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.

Shear tests of Litesteel beams with web openings

This paper presents the details of experimental studies on the shear strength of a recently developed, cold-formed steel beam known as LiteSteel Beam (LSB) with web openings. The innovative LSB sections have the beneficial characteristics of torsionally rigid closed rectangular flanges combined with economical fabrication processes from a single strip of high strength steel. They combine the stability of hot-rolled steel sections with the high strength to weight ratio of conventional cold-formed steel sections. The LSB sections are commonly used as flexural members in the building industry. Current practice in flooring systems is to include openings in the web element of floor joists or bearers so that building services can be located within them. Shear behaviour of LSBs with web openings is more complicated while their shear strengths are considerably reduced by the presence of web openings. However, limited research has been undertaken on the shear behaviour and strength of LSBs with web openings. Therefore a detailed experimental study involving 26 shear tests was undertaken to investigate the shear behaviour and strength of different LSB sections. Simply supported test specimens of LSBs with an aspect ratio of 1.5 were loaded at midspan until failure. This paper presents the details of this experimental study and the results. Experimental results showed that the current design rules in cold-formed steel structures design codes (AS/NZS 4600) [1] are very conservative for the shear design of LSBs with web openings. Improved design equations have been proposed for the shear strength of LSBs with web openings based on experimental results from this study.

Cracking the language code : NAPLAN numeracy tests in years 7 and 9

Focusing on the use of language is a crucial strategy in good mathematics teaching and a teacher’s guidance can assist students to master the language of mathematics. This article discusses the statements with reference to recent year 7 and 9 NAPLAN numeracy tests. It draws the readers’ attention to the complexities of language in the field of mathematics. Although this article refers to NAPLAN numeracy tests it also offers advice about good teaching practice.

Lateral distortional buckling tests of a new hollow flange channel beam

The LiteSteel beam (LSB) is a new hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. The LSBs are commonly used as flexural members in buildings. However, the LSB flexural members are subjected to lateral distortional buckling, which reduces their member moment capacities. Unlike the commonly observed lateral torsional buckling of steel beams, the lateral distortional buckling of LSBs is characterised by simultaneous lateral deflection, twist, and cross sectional change due to web distortion. An experimental study including more than 50 lateral buckling tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. It included the available 13 LSB sections with spans ranging from 1200 to 4000 mm. Lateral buckling tests based on a quarter point loading were conducted using a special test rig designed to simulate the required simply supported and loading conditions accurately. Experimental moment capacities were compared with the predictions from the design rules in the Australian cold-formed steel structures standard. The new design rules in the standard were able to predict the moment capacities more accurately than previous design rules. This paper presents the details of lateral distortional buckling tests, in particular the features of the lateral buckling test rig, the results and the comparisons. It also includes the results of detailed studies into the mechanical properties and residual stresses of LSBs.

Unbiased estimation of the half-life to price index convergence among U.S. cities

Estimates of the half-life to convergence of prices across a panel of cities are subject to bias from three potential sources: inappropriate cross-sectional aggregation of heterogeneous coefficients, presence of lagged dependent variables in a model with individual fixed effects, and time aggregation of commodity prices. This paper finds no evidence of heterogeneity bias in annual CPI data for 17 U.S. cities from 1918 to 2006, but correcting for the “Nickell bias” and time aggregation bias produces a half-life of 7.5 years, shorter than estimates from previous studies.

Propagation of low power low divergence Gaussian fields in unbiased self-defocusing photorefractive media and their interactions

Many optical networks are limited in speed and processing capability due to the necessity for the optical signal to be converted to an electrical signal and back again. In addition, electronically manipulated interconnects in an otherwise optical network lead to overly complicated systems. Optical spatial solitons are optical beams that propagate without spatial divergence. They are capable of phase dependent interactions, and have therefore been extensively researched as suitable all optical interconnects for over 20 years. However, they require additional external components, initially high voltage power sources were required, several years later, high power background illumination had replaced the high voltage. However, these additional components have always remained as the greatest hurdle in realising the applications of the interactions of spatial optical solitons as all optical interconnects. Recently however, self-focusing was observed in an otherwise self-defocusing photorefractive crystal. This observation raises the possibility of the formation of soliton-like fields in unbiased self-defocusing media, without the need for an applied electrical field or background illumination. This thesis will present an examination of the possibility of the formation of soliton-like low divergence fields in unbiased self-defocusing photorefractive media. The optimal incident beam and photorefractive media parameters for the formation of these fields will be presented, together with an analytical and numerical study of the effect of these parameters. In addition, preliminary examination of the interactions of two of these fields will be presented. In order to complete an analytical examination of the field propagating through the photorefractive medium, the spatial profile of the beam after propagation through the medium was determined. For a low power solution, it was found that an incident Gaussian field maintains its Gaussian profile as it propagates. This allowed the beam at all times to be described by an individual complex beam parameter, while also allowing simple analytical solutions to the appropriate wave equation. An analytical model was developed to describe the effect of the photorefractive medium on the Gaussian beam. Using this model, expressions for the required intensity dependent change in both the real and imaginary components of the refractive index were found. Numerical investigation showed that under certain conditions, a low powered Gaussian field could propagate in self-defocusing photorefractive media with divergence of approximately 0.1 % per metre. An investigation into the parameters of a Ce:BaTiO3 crystal showed that the intensity dependent absorption is wavelength dependent, and can in fact transition to intensity dependent transparency. Thus, with careful wavelength selection, the required intensity dependent change in both the real and imaginary components of the refractive index for the formation of a low divergence Gaussian field are physically realisable. A theoretical model incorporating the dependence of the change in real and imaginary components of the refractive index on propagation distance was developed. Analytical and numerical results from this model are congruent with the results from the previous model, showing low divergence fields with divergence less than 0.003 % over the propagation length of the photorefractive medium. In addition, this approach also confirmed the previously mentioned self-focusing effect of the self-defocusing media, and provided an analogy to a negative index GRIN lens with an intensity dependent focal length. Experimental results supported the findings of the numerical analysis. Two low divergence fields were found to possess the ability to interact in a Ce:BaTiO3 crystal in a soliton-like fashion. The strength of these interactions was found to be dependent on the degree of divergence of the individual beams. This research found that low-divergence fields are possible in unbiased self-defocusing photorefractive media, and that soliton-like interactions between two of these fields are possible. However, in order for these types of fields to be used in future all optical interconnects, the manipulation of these interactions, together with the ability for these fields to guide a second beam at a different wavelength, must be investigated.

The use of semantic priming as a paradigm for the detection of faking on self-report psychological tests

It is recognised that individuals do not always respond honestly when completing psychological tests. One of the foremost issues for research in this area is the inability to detect individuals attempting to fake. While a number of strategies have been identified in faking, a commonality of these strategies is the latent role of long term memory. Seven studies were conducted in order to examine whether it is possible to detect the activation of faking related cognitions using a lexical decision task. Study 1 found that engagement with experiential processing styles predicted the ability to fake successfully, confirming the role of associative processing styles in faking. After identifying appropriate stimuli for the lexical decision task (Studies 2A and 2B), Studies 3 to 5 examined whether a cognitive state of faking could be primed and subsequently identified, using a lexical decision task. Throughout the course of these studies, the experimental methodology was increasingly refined in an attempt to successfully identify the relevant priming mechanisms. The results were consistent and robust throughout the three priming studies: faking good on a personality test primed positive faking related words in the lexical decision tasks. Faking bad, however, did not result in reliable priming of negative faking related cognitions. To more completely address potential issues with the stimuli and the possible role of affective priming, two additional studies were conducted. Studies 6A and 6B revealed that negative faking related words were more arousing than positive faking related words, and that positive faking related words were more abstract than negative faking related words and neutral words. Study 7 examined whether the priming effects evident in the lexical decision tasks occurred as a result of an unintentional mood induction while faking the psychological tests. Results were equivocal in this regard. This program of research aligned the fields of psychological assessment and cognition to inform the preliminary development and validation of a new tool to detect faking. Consequently, an implicit technique to identify attempts to fake good on a psychological test has been identified, using long established and robust cognitive theories in a novel and innovative way. This approach represents a new paradigm for the detection of individuals responding strategically to psychological testing. With continuing development and validation, this technique may have immense utility in the field of psychological assessment.

Section moment capacity tests of LiteSteel Beams

The LiteSteel Beam (LSB) is a new cold-formed hollow flange channel section developed by OneSteel Australian Tube Mills using their patented dual electric resistance welding and automated continuous roll-forming process. It has a unique geometry consisting of torsionally rigid rectangular hollow flanges and a relatively slender web. In addition to this unique geometry, the LSB sections also have unique characteristics relating to their stress-strain curves, residual stresses, initial geometric imperfections and hollow flanges that are not encountered in conventional hot-rolled and cold-formed steel channel sections. An experimental study including 20 section moment capacity tests was therefore conducted to investigate the behaviour and strength of LSB flexural members. The presence of inelastic reserve bending capacity in these beams was investigated in detail although the current design rules generally limit the section moment capacities of cold-formed steel members to their first yield moments. The ultimate moment capacities from the tests were compared with the section moment capacities predicted by the current cold-formed and hot-rolled steel design standards. It was found that compact and non-compact LSB sections have greater moment capacities than their first yield moments. The current cold-formed steel design standards were found to be conservative in predicting the section moment capacities of compact and non-compact LSB sections while the hot-rolled steel design standards were able to better predict them. This paper has shown that suitable modifications are needed to the current design rules to allow the inclusion of available inelastic bending capacities of LSBs in design.

Time limitations in NAPLAN numeracy tests

The article discusses evidence that time prevented many students from showing what they could do in the 2010 Year 7 and 9 NAPLAN numeracy tests. In addition to analysing the available data, the article discusses some NAPLAN numeracy questions that contribute to this problem. It is suggested that schools should investigate whether time limitation is a problem for their own students. The article discusses the implications of these findings for teachers preparing students for NAPLAN tests and for the developers of the tests.

Non-compositional concepts and quantum tests

Compositionality is a frequently made assumption in linguistics, and yet many human subjects reveal highly non-compositional word associations when confronted with novel concept combinations. This article will show how a non-compositional account of concept combinations can be supplied by modelling them as interacting quantum systems.

Tests and Models of Non-compositional Concepts

The question of under what conditions conceptual representation is compositional remains debatable within cognitive science. This paper proposes a well developed mathematical apparatus for a probabilistic representation of concepts, drawing upon methods developed in quantum theory to propose a formal test that can determine whether a specific conceptual combination is compositional, or not. This test examines a joint probability distribution modeling the combination, asking whether or not it is factorizable. Empirical studies indicate that some combinations should be considered non-compositionally.

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.