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.

Socio-demographic vulnerability to heatwave impacts in Brisbane, Australia : a time series analysis

Objective: Examining the association between socioeconomic disadvantage and heat-related emergency department (ED) visits during heatwave periods in Brisbane, 2000–2008. Methods: Data from 10 public EDs were analysed using a generalised additive model for disease categories, age groups and gender. Results: Cumulative relative risks (RR) for non-external causes other than cardiovascular and respiratory diseases were 1.11 and 1.05 in most and least disadvantaged areas, respectively. The pattern persisted on lags 0–2. Elevated risks were observed for all age groups above 15 years in all areas. However, with RRs of 1.19–1.28, the 65–74 years age group in more disadvantaged areas stood out, compared with RR=1.08 in less disadvantaged areas. This pattern was observed on lag 0 but did not persist. The RRs for male presentations were 1.10 and 1.04 in most and less disadvantaged areas; for females, RR was 1.04 in less disadvantaged areas. This pattern persisted across lags 0–2. Conclusions: Heat-related ED visits increased during heatwaves. However, due to overlapping confidence intervals, variations across socioeconomic areas should be interpreted cautiously. Implications: ED data may be utilised for monitoring heat-related health impacts, particularly on the first day of heatwaves, to facilitate prompt interventions and targeted resource allocation.

Demographic faultlines in boards : impact of diversity and board size

Negative board diversity-organizational outcomes research findings have highlighted the importance of studying board demographic faultlines. Based on research gaps, this study focuses on gender diversity, age diversity, board size and faultlines formation in corporate boards. It proposes a positive linear diversity-faultlines relationship based on self-categorization and social identity theories, interaction effects of gender diversity and age diversity on faultlines based on contingency theories, and a U-shaped board size-faultlines strength relationship. The hypotheses were tested in 288 large companies listed on the Australian Securities Exchange using archival data. The results provided partial support for the interaction effects relationships and support to the U-shaped board size-faultlines strength relationship. The findings indicate that boards with low levels of age diversity experience a negative linear relationship between gender diversity and faultlines such that higher representation of women leads to weaker faultlines. The results also suggest that small- and large-sized boards experience stronger faultlines strength than medium-sized board. These results inform practice and underline implications of board demographic diversity and board size.

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.

Are empowered women more likely to deliver in facilities? An explorative study using the Nepal Demographic and Health Survey 2011

Development literature has argued that empowering women can effectively increase the utilisation of maternal health care. This study examines this hypothesis in the context of Nepal where only 28% of women delivered in facilities. The two-level random intercept logit models were fitted for data from the Nepal Demographic and Health Surveys 2011. Women‟s empowerment was quantified with a single index constructed from many variables. These variables captured different aspects of women‟s lives and decision-making in their households, and were combined using the principal component analysis method. The results confirmed a positive relationship between women‟s as an inevitable product of the economic development process.

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.

Initial burden of disease estimates for South Africa, 2000

BACKGROUND This paper describes the first national burden of disease study for South Africa. The main focus is the burden due to premature mortality, i.e. years of life lost (YLLs). In addition, estimates of the burden contributed by morbidity, i.e. the years lived with disability (YLDs), are obtained to calculate disability-adjusted life years (DALYs); and the impact of AIDS on premature mortality in the year 2010 is assessed. METHOD Owing to the rapid mortality transition and the lack of timely data, a modelling approach has been adopted. The total mortality for the year 2000 is estimated using a demographic and AIDS model. The non-AIDS cause-of-death profile is estimated using three sources of data: Statistics South Africa, the National Department of Home Affairs, and the National Injury Mortality Surveillance System. A ratio method is used to estimate the YLDs from the YLL estimates. RESULTS The top single cause of mortality burden was HIV/AIDS followed by homicide, tuberculosis, road traffic accidents and diarrhoea. HIV/AIDS accounted for 38% of total YLLs, which is proportionately higher for females (47%) than for males (33%). Pre-transitional diseases, usually associated with poverty and underdevelopment, accounted for 25%, non-communicable diseases 21% and injuries 16% of YLLs. The DALY estimates highlight the fact that mortality alone underestimates the burden of disease, especially with regard to unintentional injuries, respiratory disease, and nervous system, mental and sense organ disorders. The impact of HIV/AIDS is expected to more than double the burden of premature mortality by the year 2010. CONCLUSION This study has drawn together data from a range of sources to develop coherent estimates of premature mortality by cause. South Africa is experiencing a quadruple burden of disease comprising the pre-transitional diseases, the emerging chronic diseases, injuries, and HIV/AIDS. Unless interventions that reduce morbidity and delay morbidity become widely available, the burden due to HIV/AIDS can be expected to grow very rapidly in the next few years. An improved base of information is needed to assess the morbidity impact more accurately.

Provincial mortality in South Africa, 2000 - priority-setting for now and a benchmark for the future

Background. Cause-of-death statistics are an essential component of health information. Despite improvements, underregistration and misclassification of causes make it difficult to interpret the official death statistics. Objective. To estimate consistent cause-specific death rates for the year 2000 and to identify the leading causes of death and premature mortality in the provinces. Methods. Total number of deaths and population size were estimated using the Actuarial Society of South Africa ASSA2000 AIDS and demographic model. Cause-of-death profiles based on Statistics South Africa's 15% sample, adjusted for misclassification of deaths due to ill-defined causes and AIDS deaths due to indicator conditions, were applied to the total deaths by age and sex. Age-standardised rates and years of life lost were calculated using age weighting and discounting. Results. Life expectancy in KwaZulu-Natal and Mpumalanga is about 10 years lower than that in the Western Cape, the province with the lowest mortality rate. HIV/AIDS is the leading cause of premature mortality for all provinces. Mortality due to pre-transitional causes, such as diarrhoea, is more pronounced in the poorer and more rural provinces. In contrast, non-communicable disease mortality is similar across all provinces, although the cause profiles differ. Injury mortality rates are particularly high in provinces with large metropolitan areas and in Mpumalanga. Conclusion. The quadruple burden experienced in all provinces requires a broad range of interventions, including improved access to health care; ensuring that basic needs such as those related to water and sanitation are met; disease and injury prevention; and promotion of a healthy lifestyle. High death rates as a result of HIV/AIDS highlight the urgent need to accelerate the implementation of the treatment and prevention plan. In addition, there is an urgent need to improve the cause-of-death data system to provide reliable cause-of-death statistics at health district level.

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.

Alcohol use in South Africa : findings from the first demographic and health survey (1998)

Objective This study formed part of the 1998 South African Demographic and Health Survey, which included questions assessing the extent of alcohol use, risky drinking and alcohol problems among South Africans to obtain up-to-date baseline estimates of consumption and risky drinking and to inform intervention efforts. Method A two-stage random sample of 13,826 persons ages 15 or older (59% women) was included in the survey. Alcohol use was assessed through eight questions, including the CAGE questionnaire. Frequency analyses for different age groups, geographic setting, education level, population group and gender were calculated, as were odds ratios for these variables in relation to symptoms of alcohol problems. Results Current alcohol consumption was reported by 45% of the men and 17% of the women. White men (71%) were most likely and Asian women (9%) least likely to be current drinkers. Urban residents were more likely than nonurban dwellers to report current drinking. One third of the current drinkers reported risky drinking over weekends, and 28% of the men and 10% of the women scored above the cutoff level on the CAGE questionnaire. Symptoms of alcohol problems were significantly associated with lower socioeconomic status, no school education in women and being older than 25 years of age. Conclusions A comprehensive strategy is required to address the high levels of risky drinking and reported symptoms of alcohol problems.

Poverty and non-communicable diseases in South Africa

Background: High levels of wealth inequality with improved health statistics in South Africa (SA) provide an important opportunity to investigate non-communicable diseases (NCDs) among the poor. Aims: This paper uses two distinct national data sets to contrast patterns of mortality in rich and poor areas and explore the associations between poverty, risk factors, health care and selected NCDs diseases in South African adults. Methods: Causes of premature mortality in 1996 experienced in the poorest magisterial districts are compared with those in the richest, using average household wealth to classify districts. Logistic and multinomial regression are used to investigate the association of a household asset index and selected chronic conditions, related risk factors and healthcare indicators using data from the 1998 South African Demographic and Health Survey. Results: NCDs accounted for 39% and 33% of premature mortality in rich and poor districts respectively. The household survey data showed that the risk factors hypertension and obesity increased with increasing wealth, while most of the lifestyle factors, such as light smoking, domestic exposure to ``smoky'' fuels and alcohol dependence were associated with poverty. Treatment status for hypertension and asthma was worse for poor people than for rich people. Conclusions: The study suggests that NCDs and lifestyle-related risk factors are prevalent among the poor in SA and treatment for chronic diseases is lacking for poor people. The observed increase in hypertension and obesity with wealth suggests that unless comprehensive health promotion strategies are implemented, there will be an unmanageable chronic disease epidemic with future socioeconomic development in SA.

Determinants and treatment of hypertension in South Africans: The first demographic and health survey

Objectives: To identify the groups of patients with high prevalence and poor control of hypertension in South Africa. Methods: In the first national Demographic and Health Survey, 12 952 randomly selected South Africans, aged 15 years and older were surveyed. Trained interviewers completed questionnaires on socio-demographic characteristics, lifestyle and the management of hypertension. This cross-sectional survey also included blood pressure, height and weight measurements. Logistic regression analyses identified the determinants of hypertension and the treatment status in this dataset. Results: A high risk of hypertension was associated with less than tertiary education, older age groups, overweight and obese people, using alcohol in excess, and a family history of stroke and hypertension. Rural Africans had the lowest risk of hypertension, which was significantly higher in obese African women than in women with normal body mass index. Improved hypertension control was found in the wealthy, women, older persons, being Asian, and having medical insurance. Conclusions: Rural African people had lower hypertension prevalence rates than the other groups. The poorer, younger men, without health insurance had the worst level of hypertension control.