Understanding the quantitative skill base on introductory statistics : a case study from business statistics

Basic mathematical skills are critical to a student’s ability to successfully undertake an introductory statistics course. Yet in business education this vitally important area of mathematics and statistics education is under-researched. The question therefore arises as to what level of mathematical skill a typical business studies student will possess as they enter the tertiary environment, and whether there are any common deficiencies that we can identify with a view to tackling the problem. This paper will focus on a study designed to measure the level of mathematical ability of first year business students. The results provide timely insight into a growing problem faced by many tertiary educators in this field.

Statistics critical in securing our food supply

“World food security … is at its lowest in half a century,” wrote Julian Cribb FTSE, a wellknown consultant in science communication and founding editor of www.sciencealert. com.au in the lead article in the 2008 ATSE Focus magazine issue entitled “Food for the world: the nation’s challenge”. Food security continues to be a key national and international concern and it is pleasing to see this issue of Focus again exploring aspects of the topic with the aim of continuing to raise awareness of issues and influencing relevant policy decisions. Statistics (or statistical science, more broadly) has been critical to the information and decision-making value chain needed to optimise agriculture and the food supply chain. The key steps are most often addressed by multidisciplinary research groups including statisticians in collaboration with life and physical scientists, agri-industry personnel and other relevant stakeholders.

Suicide, statistics and the coroner: A comparative study of death investigations

Australia has a significantly higher suicide rate than England. Rather than accepting that this ‘statistical fact’ is a direct reflection of some positivist truth, this paper begins with the premise that how suicide is counted depends upon what counts as suicide. This study involves semi-structured interviews with coroners both in Australia and England, as well as observations at inquests. Important differences between the two coronial systems include: first, quite different logics of operation; second, the burden of proof for reaching a finding of suicide is significantly higher in England; and third, the presence of family members at English inquests results in far greater pressure being brought to bear upon coroners. These combined factors result in a reduced likelihood of English coroners reaching a finding of suicide. The conclusions are twofold. First, this research supports existing criticisms of comparative suicide statistics. Second, this research adds theoretical weight to criticisms of positivist analyses of social phenomena.

A new approach to spatial data interpolation using higher-order statistics

Interpolation techniques for spatial data have been applied frequently in various fields of geosciences. Although most conventional interpolation methods assume that it is sufficient to use first- and second-order statistics to characterize random fields, researchers have now realized that these methods cannot always provide reliable interpolation results, since geological and environmental phenomena tend to be very complex, presenting non-Gaussian distribution and/or non-linear inter-variable relationship. This paper proposes a new approach to the interpolation of spatial data, which can be applied with great flexibility. Suitable cross-variable higher-order spatial statistics are developed to measure the spatial relationship between the random variable at an unsampled location and those in its neighbourhood. Given the computed cross-variable higher-order spatial statistics, the conditional probability density function (CPDF) is approximated via polynomial expansions, which is then utilized to determine the interpolated value at the unsampled location as an expectation. In addition, the uncertainty associated with the interpolation is quantified by constructing prediction intervals of interpolated values. The proposed method is applied to a mineral deposit dataset, and the results demonstrate that it outperforms kriging methods in uncertainty quantification. The introduction of the cross-variable higher-order spatial statistics noticeably improves the quality of the interpolation since it enriches the information that can be extracted from the observed data, and this benefit is substantial when working with data that are sparse or have non-trivial dependence structures.

Multilingual lexical resources to detect cognates in non-aligned texts

The identification of cognates between two distinct languages has recently start- ed to attract the attention of NLP re- search, but there has been little research into using semantic evidence to detect cognates. The approach presented in this paper aims to detect English-French cog- nates within monolingual texts (texts that are not accompanied by aligned translat- ed equivalents), by integrating word shape similarity approaches with word sense disambiguation techniques in order to account for context. Our implementa- tion is based on BabelNet, a semantic network that incorporates a multilingual encyclopedic dictionary. Our approach is evaluated on two manually annotated da- tasets. The first one shows that across different types of natural text, our method can identify the cognates with an overall accuracy of 80%. The second one, con- sisting of control sentences with semi- cognates acting as either true cognates or false friends, shows that our method can identify 80% of semi-cognates acting as cognates but also identifies 75% of the semi-cognates acting as false friends.

Phenotyping cotton ovule fibre initiation with spatial statistics

Yield in cultivated cotton (Gossypium spp.) is affected by the number and distribution of fibres initiated on the seed surface but, apart from simple statistical summaries, little has been done to assess this phenotype quantitatively. Here we use two types of spatial statistics to describe and quantify differences in patterning of cotton ovule fibre initials (FI). The following five different species of Gossypium were analysed: G. hirsutum L., G. barbadense L., G. arboreum, G. raimondii Ulbrich. and G. trilobum (DC.) Skovsted. Scanning electron micrographs of FIs were taken on the day of anthesis. Cell centres for fibre and epidermal cells were digitised and analysed by spatial statistics methods appropriate for marked point processes and tessellations. Results were consistent with previously published reports of fibre number and spacing. However, it was shown that the spatial distributions of FIs in all of species examined exhibit regularity, and are not completely random as previously implied. The regular arrangement indicates FIs do not appear independently of each other and we surmise there may be some form of mutual inhibition specifying fibre-initial development. It is concluded that genetic control of FIs differs from that of stomata, another well studied plant idioblast. Since spatial statistics show clear species differences in the distribution of FIs within this genus, they provide a useful method for phenotyping cotton. © CSIRO 2007.

Statistics at play

Three core components in developing children’s understanding and appreciation of data — establish a context, pose and answer statistical questions, represent and interpret data — lay the foundation for the fourth component: use data to enhance existing context.

Summarising and reporting sugarcane locomotive run statistics from TOTools and GPS data

The majority of sugar mill locomotives are equipped with GPS devices from which locomotive position data is stored. Locomotive run information (e.g. start times, run destinations and activities) is electronically stored in software called TOTools. The latest software development allows TOTools to interpret historical GPS information by combining this data with run information recorded in TOTools and geographic information from a GIS application called MapInfo. As a result, TOTools is capable of summarising run activity details such as run start and finish times and shunt activities with great accuracy. This paper presents 15 reports developed to summarise run activities and speed information. The reports will be of use pre-season to assist in developing the next year's schedule and for determining priorities for investment in the track infrastructure. They will also be of benefit during the season to closely monitor locomotive run performance against the existing schedule.

How do experts think about statistics? Hints for improving undergraduate and postgraduate training

Experts are increasingly being called upon to quantify their knowledge, particularly in situations where data is not yet available or of limited relevance. In many cases this involves asking experts to estimate probabilities. For example experts, in ecology or related fields, might be called upon to estimate probabilities of incidence or abundance of species, and how they relate to environmental factors. Although many ecologists undergo some training in statistics at undergraduate and postgraduate levels, this does not necessarily focus on interpretations of probabilities. More accurate elicitation can be obtained by training experts prior to elicitation, and if necessary tailoring elicitation to address the expert’s strengths and weaknesses. Here we address the first step of diagnosing conceptual understanding of probabilities. We refer to the psychological literature which identifies several common biases or fallacies that arise during elicitation. These form the basis for developing a diagnostic questionnaire, as a tool for supporting accurate elicitation, particularly when several experts or elicitors are involved. We report on a qualitative assessment of results from a pilot of this questionnaire. These results raise several implications for training experts, not only prior to elicitation, but more strategically by targeting them whilst still undergraduate or postgraduate students.

Top-down influences on lexical selection during spoken word production: A 4T fMRI investigation of refractory effects in picture naming

Spoken word production is assumed to involve stages of processing in which activation spreads through layers of units comprising lexical-conceptual knowledge and their corresponding phonological word forms. Using high-field (4T) functional magnetic resonance imagine (fMRI), we assessed whether the relationship between these stages is strictly serial or involves cascaded-interactive processing, and whether central (decision/control) processing mechanisms are involved in lexical selection. Participants performed the competitor priming paradigm in which distractor words, named from a definition and semantically related to a subsequently presented target picture, slow picture-naming latency compared to that with unrelated words. The paradigm intersperses two trials between the definition and the picture to be named, temporally separating activation in the word perception and production networks. Priming semantic competitors of target picture names significantly increased activation in the left posterior temporal cortex, and to a lesser extent the left middle temporal cortex, consistent with the predictions of cascaded-interactive models of lexical access. In addition, extensive activation was detected in the anterior cingulate and pars orbitalis of the inferior frontal gyrus. The findings indicate that lexical selection during competitor priming is biased by top-down mechanisms to reverse associations between primed distractor words and target pictures to select words that meet the current goal of speech.

Perfusion fMRI evidence for priming of shared feature-to-lexical connections during cumulative semantic interference in spoken word production

The speed at which target pictures are named increases monotonically as a function of prior retrieval of other exemplars of the same semantic category and is unaffected by the number of intervening items. This cumulative semantic interference effect is generally attributed to three mechanisms: shared feature activation, priming and lexical-level selection. However, at least two additional mechanisms have been proposed: (1) a 'booster' to amplify lexical-level activation and (2) retrieval-induced forgetting (RIF). In a perfusion functional Magnetic Resonance Imaging (fMRI) experiment, we tested hypotheses concerning the involvement of all five mechanisms. Our results demonstrate that the cumulative interference effect is associated with perfusion signal changes in the left perirhinal and middle temporal cortices that increase monotonically according to the ordinal position of exemplars being named. The left inferior frontal gyrus (LIFG) also showed significant perfusion signal changes across ordinal presentations; however, these responses did not conform to a monotonically increasing function. None of the cerebral regions linked with RIF in prior neuroimaging and modelling studies showed significant effects. This might be due to methodological differences between the RIF paradigm and continuous naming as the latter does not involve practicing particular information. We interpret the results as indicating priming of shared features and lexical-level selection mechanisms contribute to the cumulative interference effect, while adding noise to a booster mechanism could account for the pattern of responses observed in the LIFG.

Independent distractor frequency and age-of-acquisition dffects in picture-word interference: FMRI evidence for post-lexical and lexical accounts according to distractor type

In two fMRI experiments, participants named pictures with superimposed distractors that were high or low in frequency or varied in terms of age of acquisition. Pictures superimposed with low-frequency words were named more slowly than those superimposed with high-frequency words, and late-acquired words interfered with picture naming to a greater extent than early-acquired words. The distractor frequency effect (Experiment 1) was associated with increased activity in left premotor and posterior superior temporal cortices, consistent with the operation of an articulatory response buffer and verbal selfmonitoring system. Conversely, the distractor age-of-acquisition effect (Experiment 2) was associated with increased activity in the left middle and posterior middle temporal cortex, consistent with the operation of lexical level processes such as lemma and phonological word form retrieval. The spatially dissociated patterns of activity across the two experiments indicate that distractor effects in picture-word interference may occur at lexical or postlexical levels of processing in speech production.