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 phylogeographic tests of competing 'Lake Carpentaria hypotheses' in the mouth-brooding freshwater fish, Glossamia aprion (Apogonidae)

Glacial cycles during the Pleistocene reduced sea levels and created new land connections in northern Australia, where many currently isolated rivers also became connected via an extensive paleo-lake system, 'Lake Carpentaria'. However, the most recent period during which populations of freshwater species were connected by gene flow across Lake Carpentaria is debated: various 'Lake Carpentaria hypotheses' have been proposed. Here, we used a statistical phylogeographic approach to assess the timing of past population connectivity across the Carpentaria region in the obligate freshwater fish, Glossamia aprion. Results for this species indicate that the most recent period of genetic exchange across the Carpentaria region coincided with the mid- to late Pleistocene, a result shown previously for other freshwater and diadromous species. Based on these findings and published studies for various freshwater, diadromous and marine species, we propose a set of 'Lake Carpentaria' hypotheses to explain past population connectivity in aquatic species: (1) strictly freshwater species had widespread gene flow in the mid- to late Pleistocene before the last glacial maximum; (2) marine species were subdivided into eastern and western populations by land during Pleistocene glacial phases; and (3) past connectivity in diadromous species reflects the relative strength of their marine affinity.

Multiple map hypotheses for planning and navigating in non-stationary environments

This paper presents a method to enable a mobile robot working in non-stationary environments to plan its path and localize within multiple map hypotheses simultaneously. The maps are generated using a long-term and short-term memory mechanism that ensures only persistent configurations in the environment are selected to create the maps. In order to evaluate the proposed method, experimentation is conducted in an office environment. Compared to navigation systems that use only one map, our system produces superior path planning and navigation in a non-stationary environment where paths can be blocked periodically, a common scenario which poses significant challenges for typical planners.

Simultaneous localization and planning on multiple map hypotheses

This paper presents a novel method to rank map hypotheses by the quality of localization they afford. The highest ranked hypothesis at any moment becomes the active representation that is used to guide the robot to its goal location. A single static representation is insufficient for navigation in dynamic environments where paths can be blocked periodically, a common scenario which poses significant challenges for typical planners. In our approach we simultaneously rank multiple map hypotheses by the influence that localization in each of them has on locally accurate odometry. This is done online for the current locally accurate window by formulating a factor graph of odometry relaxed by localization constraints. Comparison of the resulting perturbed odometry of each hypothesis with the original odometry yields a score that can be used to rank map hypotheses by their utility. We deploy the proposed approach on a real robot navigating a structurally noisy office environment. The configuration of the environment is physically altered outside the robots sensory horizon during navigation tasks to demonstrate the proposed approach of hypothesis selection.

Multi-Hypotheses Tracking using the Dempster–Shafer Theory, application to ambiguous road context

This paper presents a Multi-Hypotheses Tracking (MHT) approach that allows solving ambiguities that arise with previous methods of associating targets and tracks within a highly volatile vehicular environment. The previous approach based on the Dempster–Shafer Theory assumes that associations between tracks and targets are unique; this was shown to allow the formation of ghost tracks when there was too much ambiguity or conflict for the system to take a meaningful decision. The MHT algorithm described in this paper removes this uniqueness condition, allowing the system to include ambiguity and even to prevent making any decision if available data are poor. We provide a general introduction to the Dempster–Shafer Theory and present the previously used approach. Then, we explain our MHT mechanism and provide evidence of its increased performance in reducing the amount of ghost tracks and false positive processed by the tracking system.

The missing link of crime analysis: A systematic approach to testing competing hypotheses

Crime analysts have traditionally received little guidance from academic researchers in key tasks in the analysis process, specifically the testing of multiple hypotheses and evaluating evidence in a scientific fashion. This article attempts to fill this gap by outlining a method (the Analysis of Competing Hypotheses) of systematically analysing multiple explanations for crime problems. The method is systematic, avoids many cognitive errors common in analysis, and is explicit. It is argued that the implementation of this approach makes analytic products audit-able, the reasoning underpinning them transparent, and provides intelligence managers a rational professional development tool for individual analysts.

Structural Hypotheses And Raman-Spectroscopy Investigations Of Glasses Belonging To The B2s3-Li2s-Lii System

A previous B-11 nuclear magnetic resonance investigation of glasses belonging to the B2S3-Li2S-LiI system had allowed the authors to determine the variation of the number of three and four coordinated boron atoms with composition. These results, in addition to the observation that vitreous B2S3 quite easily forms fibres during casting, have led us to propose structural hypotheses for B2S3 based glasses, which are supported by the present Raman spectroscopy study. For vitreous B2S3 the spectra were accounted for on the basis of the various types of BS3/2 triangles proposed by the model. Molecular orbital considerations allowed us to assign the most significant lines for the binary glasses by assuming that BS3/2 triangles (with or without nonbridging sulphur atoms) and BS4 tetrahedra were present. In the ternary system, lithium iodide has been found to interact slightly on the structural entities, altering their vibrational characteristics without fundamentally modifying their nature.

Thermodynamic Models for the Size-dependent Melting of Nanoparticles: Different Hypotheses

A careful comparison of the experimental results reported in the literature reveals different variations of the melting temperature even for the same materials. Though there are different theoretical models, thermodynamic model has been extensively used to understand different variations of size-dependent melting of nanoparticles. There are different hypotheses such as homogeneous melting (HMH), liquid nucleation and growth (LNG) and liquid skin melting (LSM) to resolve different variations of melting temperature as reported in the literature. HMH and LNG account for the linear variation where as LSM is applied to understand the nonlinear behaviour in the plot of melting temperature against reciprocal of particle size. However, a bird's eye view reveals that either HMH or LSM has been extensively used by experimentalists. It has also been observed that not a single hypothesis can explain the size-dependent melting in the complete range. Therefore we describe an approach which can predict the plausible hypothesis for a given data set of the size-dependent melting temperature. A variety of data have been analyzed to ascertain the hypothesis and to test the approach.