Using On-Line Quizzes to Help Students Learn Probability and Statistics

Online quizzes can be an effective and flexible means of helping learners develop key skills in probability and statistics. Quizzes give instant feedback, to help reinforce correct understanding and eliminate fundamental errors at an early stage in learning. We will describe our experience of designing and using quizzes with non-specialist and specialist students, on several different platforms including, most recently, Moodle. We describe Model Choice, a tool that helps students identify from a brief scenario the standard family of probability distributions they should work with to solve a problem. We will emphasize key design aspects of a successful quiz system, such as the importance of giving informative feedback to the learner. Using a standard platform, such as Moodle, is likely to require some compromise on design principles but building a stand-alone system to implement ideal design choices is very time-consuming

Methods of Inference for Nonparametric Curves and Surfaces

Nonparametric regression models offer attractive extensions to the familiar approaches of parametric regression. They adapt to departures from standard parametric forms and therefore have the potential to capture features which may otherwise go unnoticed. This property accounts for the large volume of work in the area of estimation of nonparametric models which has emerged over the last two decades. Inferential techniques using nonparametric model fits, however, have not been so quick to develop. This thesis contributes to this area of research by examining the task of assessing covariate effects via comparisons of nonparametric model fits. In particular, the asymptotic and finite sample bias properties of estimates obtained via local linear smoothers are a major consideration and methods of inference which take into account these properties are developed. Chapter 1 introduces and presents an overview of existing methods of estimation and inference amongst nonparametric regression. Chapter 2 focuses on the task of inference by considering the estimation of the error variance in the nonparametric model context. Special attention is given to the development and assessment of difference based estimators in the presence of two covariates. It is shown that difference based estimators are a viable alternative, in terms of accuracy, to standard residual based estimators. Chapters 3 and 4 employ the estimators of Chapter 2 in the development of test procedures which make comparisons amongst a class of bivariate nonparametric regression models. Chapter 3 develops the theoretical properties of several forms of the test statistic, with particular attention given to statistics based on direct comparisons of fitted values. The theory also highlights the role of centred smoothers and equivalent degrees of smoothing when nonparametric model fits are compared. The simulation studies reported in Chapter 4 compare the novel approaches developed in Chapter 3 with standard approaches based on differences in residual sums of squares, i.e. approximate F-tests. The results show that direct comparisons of fitted values offer an improvement in some settings and never perform less favourably in others. The choice of the error variance estimator is shown to be crucial, with different design spaces requiring different estimators. Specific attention is also given to the effect of correlation amongst the covariates on the tests' performances. Chapter 4 closes with an application of the methods to a real data set describing the spatial distribution of sea bed fauna in the Great Barrier Reef. Chapter 5 extends these methods beyond models with two covariates to models with an unlimited number of additive linear terms and a nonparametric component involving at most two covariates. Recent results which derive the asymptotic properties of models of this form show that the favourable properties of local linear regression in the bivariate setting extend to this multidimensional setting. Results of a simulation study are reported and show that there is much to be gained by making a direct comparison of fitted values in conjunction with a careful choice of the estimator of error variance. Chapters 6 and 7 describe applied projects in environmental and medical contexts respectively. Both of the sets of data contain relationships amongst covariates which are best described using nonparametric models. Chapter 6 considers 14 years of water quality monitoring data from the Firth of Clyde, Scotland. Interest lies in describing relationships between pollutants and environmental factors, including long term trends and seasonal patterns. Chapter 7 investigates the relationship between short term dosage of an immunosuppressive drug and the long term outcome of kidney transplantation patients. Chapter 8 concludes with a summary of the main findings of the thesis and a discussion of potential future work in this area. Although progress has been made in the settings considered in the thesis, further extensions are required before nonparametric modelling will achieve its full potential

The impact of remote teaching on statistics learning and anxiety

In March 2020, staff and students at UK universities had to suddenly transition from on-campus teaching to remote learning as a result of the pandemic, which continued throughout the 2020/21 academic year. Unlike traditional online learners, students may lack the motivation or confidence to learn as effectively online particularly for modules such as statistics which students often find difficult or stressful face to face.This paper uses survey results from students studying elective and compulsory statistics modules in the 2020/21 academic year to gain an insight into remote learning of statistics from the students’ perspective.When compared to previous face to face teaching of statistics, students were less likely to actively engage with material, ask for help or work with peers remotely. Emotional wellbeing, motivation to learn, statistics anxiety and having a suitable learning environment all impacted on being able to learn statistics remotely. Although statistics anxiety in online teaching situations was generally lower, there was no evidence to suggest anxious students would benefit from online learning going forward

A new approach to estimation of global air-sea gas transfer velocity fields using dual-frequency altimeter backscatter

Author Posting. © American Geophysical Union, 2007. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Journal of Geophysical Research 112 (2007): C11003, doi:10.1029/2006JC003819.A new approach to estimating air-sea gas transfer velocities based on normalized backscatter from the dual-frequency TOPEX and Jason-1 altimeters is described. The differential scattering of Ku-band (13.6 GHz) and C-band (5.3 GHz) microwave pulses is used to isolate the contribution of small-scale waves to mean square slope and gas transfer. Mean square slope is derived for the nominal wave number range 40–100 rad m−1 by differencing mean square slope estimates computed from the normalized backscatter in each band, using a simple geometric optics model. Model parameters for calculating the differenced mean square slope over this wave number range are optimized using in situ optical slope measurements. An empirical relation between gas transfer velocity and mean square slope, also based on field measurements, is then used to derive gas transfer velocities. Initial results demonstrate that the calculated transfer velocities exhibit magnitudes and a dynamic range which are generally consistent with existing field measurements. The new algorithm is used to construct monthly global maps of gas transfer velocity and to illustrate seasonal transfer velocity variations over a 1-year period. The measurement precision estimated from >106 duplicate observations of the sea surface by TOPEX and Jason-1 altimeters orbiting in tandem is better than 10%. The estimated overall uncertainty of the method is ±30%. The long-term global, area-weighted, Schmidt number corrected, mean gas transfer velocity is 13.7 ± 4.1 cm h−1. The new approach, based on surface roughness, represents a potential alternative to commonly used parameterizations based on wind speed.Financial support for this research from the National Aeronautics and Space Administration through Jet Propulsion Laboratory contract 961425 and the NOAA Global Carbon Cycle Program under grant NA16GP2918, Office of Global Programs is gratefully acknowledged

State of the climate in 2018

In 2018, the dominant greenhouse gases released into Earth’s atmosphere—carbon dioxide, methane, and nitrous oxide—continued their increase. The annual global average carbon dioxide concentration at Earth’s surface was 407.4 ± 0.1 ppm, the highest in the modern instrumental record and in ice core records dating back 800 000 years. Combined, greenhouse gases and several halogenated gases contribute just over 3 W m−2 to radiative forcing and represent a nearly 43% increase since 1990. Carbon dioxide is responsible for about 65% of this radiative forcing. With a weak La Niña in early 2018 transitioning to a weak El Niño by the year’s end, the global surface (land and ocean) temperature was the fourth highest on record, with only 2015 through 2017 being warmer. Several European countries reported record high annual temperatures. There were also more high, and fewer low, temperature extremes than in nearly all of the 68-year extremes record. Madagascar recorded a record daily temperature of 40.5°C in Morondava in March, while South Korea set its record high of 41.0°C in August in Hongcheon. Nawabshah, Pakistan, recorded its highest temperature of 50.2°C, which may be a new daily world record for April. Globally, the annual lower troposphere temperature was third to seventh highest, depending on the dataset analyzed. The lower stratospheric temperature was approximately fifth lowest. The 2018 Arctic land surface temperature was 1.2°C above the 1981–2010 average, tying for third highest in the 118-year record, following 2016 and 2017. June’s Arctic snow cover extent was almost half of what it was 35 years ago. Across Greenland, however, regional summer temperatures were generally below or near average. Additionally, a satellite survey of 47 glaciers in Greenland indicated a net increase in area for the first time since records began in 1999. Increasing permafrost temperatures were reported at most observation sites in the Arctic, with the overall increase of 0.1°–0.2°C between 2017 and 2018 being comparable to the highest rate of warming ever observed in the region. On 17 March, Arctic sea ice extent marked the second smallest annual maximum in the 38-year record, larger than only 2017. The minimum extent in 2018 was reached on 19 September and again on 23 September, tying 2008 and 2010 for the sixth lowest extent on record. The 23 September date tied 1997 as the latest sea ice minimum date on record. First-year ice now dominates the ice cover, comprising 77% of the March 2018 ice pack compared to 55% during the 1980s. Because thinner, younger ice is more vulnerable to melting out in summer, this shift in sea ice age has contributed to the decreasing trend in minimum ice extent. Regionally, Bering Sea ice extent was at record lows for almost the entire 2017/18 ice season. For the Antarctic continent as a whole, 2018 was warmer than average. On the highest points of the Antarctic Plateau, the automatic weather station Relay (74°S) broke or tied six monthly temperature records throughout the year, with August breaking its record by nearly 8°C. However, cool conditions in the western Bellingshausen Sea and Amundsen Sea sector contributed to a low melt season overall for 2017/18. High SSTs contributed to low summer sea ice extent in the Ross and Weddell Seas in 2018, underpinning the second lowest Antarctic summer minimum sea ice extent on record. Despite conducive conditions for its formation, the ozone hole at its maximum extent in September was near the 2000–18 mean, likely due to an ongoing slow decline in stratospheric chlorine monoxide concentration. Across the oceans, globally averaged SST decreased slightly since the record El Niño year of 2016 but was still far above the climatological mean. On average, SST is increasing at a rate of 0.10° ± 0.01°C decade−1 since 1950. The warming appeared largest in the tropical Indian Ocean and smallest in the North Pacific. The deeper ocean continues to warm year after year. For the seventh consecutive year, global annual mean sea level became the highest in the 26-year record, rising to 81 mm above the 1993 average. As anticipated in a warming climate, the hydrological cycle over the ocean is accelerating: dry regions are becoming drier and wet regions rainier. Closer to the equator, 95 named tropical storms were observed during 2018, well above the 1981–2010 average of 82. Eleven tropical cyclones reached Saffir–Simpson scale Category 5 intensity. North Atlantic Major Hurricane Michael’s landfall intensity of 140 kt was the fourth strongest for any continental U.S. hurricane landfall in the 168-year record. Michael caused more than 30 fatalities and $25 billion (U.S. dollars) in damages. In the western North Pacific, Super Typhoon Mangkhut led to 160 fatalities and$6 billion (U.S. dollars) in damages across the Philippines, Hong Kong, Macau, mainland China, Guam, and the Northern Mariana Islands. Tropical Storm Son-Tinh was responsible for 170 fatalities in Vietnam and Laos. Nearly all the islands of Micronesia experienced at least moderate impacts from various tropical cyclones. Across land, many areas around the globe received copious precipitation, notable at different time scales. Rodrigues and Réunion Island near southern Africa each reported their third wettest year on record. In Hawaii, 1262 mm precipitation at Waipā Gardens (Kauai) on 14–15 April set a new U.S. record for 24-h precipitation. In Brazil, the city of Belo Horizonte received nearly 75 mm of rain in just 20 minutes, nearly half its monthly average. Globally, fire activity during 2018 was the lowest since the start of the record in 1997, with a combined burned area of about 500 million hectares. This reinforced the long-term downward trend in fire emissions driven by changes in land use in frequently burning savannas. However, wildfires burned 3.5 million hectares across the United States, well above the 2000–10 average of 2.7 million hectares. Combined, U.S. wildfire damages for the 2017 and 2018 wildfire seasons exceeded $40 billion (U.S. dollars)

Investigating Perceived Student Learning from Peer Review in Statistics Education

Peer review is not regularly used in statistics education despite previous studies demonstrating it enhancing student achievement. This paper expands this knowledge by exploring how peer review contributes to perceived student learning in statistics education and how educators can stimulate students’ learning through internal feedback. This study focused on two cohorts of statistics students with differing attributes. Students were surveyed post a peer review exercise. The post review questionnaire looked at the different stages of peer review and its impact on perceived student learning. Initial impressions indicate that the peer review activity contributed to student learning with comparing their work to a peers’ contributing most on average to their perceived learning

Study Design & Quantitative Analysis in Learning and Teaching Scholarship: Case Study Exploring Student Attitudes to Introductory Statistics

This talk describes the design, execution and analysis phases of a scholarship project undertaken to better understand students’ attitudes to studying introductory statistics at university. Specifically, the scholarship project adds to the understanding of issues surrounding statistical anxiety and self-efficacy and their relationship with performance by examining three cohorts of students. Within each cohort, students were asked about their demographic and academic backgrounds and their general attitudes to studying statistics via both qualitative and quantitative questions. To enable comparisons with previous studies, validated instruments measuring statistical anxiety and general self-efficacy were administered to students to quantify these characteristics. Finally, the responses were matched with grades obtained in the course as a measure of performance. The emphasis of the talk will be on illustrating key issues of quantitative scholarship using the practicalities of the project, especially the approaches taken to: 1. Design and administer a survey using Moodle to provide both quantitative and qualitative information on students’ attitudes and backgrounds 2. Extract and prepare data for analysis 3. Analyse the data and disseminate the findings 4. Implement changes to course design and teaching practice in light of the findings 5. Reflections on this scholarshi

Exploring Statistics Anxiety in Several Introductory Statistics Courses to Understand Differences Between Types of Students and Types of Courses

Despite its importance in modern curricula, many students find statistics courses challenging, and the existence of barriers among students to learning statistical reasoning is an important area of study. This study explores the presence and level of statistics anxiety in several cohorts of students studying introductory statistics. The relationship with statistical anxiety dependent on specialisms is explored, along with their curricular choices. An online questionnaire was developed to explore the effects of statistical anxiety and attitudes towards learning statistics. Comparisons were made both within and between the cohorts of students and showed that demographic factors and gender play a minor but statistically significant role in explaining levels of statistical anxiety, but that no significant differences in statistics anxiety existed between cohorts

Statistics Students' Perspectives of Forced Online Learning

We describe a study that explored perceptions and experiences of statistics students at universities in the United Kingdom who had to adjust to learning online as a result of COVID-19 restrictions. Students from two universities (one research-intensive, the other with a teaching focus), and groups of first- through third-year students from five undergraduate statistics courses were surveyed. The wellbeing of students studying online differed between the two universities, and wellbeing was related to students’ experiences of learning remotely, with more negative wellbeing scores associated with worsening online learning experiences. Students did not feel they interacted as well with their peers or lecturers in an online learning environment compared to in-person learning. This study can inform statistics educators how to better support their students’ learning