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.

Possible impact of human CYP2E1 polymorphisms on the metabolism of acrylonitrile

Case reports of human accidental poisonings point to significant individual differences in human acrylonitrile metabolism and toxicity. A cohort of 59 persons with industrial handling of low levels of acrylonitrile has repetitively been studied from 1994 through 1999 as part of a medical surveillance programme. The analyses included adduct determinations of N-terminal N-(cyanoethyl)valine in haemoglobin and genotypings of the following cytochrome P-450 2E1 (CYP2E1) polymorphisms: G-1259C and C-1019T (two subjects heterozygous), A-316G (three subjects heterozygous), T-297A (15 subjects heterozygous), G-35T (eight subjects heterozygous), G4804A (two subjects heterozygous), T7668A (six subjects heterozygous). N-(Cyanoethyl)valine adduct levels were, if any, only slightly influenced by smoking and mainly determined by the external acrylonitrile exposures. The individual means and medians of N-(cyanoethyl)valine levels over the entire observation period were compared with the CYP2E1 variants (Wilcoxon rank sum test). No influences of the investigated CYP2E1 polymorphisms on the N-(cyanoethyl)valine levels appeared at the 5% level. However, there was a trend, at a level of P≃0.1, pointing to higher acrylonitrile-specific adduct levels in persons with the A-316G mutation. Higher adduct levels would be compatible with a slower CYP2E1-mediated metabolism of acrylonitrile and with lower extents of toxification to cyanide.

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.

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.

Whole-genome screening in ankylosing spondylitis: Evidence of non-MHC genetic-susceptibility loci

Ankylosing spondylitis (AS) is a common inflammatory arthritis predominantly affecting the axial skeleton. Susceptibility to the disease is thought to be oligogenic. To identify the genes involved, we have performed a genomewide scan in 185 families containing 255 affected sibling pairs. Two-point and multipoint nonparametric linkage analysis was performed. Regions were identified showing "suggestive" or stronger linkage with the disease on chromosomes 1p, 2q, 6p, 9q, 10q, 16q, and 19q. The MHC locus was identified as encoding the greatest component of susceptibility, with an overall LOD score of 15.6. The strongest non-MHC linkage lies on chromosome 16q (overall LOD score 4.7). These results strongly support the presence of non-MHC genetic-susceptibility factors in AS and point to their likely locations.

An immunodiagnostic assay for quantitation of specific ige to the major pollen allergen component, pas n 1, of the subtropical bahia grass

Background Pollens of the Panicoideae subfamily of grasses including Bahia (Paspalum notatum) are important allergen sources in subtropical regions of the world. An assay for specific IgE to the major molecular allergenic component, Pas n 1, of Bahia grass pollen (BaGP) would have immunodiagnostic utility for patients with pollen allergy in these regions. Methods Biotinylated Pas n 1 purified from BaGP was coated onto streptavidin ImmunoCAPs. Subjects were assessed by clinical history of allergic rhinitis and skin prick test (SPT) to aeroallergens. Serum total, BaGP-specific and Pas n 1-specific IgE were measured. Results: Pas n 1 IgE concentrations were highly correlated with BaGP SPT (r = 0.795, p < 0.0001) and BaGP IgE (r = 0.915, p < 0.0001). At 0.23 kU/l Pas n 1 IgE, the diagnostic sensitivity (92.4%) and specificity (93.1%) for the detection of BaGP allergy was high (area under receiver operator curve 0.960, p < 0.0001). The median concentrations of Pas n 1 IgE in non-Atopic subjects (0.01 kU/l, n = 67) and those with other allergies (0.02 kU/l, n = 59) showed no inter-group difference, whilst grass pollen-Allergic patients with allergic rhinitis showed elevated Pas n 1 IgE (6.71 kU/l, n = 182, p < 0.0001). The inter-Assay coefficient of variation for the BaGP-Allergic serum pool was 6.92%. Conclusions Pas n 1 IgE appears to account for most of the BaGP-specific IgE. This molecular component immunoassay for Pas n 1 IgE has potential utility to improve the sensitivity and accuracy of diagnosis of BaGP allergy for patients in subtropical regions.

Introducing the practice of statistics: are we environmentally friendly?

The practice of statistics is the focus of the world in which professional statisticians live. To understand meaningfully what this practice is about, students need to engage in it themselves. Acknowledging the limitations of a genuine classroom setting, this study attempted to expose four classes of year 5 students (n=91) to an authentic experience of the practice of statistics. Setting an overall context of people’s habits that are considered environmentally friendly, the students sampled their class and set criteria for being environmentally friendly based on questions from the Australian Bureau of Statistics CensusAtSchool site. They then analysed the data and made decisions, acknowledging their degree of certainty, about three populations based on their criteria: their class, year 5 students in their school and year 5 students in Australia. The next step was to collect a random sample the size of their class from an Australian Bureau of Statistics ‘population’, analyse it and again make a decision about Australian year 5 students. At the end, they suggested what further research they might do. The analysis of students’ responses gives insight into primary students’ capacity to appreciate and understand decision making, and to participate in the practice of statistics, a topic that has received very little attention in the literature. Based on the total possible score of 23 from student workbook entries, 80 % of students achieved at least a score of 11.

Rank regression for analyzing ordinal qualitative data for treatment comparison

Ordinal qualitative data are often collected for phenotypical measurements in plant pathology and other biological sciences. Statistical methods, such as t tests or analysis of variance, are usually used to analyze ordinal data when comparing two groups or multiple groups. However, the underlying assumptions such as normality and homogeneous variances are often violated for qualitative data. To this end, we investigated an alternative methodology, rank regression, for analyzing the ordinal data. The rank-based methods are essentially based on pairwise comparisons and, therefore, can deal with qualitative data naturally. They require neither normality assumption nor data transformation. Apart from robustness against outliers and high efficiency, the rank regression can also incorporate covariate effects in the same way as the ordinary regression. By reanalyzing a data set from a wheat Fusarium crown rot study, we illustrated the use of the rank regression methodology and demonstrated that the rank regression models appear to be more appropriate and sensible for analyzing nonnormal data and data with outliers.

Nonparametric rank regression for analyzing water quality concentration data with multiple detection limits

Environmental data usually include measurements, such as water quality data, which fall below detection limits, because of limitations of the instruments or of certain analytical methods used. The fact that some responses are not detected needs to be properly taken into account in statistical analysis of such data. However, it is well-known that it is challenging to analyze a data set with detection limits, and we often have to rely on the traditional parametric methods or simple imputation methods. Distributional assumptions can lead to biased inference and justification of distributions is often not possible when the data are correlated and there is a large proportion of data below detection limits. The extent of bias is usually unknown. To draw valid conclusions and hence provide useful advice for environmental management authorities, it is essential to develop and apply an appropriate statistical methodology. This paper proposes rank-based procedures for analyzing non-normally distributed data collected at different sites over a period of time in the presence of multiple detection limits. To take account of temporal correlations within each site, we propose an optimal linear combination of estimating functions and apply the induced smoothing method to reduce the computational burden. Finally, we apply the proposed method to the water quality data collected at Susquehanna River Basin in United States of America, which dearly demonstrates the advantages of the rank regression models.