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Identifying Non-linearity in Construction Workers' Personality Safety Behaviour Predictive Relationship Using Neural Network and Linear Regression Modelling
Published in M.Z. Naser, Leveraging Artificial Intelligence in Engineering, Management, and Safety of Infrastructure, 2023
Yifan Gao, Vicente A. González, Wing Tak Yiu, Guillermo Cabrera-Guerrero
The Chow test was conducted using the computer programme SAS (Song et al., 2019). The results showed that there was one structural break in the whole dataset, resulting in two split sub-datasets and the following Rw, R1 and R2 for the LR formulas (2.5) and (2.6) respectively: 33.497, 18.143, and 15.136 (p < 0.001); 82.325, 39.693, and 41.667 (p < 0.001). Applying the formula (2.7) above, the F values were computed respectively for the LR formulas (5) and (6) as follows: 0.37 (p < 0.001) and 0.65 (p < 0.001). According to the criteria of Chow test (Song et al., 2019), the parameters of an LR model are considered structurally stable when the calculated F value is less than the F-critical value with (k, N-2k) degrees of freedom which can be retrieved from the F-distribution table (available online at: www.stat.purdue.edu/~jtroisi/STAT350Spring2015/tables/FTable.pdf). As predefined, the values of k and N equal to 4 and 228, respectively. The degrees of freedom for the F-critical value are thereby determined as (4, 220). According to the F-distribution table, the F-critical value with degrees of freedom (4, 220) and p-value less than 0.001 is 4.81. The calculated F values, 0.37 (p < 0.001) and 0.65 (p < 0.001) are therefore well below the F-critical value 4.81 (p < 0.001), which indicates that the parameters of the LR formulas (2.5) and (2.6) are structurally stable.
Bayesian Regression
Published in Daniel B. Rowe, Multivariate Bayesian Statistics, 2002
follows a Scalar Student t-distribution with n* − q − p degrees of freedom, and t2 follows an F-distribution with 1 and n* − q − p numerator and denominator degrees of freedom. The F-distribution is commonly used in Regression [1, 68] and derived from a likelihood ratio test of reduced and full models when testing coefficients. By using a t statistic instead of an F statistic, positive and negative coefficient values can be identified. Even for a modest sample size, this Scalar Student t-distribution typically has a large number of degrees of freedom (n + ν − q − 2p + 1) so that it is nearly equivalent to a Scalar Normal distribution as noted in Chapter 2.
Biostatistics and Bioaerosols
Published in Harriet A. Burge, Bioaerosols, 2020
Lynn Eudey, H. Jenny Su, Harriet A. Burge
The F distribution is another continuous distribution often used in parametric statistical inference, particularly in analysis of variance and in regression analysis. The F-statistic is the ratio of two chi-square random variables (usually the ratio of two variance estimates) after being divided by their respective degrees of freedom. It is always non-negative and is asymmetric. It too is indexed by its degrees of freedom but the F-statistic has degrees of freedom for both the numerator and the denominator (from the respective chisquare statistics).
Modeling of coal and gangue volume based on shape clustering and image analysis
Published in International Journal of Coal Preparation and Utilization, 2023
Haoxiang Huang, Dongyang Dou, Gangyang Liu
The volume feature set was selected as the independent variable. Gangue volume was selected as the dependent variable. The gangue samples were segregated based on particle size, and a regression model was established. The verification results of the model are shown in Table 7. In the statistical model, the degree of freedom (DOF) refers to the number of variables that can be changed unrestrictedly in the sample. When constraints exist, the degrees of freedom decreased. F test is a test that the statistic follows the F-distribution under the null hypothesis. It is usually used to analyze statistical models that use more than one parameter to determine whether all or some of the parameters in the model are suitable for estimating the parent. The t test is mainly used for normal distribution with small sample size and unknown population standard deviation, which uses the t-distribution theory to infer the probability of a difference, so as to compare whether the difference between two means is significant.
Optimization of process parameters for adsorption of heavy metals from aqueous solutions by alumina-onion skin composite
Published in Chemical Engineering Communications, 2021
Adeyinka Sikiru Yusuff, John Olusoji Owolabi, Chiamaka Ogechi Igbomezie
The model adequacy was further tested by analysis of variance (ANOVA). The ANOVA for Pb2+ and Cd2+ removal efficiencies are presented in Tables 4 and 5, respectively. As can be seen in these tables, the model F-values for the Pb2+ and Cd2+ removal efficiencies were determined to be 15.05 and 6.91, respectively. The F-value indicates if the model is a good predictor of the experimental results and it should be greater than the tabulated value of the F-distribution for a certain number of degrees of freedom in the model at a level of significance α. However, since F-values obtained for the two models are greater than the tabulated F (4.54 at 95% significance) and (4.10 at 95% significance) for Pb2+ and Cd2+ removal percentages, respectively. The adequacies of the two models are confirmed.
Influence of thermal history on the intermediate and low-temperature reversible aging properties of asphalt binders
Published in Road Materials and Pavement Design, 2020
Haibo Ding, Yanjun Qiu, Ali Rahman
DENT tests were conducted on samples A and B + 3% wax, both of which have severe physical hardening trend at low temperature, to check if isothermal storage also has an influence on the damage properties of asphalt binder at intermediate temperatures. Load–displacement curves of two samples are shown in Figures 9 and 10. A one-way analysis of variance (ANOVA) was performed to check the significance of extending conditioning time on the design objectives. The yield load, displacement at failure for three ligament lengths and CTOD were considered as the dependent variable. The null hypothesis is that there is no significant effect of two conditioning time (2 and 24 h) on the mechanical response of DENT results. F-test was conducted on the basis of the F-distribution. The significance was tested considering 95% confidence interval. ANOVA for conditioning time of Sample A and Sample B + 3% wax are shown in Tables 2 and 3, respectively. From statistical analysis results, it can be concluded that extending DENT conditioning time from 2 to 24 h did not have a significant impact on the yield load and displacement at failure for three ligament lengths. Nowadays, the materials specification of the ministry of transportation of Ontario (MTO) specifies CTOD as quality acceptance criterion for ductile resistance of asphalt cement.