Conducting statistical tests of hypotheses : five common misconceptions found in transportation research

Most statistical methods use hypothesis testing. Analysis of variance, regression, discrete choice models, contingency tables, and other analysis methods commonly used in transportation research share hypothesis testing as the means of making inferences about the population of interest. Despite the fact that hypothesis testing has been a cornerstone of empirical research for many years, various aspects of hypothesis tests commonly are incorrectly applied, misinterpreted, and ignored—by novices and expert researchers alike. On initial glance, hypothesis testing appears straightforward: develop the null and alternative hypotheses, compute the test statistic to compare to a standard distribution, estimate the probability of rejecting the null hypothesis, and then make claims about the importance of the finding. This is an oversimplification of the process of hypothesis testing. Hypothesis testing as applied in empirical research is examined here. The reader is assumed to have a basic knowledge of the role of hypothesis testing in various statistical methods. Through the use of an example, the mechanics of hypothesis testing is first reviewed. Then, five precautions surrounding the use and interpretation of hypothesis tests are developed; examples of each are provided to demonstrate how errors are made, and solutions are identified so similar errors can be avoided. Remedies are provided for common errors, and conclusions are drawn on how to use the results of this paper to improve the conduct of empirical research in transportation.

Statistical modeling to determine resonant frequency information present in combustion chamber pressure signals

A statistical modeling method to accurately determine combustion chamber resonance is proposed and demonstrated. This method utilises Markov-chain Monte Carlo (MCMC) through the use of the Metropolis-Hastings (MH) algorithm to yield a probability density function for the combustion chamber frequency and find the best estimate of the resonant frequency, along with uncertainty. The accurate determination of combustion chamber resonance is then used to investigate various engine phenomena, with appropriate uncertainty, for a range of engine cycles. It is shown that, when operating on various ethanol/diesel fuel combinations, a 20% substitution yields the least amount of inter-cycle variability, in relation to combustion chamber resonance.

Validation of the MEASURE automobile emissions model : a statistical analysis

The Mobile Emissions Assessment System for Urban and Regional Evaluation (MEASURE) model provides an external validation capability for hot stabilized option; the model is one of several new modal emissions models designed to predict hot stabilized emission rates for various motor vehicle groups as a function of the conditions under which the vehicles are operating. The validation of aggregate measurements, such as speed and acceleration profile, is performed on an independent data set using three statistical criteria. The MEASURE algorithms have proved to provide significant improvements in both average emission estimates and explanatory power over some earlier models for pollutants across almost every operating cycle tested.

On the nature of over-dispersion in motor vehicle crash prediction models

Statistical modeling of traffic crashes has been of interest to researchers for decades. Over the most recent decade many crash models have accounted for extra-variation in crash counts—variation over and above that accounted for by the Poisson density. The extra-variation – or dispersion – is theorized to capture unaccounted for variation in crashes across sites. The majority of studies have assumed fixed dispersion parameters in over-dispersed crash models—tantamount to assuming that unaccounted for variation is proportional to the expected crash count. Miaou and Lord [Miaou, S.P., Lord, D., 2003. Modeling traffic crash-flow relationships for intersections: dispersion parameter, functional form, and Bayes versus empirical Bayes methods. Transport. Res. Rec. 1840, 31–40] challenged the fixed dispersion parameter assumption, and examined various dispersion parameter relationships when modeling urban signalized intersection accidents in Toronto. They suggested that further work is needed to determine the appropriateness of the findings for rural as well as other intersection types, to corroborate their findings, and to explore alternative dispersion functions. This study builds upon the work of Miaou and Lord, with exploration of additional dispersion functions, the use of an independent data set, and presents an opportunity to corroborate their findings. Data from Georgia are used in this study. A Bayesian modeling approach with non-informative priors is adopted, using sampling-based estimation via Markov Chain Monte Carlo (MCMC) and the Gibbs sampler. A total of eight model specifications were developed; four of them employed traffic flows as explanatory factors in mean structure while the remainder of them included geometric factors in addition to major and minor road traffic flows. The models were compared and contrasted using the significance of coefficients, standard deviance, chi-square goodness-of-fit, and deviance information criteria (DIC) statistics. The findings indicate that the modeling of the dispersion parameter, which essentially explains the extra-variance structure, depends greatly on how the mean structure is modeled. In the presence of a well-defined mean function, the extra-variance structure generally becomes insignificant, i.e. the variance structure is a simple function of the mean. It appears that extra-variation is a function of covariates when the mean structure (expected crash count) is poorly specified and suffers from omitted variables. In contrast, when sufficient explanatory variables are used to model the mean (expected crash count), extra-Poisson variation is not significantly related to these variables. If these results are generalizable, they suggest that model specification may be improved by testing extra-variation functions for significance. They also suggest that known influences of expected crash counts are likely to be different than factors that might help to explain unaccounted for variation in crashes across sites