The experience of teaching statistics to non-specialist students in Saudi universities

Undoubtedly, statistics has become one of the most important subjects in the modern world, where its applications are ubiquitous. The importance of statistics is not limited to statisticians, but also impacts upon non-statisticians who have to use statistics within their own disciplines. Several studies have indicated that most of the academic departments around the world have realized the importance of statistics to non-specialist students. Therefore, the number of students enrolled in statistics courses has vastly increased, coming from a variety of disciplines. Consequently, research within the scope of statistics education has been able to develop throughout the last few years. One important issue is how statistics is best taught to, and learned by, non-specialist students. This issue is controlled by several factors that affect the learning and teaching of statistics to non-specialist students, such as the use of technology, the role of the English language (especially for those whose first language is not English), the effectiveness of statistics teachers and their approach towards teaching statistics courses, students’ motivation to learn statistics and the relevance of statistics courses to the main subjects of non-specialist students. Several studies, focused on aspects of learning and teaching statistics, have been conducted in different countries around the world, particularly in Western countries. Conversely, the situation in Arab countries, especially in Saudi Arabia, is different; here, there is very little research in this scope, and what there is does not meet the needs of those countries towards the development of learning and teaching statistics to non-specialist students. This research was instituted in order to develop the field of statistics education. The purpose of this mixed methods study was to generate new insights into this subject by investigating how statistics courses are currently taught to non-specialist students in Saudi universities. Hence, this study will contribute towards filling the knowledge gap that exists in Saudi Arabia. This study used multiple data collection approaches, including questionnaire surveys from 1053 non-specialist students who had completed at least one statistics course in different colleges of the universities in Saudi Arabia. These surveys were followed up with qualitative data collected via semi-structured interviews with 16 teachers of statistics from colleges within all six universities where statistics is taught to non-specialist students in Saudi Arabia’s Eastern Region. The data from questionnaires included several types, so different techniques were used in analysis. Descriptive statistics were used to identify the demographic characteristics of the participants. The chi-square test was used to determine associations between variables. Based on the main issues that are raised from literature review, the questions (items scales) were grouped and five key groups of questions were obtained which are: 1) Effectiveness of Teachers; 2) English Language; 3) Relevance of Course; 4) Student Engagement; 5) Using Technology. Exploratory data analysis was used to explore these issues in more detail. Furthermore, with the existence of clustering in the data (students within departments within colleges, within universities), multilevel generalized linear models for dichotomous analysis have been used to clarify the effects of clustering at those levels. Factor analysis was conducted confirming the dimension reduction of variables (items scales). The data from teachers’ interviews were analysed on an individual basis. The responses were assigned to one of the eight themes that emerged from within the data: 1) the lack of students’ motivation to learn statistics; 2) students' participation; 3) students’ assessment; 4) the effective use of technology; 5) the level of previous mathematical and statistical skills of non-specialist students; 6) the English language ability of non-specialist students; 7) the need for extra time for teaching and learning statistics; and 8) the role of administrators. All the data from students and teachers indicated that the situation of learning and teaching statistics to non-specialist students in Saudi universities needs to be improved in order to meet the needs of those students. The findings of this study suggested a weakness in the use of statistical software applications in these courses. This study showed that there is lack of application of technology such as statistical software programs in these courses, which would allow non-specialist students to consolidate their knowledge. The results also indicated that English language is considered one of the main challenges in learning and teaching statistics, particularly in institutions where English is not used as the main language. Moreover, the weakness of mathematical skills of students is considered another major challenge. Additionally, the results indicated that there was a need to tailor statistics courses to the needs of non-specialist students based on their main subjects. The findings indicate that statistics teachers need to choose appropriate methods when teaching statistics courses.

A comparison of the physiological demands of rugby union match-play when determined by absolute (ABS) or individual (IND) velocity bands in Global Positioning System (GPS) analysis

Since turning professional in 1995 there have been considerable advances in the research on the demands of rugby union, largely using Global Positioning System (GPS) analysis over the last 10 years. A systematic review on the use of GPS, particularly the setting of absolute (ABS) and individual (IND) velocity bands in field based, intermittent, high-intensity (HI) team sports was undertaken. From 3669 records identified, 38 studies were included for qualitative analysis. Little agreement on the definition of movement intensities within team sports was found, only three papers, all on rugby union, had used IND bands, with only one comparing ABS and IND methods. Thus, the aim of this study was to determine if there is a difference in the demands within positions when comparing ABS and IND methods for GPS analysis and if these differences are significantly different between the forward and back positional groups. A total of 214 data files were recorded from 26 players in 17 matches of the 2015/2016 Scottish BT Premiership. ABS velocity zones 1-7 were set at 1) 0-6, 2) 6.1-11, 3) 11.1-15, 4) 15.1-18, 5) 18.1-21, 6) 21.1-15 and 7) 25.1-40km.h-1 while IND zones 1-7 were 1) <20, 2) 20-40, 3) 40-50, 4) 50-70, 5) 70-80, 6) 80-95 and 7) 95-100% of player’s individually determined maximum velocity (Vmax). A 40m sprint test measured Vmax using OptaPro S4 10 Hz (catapult, Australia) GPS units to derive IND bands. The same GPS units were worn during matches. GPS outputs analysed were % distance, % time, high intensity efforts (HIEs) over 18.1 km.h-1 / 70% max velocity and repeated high intensity efforts (RHIEs) which consists of three HIEs in 21secs. General linear model (GLM) analysis identified a significant difference in the measurement of % total distance covered, between the ABS and IND methods in all zones for forwards (p<0.05) and backs (p<0.05). This difference was also significant between forwards and backs in zones 1, shown as mean difference ± standard deviation (3.7±0.7%), 6 (1.2±0.4%) and 7 (1.0±0.0%) respectively (p<0.05). Percentage time estimations were significantly different between ABS and IND analysis within forwards in zones 1 (1.7±1.7%), 2 (-2.9±1.3%), 3 (1.9±0.8%), 4 (-1.4±0.8%) and 5 (0.2±0.4%), and within backs in zones 1 (-10±1.5%), 2 (-1.2±1.1%), 3 (1.8±0.9%) and 5 (0.6±0.5%) (p<0.05). The difference between groups was significant in zones 1, 2, 4 and 5 (p<0.05). The number of HIEs was significantly different between forwards and backs in zones 6 (6±2) and 7 (3±2). RHIEs were significantly different between ABS and IND for forwards (1±2, p<0.05) although not between groups. Until more research on the differences in ABS and IND methods is carried out, then neither can be deemed a criterion method. In conclusion, there are significant differences between the ABS and IND methods of GPS analysis of the physical demands of rugby union, which must be considered when used to inform training load and recovery to improve performance and reduce injuries.

Quantification of air quality in space and time and its effects on health

The long-term adverse effects on health associated with air pollution exposure can be estimated using either cohort or spatio-temporal ecological designs. In a cohort study, the health status of a cohort of people are assessed periodically over a number of years, and then related to estimated ambient pollution concentrations in the cities in which they live. However, such cohort studies are expensive and time consuming to implement, due to the long-term follow up required for the cohort. Therefore, spatio-temporal ecological studies are also being used to estimate the long-term health effects of air pollution as they are easy to implement due to the routine availability of the required data. Spatio-temporal ecological studies estimate the health impact of air pollution by utilising geographical and temporal contrasts in air pollution and disease risk across $n$ contiguous small-areas, such as census tracts or electoral wards, for multiple time periods. The disease data are counts of the numbers of disease cases occurring in each areal unit and time period, and thus Poisson log-linear models are typically used for the analysis. The linear predictor includes pollutant concentrations and known confounders such as socio-economic deprivation. However, as the disease data typically contain residual spatial or spatio-temporal autocorrelation after the covariate effects have been accounted for, these known covariates are augmented by a set of random effects. One key problem in these studies is estimating spatially representative pollution concentrations in each areal which are typically estimated by applying Kriging to data from a sparse monitoring network, or by computing averages over modelled concentrations (grid level) from an atmospheric dispersion model. The aim of this thesis is to investigate the health effects of long-term exposure to Nitrogen Dioxide (NO2) and Particular matter (PM10) in mainland Scotland, UK. In order to have an initial impression about the air pollution health effects in mainland Scotland, chapter 3 presents a standard epidemiological study using a benchmark method. The remaining main chapters (4, 5, 6) cover the main methodological focus in this thesis which has been threefold: (i) how to better estimate pollution by developing a multivariate spatio-temporal fusion model that relates monitored and modelled pollution data over space, time and pollutant; (ii) how to simultaneously estimate the joint effects of multiple pollutants; and (iii) how to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. Specifically, chapters 4 and 5 are developed to achieve (i), while chapter 6 focuses on (ii) and (iii). In chapter 4, I propose an integrated model for estimating the long-term health effects of NO2, that fuses modelled and measured pollution data to provide improved predictions of areal level pollution concentrations and hence health effects. The air pollution fusion model proposed is a Bayesian space-time linear regression model for relating the measured concentrations to the modelled concentrations for a single pollutant, whilst allowing for additional covariate information such as site type (e.g. roadside, rural, etc) and temperature. However, it is known that some pollutants might be correlated because they may be generated by common processes or be driven by similar factors such as meteorology. The correlation between pollutants can help to predict one pollutant by borrowing strength from the others. Therefore, in chapter 5, I propose a multi-pollutant model which is a multivariate spatio-temporal fusion model that extends the single pollutant model in chapter 4, which relates monitored and modelled pollution data over space, time and pollutant to predict pollution across mainland Scotland. Considering that we are exposed to multiple pollutants simultaneously because the air we breathe contains a complex mixture of particle and gas phase pollutants, the health effects of exposure to multiple pollutants have been investigated in chapter 6. Therefore, this is a natural extension to the single pollutant health effects in chapter 4. Given NO2 and PM10 are highly correlated (multicollinearity issue) in my data, I first propose a temporally-varying linear model to regress one pollutant (e.g. NO2) against another (e.g. PM10) and then use the residuals in the disease model as well as PM10, thus investigating the health effects of exposure to both pollutants simultaneously. Another issue considered in chapter 6 is to allow for the uncertainty in the estimated pollution concentrations when estimating their health effects. There are in total four approaches being developed to adjust the exposure uncertainty. Finally, chapter 7 summarises the work contained within this thesis and discusses the implications for future research.