials and Manufacturing Processes, 2020
Heat-maps evaluated the different concentrations of elements in the body of the ceramic analyzed by XRF so as to obtain the best relationship between the bulk chemical compositions of materials at both sites.[24] These simple heat maps provide an immediate visual summary of total element/oxide densities in all samples at the two separate locations. All samples were combined and the evaluation focused on element density variations related to the ancient sites[24,25] (Fig. 3b). The relationship between the measured concentrations of oxides in this diagram was then interpreted through the value of the concentration of each element represented by color. In this case, the dark red color indicates a high concentration that diminishes to zero when white. Each horizontal line (each scan of x-axes) belongs to the definite oxides (in w%) defined for each group of samples and from each site. Statistical analysis (GLMM: Imer) showed that there are significant differences in element composition between the two regions. To show the similarities, a Chi-square test was elaborated to quantitatively test how likely an observed distribution was. The so-called “goodness of fit” is approached depending on how well the observed distribution of data fits with the distribution that is expected when the variables are independent.[26] The chi-square in our statistical measurements is about 9.70. This means that, due to the low goodness of fit of the distribution on both sites, there was enormous discrimination between the two sites regarding the chemical composition of the ceramics.
Development of new reliability measure for bus routes using trajectory data
Published in Transportation Letters, 2020
Akhilesh Chepuri, Sanskruti Joshi, Shriniwas Arkatkar, Gaurang Joshi, Ashish Bhaskar
The route level travel time data sets in three levels are investigated with three potential statistical distributions namely Burr, lognormal, and generalized extreme value (GEV) distributions. These three distributions are selected based on the literature review. It has been observed that the travel time data sets in all the cases are fitting into any one of three potential distributions investigated based on the goodness-of-fit test. Kolmogorov–Smirnov test is used to check the goodness-of-fit for chosen distributions. The period of the day and day of the week distribution fitting has been carried out for all the six routes in both the directions, whereas for each of the bus stop from the origin, it has been carried out for the two routes in both the directions. In the present study, GEV distribution is observed to be the best-fitted distribution for the travel time’s at all three levels. GEV distribution is a family of continuous probability distributions developed within the extreme value theory. GEV distribution contains location parameter µ, scale parameter σ, and shape parameter k ≠ 0.The change in the shape of the PDF curve along with ‘k’ value is used to define the travel time variability.