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Engineering Statistics
Published in William F. Ames, George Cain, Y.L. Tong, W. Glenn Steele, Hugh W. Coleman, Richard L. Kautz, Dan M. Frangopol, Paul Norton, Mathematics for Mechanical Engineers, 2022
Fact 4. The distribution of the statistic T=n(X¯−μ)/S, where S=S2 is the sample standard deviation, is called a Student’s t distribution with ν = n − 1 degrees of freedom, in symbols. i(n − 1), This distribution is useful for making inference on μ when σ2 is unknown; a table of the percentiles can be found in most statistics textbooks.
Research Methodology
Published in Arwa Ahmed Gasm Elseid, Alnazier Osman Mohammed Hamza, Computer-Aided Glaucoma Diagnosis System, 2020
Arwa Ahmed Gasm Elseid, Alnazier Osman Mohammed Hamza
This is the process of selecting a subset of relevant features (variables, predictors) to be used in model construction. In this research, two types of features were selected: Sequential feature selection;t-test feature selection. SFS: the removal (or addition) of one feature at a time, based on the classifier’s performance, until a feature subset of the desired size is reached.t-test: the t-test is any statistical hypothesis in which the test’s statistics follow a student’s t-distribution under the null hypothesis. It is used to determine if two sets of data are significantly different from each other, and it does this by assessing whether the means of two groups are statistically different from each other. Here, 78 features were applied to the OD, OC, and RNFL. The relevant features were then chosen by these two selection methods, resulting in eight features that were used in the final glaucoma classification.
Image Statistics
Published in Morton John Canty, Image Analysis, Classification, and Change Detection in Remote Sensing, 2019
The Student-t distribution is used to make statements regarding the mean when the variance is unknown. Thus if Zi, ν = 1 … m, is a sample from a normal distribution with mean μ and unknown variance, and Z¯=1m∑i=1mZi,S=1m∑i=1m(Zi−Z¯)2,
The impact resistance and mechanical properties of fiber reinforced self-compacting concrete (SCC) containing nano-SiO2 and silica fume
Published in European Journal of Environmental and Civil Engineering, 2018
where, t is the value of Student t-distribution for the specified level of confidence. The value of Student t-distribution “t” not only depends on the level of confidence, but it is also dependent on the degree of freedom, which is related to the number of samples. For degrees of freedom more than 120, the value of “t” approaches 1.645 and 1.282 at 95 and 90% level of confidence, respectively (Box, Hunter, & Hunter, 1978; Moore & McCabe, 1989). Table 6 lists the minimum number of replications required to keep the error under specified limits at the 95 and 90% level of confidence. Table 6 indicates that, if the error is retained lower than 10% for the first crack impact resistance and the ultimate crack impact resistance, the minimum number of required replications would be 36 and 39, respectively at 90% level of confidence. This table also indicates if the error is kept lower than 10%, the minimum numbers of replications for specimens are 59 and 65 for the first-crack strength and the failure strength, respectively at 95% level of confidence.
Effect of surface modification and knife penetration angle on the Quasi-Static Knife Penetration Resistance of para-aramid fabrics
Published in The Journal of The Textile Institute, 2019
Muhammad Usman Javaid, Jiří Militký, Jakub Wiener, Abdul Jabbar, Jana Salačová, Muhammad Umair
The coefficient of surface friction of different samples was also analysed, and the results are given in Table 4. The values in parenthesis show the Student’s t-Distribution at 95% confidence interval. The coefficient of friction is found to be increased in order of S2 > S1 > N. It may indicate that the deposition of SiO2 causes the surface to become irregular and coarser and hence resulting in the higher coefficient of friction for fabric surface. Furthermore, a greater amount of deposition of SiO2 on treated samples resulted in a greater increase in frictional coefficient (as evident from Tables 3 and 4).
Evidence-based assessment of energy performance of two large centrifugal chillers over nine cooling seasons
Published in Science and Technology for the Built Environment, 2021
The critical region of the Student’s t-distribution for the two-tailed test is defined as: t > tCR,α/2,n-1, and t < - tCR, α/2, n-1. The critical value tCR is selected by using the significance level α/2 = 0.025 (2.5% probability of committing a Type I error, or rejection of null hypothesis when it is true); and number of degrees of freedom d.f. = n-1. The null hypothesis is rejected if t is in the critical region of the Student’s t-distribution.