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Statistics
Published in Patrick F. Dunn, Michael P. Davis, Measurement and Data Analysis for Engineering and Science, 2017
Patrick F. Dunn, Michael P. Davis
The t-statistic can be thought of as the number of standard deviation of the means the sample mean value is from the population mean value. The p-value is then taken as the appropriate tail area from the student-t distribution based on the number of degrees of freedom, ν, where ν = N − 1. For a one-sided hypothesis test, either the right or left tail area is used, whereas for a two-sided hypothesis test, twice the tail area is the p-value.
Stochastic-based pavement rehabilitation model at the network level with prediction uncertainty considerations
Published in Road Materials and Pavement Design, 2023
In case the sample size is less than (30), then the normal statistic () is replaced by the t-statistic (), which is the case in the previously presented case study wherein (N = 12). The t-statistic is equal to (2.201) for a sample size with (11) degree of freedom (N-1) and 95% confidence level. The mean and standard deviation associated with the initial transition probabilities provided in Table 1 are computed to be equal to (A1,2 = 0.386) and (S1,2 = 0.141), respectively. Similarly, the mean and standard deviation for the terminal transition probabilities are calculated to be (A4,5 = 0.549) and (S4,5 = 0.171), respectively. Equation (16) results in (0.296) and (0.476) as the lower and upper-limit values, respectively, for the mean initial transition probability (A1,2). It also yields (0.439) and (0.659) as the limits for the mean terminal transition probability (A4,5).
Human factors affecting visual inspection of fatigue cracking in steel bridges
Published in Structure and Infrastructure Engineering, 2021
Leslie E. Campbell, Robert J. Connor, Julie M. Whitehead, Glenn A. Washer
Initially, a simple univariate regression analysis was used to identify statistically significant correlations between inspection performance and individual variables. The strength of the linear relationship was described using the Pearson correlation coefficient which varies from +1 (complete positive correlation) to −1 (complete negative correlation). A correlation coefficient of 0 indicates no linear correlation. The correlation coefficient was calculated by dividing the covariance of the two variables by the product of their standard deviations (Washington, Karlaftis, & Mannering, 2011). Then, a multivariate linear regression model was used to predict the influence that multiple variables, considered simultaneously, had on inspection performance. To understand the significance of the models, the test statistic (t-statistic) was used to determine the probability that the independent variable has no effect on the value of the dependent variable. For linear regression, the t-statistic is defined as the estimate of the coefficient of the independent variable divided by the standard error of the estimated coefficient. The t-statistic was assumed to have a t distribution with degrees of freedom equal to the number of observations minus the number of model parameters.
Examining freight performance of third-party logistics providers within the automotive industry in India: an environmental sustainability perspective
Published in International Journal of Production Research, 2020
Mohit Goswami, Arijit De, Muhammad Khoirul Khakim Habibi, Yash Daultani
The measurement model developed as illustrated in Figure 1 consists of four constructs: information sharing, internal enablers, external enablers, and sustainable freight transportation (dependent variable) and twelve independent variables. After conducting the reliability and validity tests, the data gathered were used to validate hypotheses. Bootstrap procedure was applied using SmartPLS 3. Bootstrap refers to selection of sample of samples repeatedly from the collected data with replacements. The means and variances of the samples thus compiled is compared with the original mean and variance to compute the t-statistic. Statistic related to the inter-construct variables corresponding to the information sharing, internal enablers and external enablers are illustrated in Tables 7–9.