Statistical investigations - drawing it all together

The author's approach to teaching an integrative unit to a small group of master’s level Applied Statistics students in 2000-2001 is described. Details of the various activities such as data analysis, reading and discussion of papers, and training in consultancy skills are given, as also are details of the assessment. The students’ and lecturer’s views of the unit are discussed.

Exploring variation in measurement as a foundation for statistical thinking in the elementary school

This study was based on the premise that variation is the foundation of statistics and statistical investigations. The study followed the development of fourth-grade students' understanding of variation through participation in a sequence of two lessons based on measurement. In the first lesson all students measured the arm span of one student, revealing pathways students follow in developing understanding of variation and linear measurement (related to research question 1). In the second lesson each student's arm span was measured once, introducing a different aspect of variation for students to observe and contrast. From this second lesson, students' development of the ability to compare their representations for the two scenarios and explain differences in terms of variation was explored (research question 2). Students' documentation, in both workbook and software formats, enabled us to monitor their engagement and identify their increasing appreciation of the need to observe, represent, and contrast the variation in the data. Following the lessons, a written student assessment was used for judging retention of understanding of variation developed through the lessons and the degree of transfer of understanding to a different scenario (research question 3).

Statistical literacy in the elementary school: Opportunities for problem posing

This chapter addresses opportunities for problem posing in developing young children’s statistical literacy, with a focus on student-directed investigations. Although the notion of problem posing has broadened in recent years, there nevertheless remains limited research on how problem posing can be integrated within the regular mathematics curriculum, especially in the areas of statistics and probability. The chapter first reviews briefly aspects of problem posing that have featured in the literature over the years. Consideration is next given to the importance of developing children’s statistical literacy in which problem posing is an inherent feature. Some findings from a school playground investigation conducted in four, fourth-grade classes illustrate the different ways in which children posed investigative questions, how they made predictions about their outcomes and compared these with their findings, and the ways in which they chose to represent their findings.

O conhecimento de estatística e da sua didática de futuros professores

Tese de doutoramento, Educação (Didática da Matemática), Universidade de Lisboa, Instituto de Educação, 2015

Soil sampling design and sampling techniques for soil properties monitoring – common difficulties related to forest soils

Mathematical models and statistical analysis are key instruments in soil science scientific research as they can describe and/or predict the current state of a soil system. These tools allow us to explore the behavior of soil related processes and properties as well as to generate new hypotheses for future experimentation. A good model and analysis of soil properties variations, that permit us to extract suitable conclusions and estimating spatially correlated variables at unsampled locations, is clearly dependent on the amount and quality of data and of the robustness techniques and estimators. On the other hand, the quality of data is obviously dependent from a competent data collection procedure and from a capable laboratory analytical work. Following the standard soil sampling protocols available, soil samples should be collected according to key points such as a convenient spatial scale, landscape homogeneity (or non-homogeneity), land color, soil texture, land slope, land solar exposition. Obtaining good quality data from forest soils is predictably expensive as it is labor intensive and demands many manpower and equipment both in field work and in laboratory analysis. Also, the sampling collection scheme that should be used on a data collection procedure in forest field is not simple to design as the sampling strategies chosen are strongly dependent on soil taxonomy. In fact, a sampling grid will not be able to be followed if rocks at the predicted collecting depth are found, or no soil at all is found, or large trees bar the soil collection. Considering this, a proficient design of a soil data sampling campaign in forest field is not always a simple process and sometimes represents a truly huge challenge. In this work, we present some difficulties that have occurred during two experiments on forest soil that were conducted in order to study the spatial variation of some soil physical-chemical properties. Two different sampling protocols were considered for monitoring two types of forest soils located in NW Portugal: umbric regosol and lithosol. Two different equipments for sampling collection were also used: a manual auger and a shovel. Both scenarios were analyzed and the results achieved have allowed us to consider that monitoring forest soil in order to do some mathematical and statistical investigations needs a sampling procedure to data collection compatible to established protocols but a pre-defined grid assumption often fail when the variability of the soil property is not uniform in space. In this case, sampling grid should be conveniently adapted from one part of the landscape to another and this fact should be taken into consideration of a mathematical procedure.

Assessing the effectiveness of ISO 3382 for evaluating the acoustical quality of italian historical theatres: the case study of the Bonci Theatre

The present study concerns the acoustical characterisation of Italian historical theatres. It moved from the ISO 3382 which provides the guidelines for the measurement of a well established set of room acoustic parameters inside performance spaces. Nevertheless, the peculiarity of Italian historical theatres needs a more specific approach. The Charter of Ferrara goes in this direction, aiming at qualifying the sound field in this kind of halls and the present work pursues the way forward. Trying to understand how the acoustical qualification should be done, the Bonci Theatre in Cesena has been taken as a case study. In September 2012 acoustical measurements were carried out in the theatre, recording monaural e binaural impulse responses at each seat in the hall. The values of the time criteria, energy criteria and psycho-acoustical and spatial criteria have been extracted according to ISO 3382. Statistics were performed and a 3D model of the theatre was realised and tuned. Statistical investigations were carried out on the whole set of measurement positions and on carefully chosen reduced subsets; it turned out that these subsets are representative only of the “average” acoustics of the hall. Normality tests were carried out to verify whether EDT, T30 and C80 could be described with some degree of reliability with a theoretical distribution. Different results, according to the varying assumptions underlying each test, were found. Finally, an attempt was made to correlate the numerical results emerged from the statistical analysis to the perceptual sphere. Looking for “acoustical equivalent areas”, relative difference limens were considered as threshold values. No rule of thumb emerged. Finally, the significance of the usual representation through mean values and standard deviation, which may be meaningful for normal distributed data, was investigated.

Studies in word-association; experiments in the diagnosis of psychopathological conditions carried out at the Psychiatric clinic of the University of Zurich, under the direction of C.G. Jung ...

"This book is a translation of a series of papers on the results of the association method applied to normal and abnormal persons, which appeared in the Journal für psychologie und neurologie (vols. III-XVI) and were afterwards collectecd into two volumes."--Translator's pref.

Investigations on the number of trials required for statistical comparison of fishing gears

The number of fishing trials required for comparing the efficiency of fishing gears was investigated. A unique solution to this problem did not appear to exist because of the heterogeneity of the experimental material. Sequential experimentation and analysis have been found to be a practical approach to this problem. By this, the experiment can be terminated almost after 35 days fishing for catches with standard error per unit as per cent of the mean about 30% or less (after logarithmic transformation). For data with mean catches less than 1.5 kg analysis of variance approach does not appear to be meaningful.

Bayesian versus frequentist statistical inference for investi gating a one-off cancer cluster reported to a health department

Background The problem of silent multiple comparisons is one of the most difficult statistical problems faced by scientists. It is a particular problem for investigating a one-off cancer cluster reported to a health department because any one of hundreds, or possibly thousands, of neighbourhoods, schools, or workplaces could have reported a cluster, which could have been for any one of several types of cancer or any one of several time periods. Methods This paper contrasts the frequentist approach with a Bayesian approach for dealing with silent multiple comparisons in the context of a one-off cluster reported to a health department. Two published cluster investigations were re-analysed using the Dunn-Sidak method to adjust frequentist p-values and confidence intervals for silent multiple comparisons. Bayesian methods were based on the Gamma distribution. Results Bayesian analysis with non-informative priors produced results similar to the frequentist analysis, and suggested that both clusters represented a statistical excess. In the frequentist framework, the statistical significance of both clusters was extremely sensitive to the number of silent multiple comparisons, which can only ever be a subjective "guesstimate". The Bayesian approach is also subjective: whether there is an apparent statistical excess depends on the specified prior. Conclusion In cluster investigations, the frequentist approach is just as subjective as the Bayesian approach, but the Bayesian approach is less ambitious in that it treats the analysis as a synthesis of data and personal judgements (possibly poor ones), rather than objective reality. Bayesian analysis is (arguably) a useful tool to support complicated decision-making, because it makes the uncertainty associated with silent multiple comparisons explicit.

Non-invasive, quantitative analysis of drug mixtures in containers using spatially offset Raman spectroscopy (SORS) and multivariate statistical analysis

In this paper, spatially offset Raman spectroscopy (SORS) is demonstrated for non-invasively investigating the composition of drug mixtures inside an opaque plastic container. The mixtures consisted of three components including a target drug (acetaminophen or phenylephrine hydrochloride) and two diluents (glucose and caffeine). The target drug concentrations ranged from 5% to 100%. After conducting SORS analysis to ascertain the Raman spectra of the concealed mixtures, principal component analysis (PCA) was performed on the SORS spectra to reveal trends within the data. Partial least squares (PLS) regression was used to construct models that predicted the concentration of each target drug, in the presence of the other two diluents. The PLS models were able to predict the concentration of acetaminophen in the validation samples with a root-mean-square error of prediction (RMSEP) of 3.8% and the concentration of phenylephrine hydrochloride with an RMSEP of 4.6%. This work demonstrates the potential of SORS, used in conjunction with multivariate statistical techniques, to perform non-invasive, quantitative analysis on mixtures inside opaque containers. This has applications for pharmaceutical analysis, such as monitoring the degradation of pharmaceutical products on the shelf, in forensic investigations of counterfeit drugs, and for the analysis of illicit drug mixtures which may contain multiple components.

Performance evaluation of onsite sewage treatment : results of soil investigations

Background The onsite treatment of sewage and effluent disposal is widely prevalent in rural and urban fringe areas due to the general unavailability of reticulated wastewater collection systems. Despite the low technology of the systems, failure is common and in many cases leading to adverse public health and environmental consequences. It is important therefore that careful consideration is given to the design and location of onsite sewage treatment systems. This requires an understanding of the factors that influence treatment performance. The use of subsurface absorption systems is the most common form of effluent disposal for onsite sewage treatment, particularly for septic tanks. Also, in the case of septic tanks, a subsurface disposal system is generally an integral component of the sewage treatment process. Site specific factors play a key role in the onsite treatment of sewage. The project The primary aims of the research project were: • to relate treatment performance of onsite sewage treatment systems to soil conditions at site; • to evaluate current research relating to onsite sewage treatment; and, • to identify key issues where currently there is a lack of relevant research. These tasks were undertaken with the objective of facilitating the development of performance based planning and management strategies for onsite sewage treatment. The primary focus of this research project has been on septic tanks. By implication, the investigation has been confined to subsurface soil absorption systems. The design and treatment processes taking place within the septic tank chamber itself did not form a part of the investigation. Five broad categories of soil types prevalent in the Brisbane region have been considered in this project. The number of systems investigated was based on the proportionate area of urban development within the Brisbane region located on each of the different soil types. In the initial phase of the investigation, the majority of the systems evaluated were septic tanks. However, a small number of aerobic wastewater treatment systems (AWTS) were also included. The primary aim was to compare the effluent quality of systems employing different generic treatment processes. It is important to note that the number of each different type of system investigated was relatively small. Consequently, this does not permit a statistical analysis to be undertaken of the results obtained for comparing different systems. This is an important issue considering the large number of soil physico-chemical parameters and landscape factors that can influence treatment performance and their wide variability. The report This report is the last in a series of three reports focussing on the performance evaluation of onsite treatment of sewage. The research project was initiated at the request of the Brisbane City Council. The project component discussed in the current report outlines the detailed soil investigations undertaken at a selected number of sites. In the initial field sampling, a number of soil chemical properties were assessed as indicators to investigate the extent of effluent flow and to help understand what soil factors renovate the applied effluent. The soil profile attributes, especially texture, structure and moisture regime were examined more in an engineering sense to determine the effect of movement of water into and through the soil. It is important to note that it is not only the physical characteristics, but also the chemical characteristics of the soil as well as landscape factors play a key role in the effluent renovation process. In order to understand the complex processes taking place in a subsurface effluent disposal area, influential parameters were identified using soil chemical concepts. Accordingly, the primary focus of this final phase of the research project was to identify linkages between various soil chemical parameters and landscape patterns and their contribution to the effluent renovation process. The research outcomes will contribute to the development of robust criteria for evaluating the performance of subsurface effluent disposal systems. The outcomes The key findings from the soil investigations undertaken are: • Effluent renovation is primarily undertaken by a combination of various soil physico-chemical parameters and landscape factors, thereby making the effluent renovation processes strongly site dependent. • Decisions regarding site suitability for effluent disposal should not be based purely in terms of the soil type. A number of other factors such as the site location in the catena, the drainage characteristics and other physical and chemical characteristics, also exert a strong influence on site suitability. • Sites, which are difficult to characterise in terms of suitability for effluent disposal, will require a detailed soil physical and chemical analysis to be undertaken to a minimum depth of at least 1.2 m. • The Ca:Mg ratio and Exchangeable Sodium Percentage are important parameters in soil suitability assessment. A Ca:Mg ratio of less than 0.5 would generally indicate a high ESP. This in turn would mean that Na and possibly Mg are the dominant exchangeable cations, leading to probable clay dispersion. • A Ca:Mg ratio greater than 0.5 would generally indicate a low ESP in the profile, which in turn indicates increased soil stability. • In higher clay percentage soils, low ESP can have a significant effect. • The presence of high exchangeable Na can be counteracted by the presence of swelling clays, and an exchange complex co-dominated by exchangeable Ca and exchangeable Mg. This aids absorption of cations at depth, thereby reducing the likelihood of dispersion. • Salt is continually added to the soil by the effluent and problems may arise if the added salts accumulate to a concentration that is harmful to the soil structure. Under such conditions, good drainage is essential in order to allow continuous movement of water and salt through the profile. Therefore, for a site to be sustainable, it would have a maximum application rate of effluent. This would be dependent on subsurface characteristics and the surface area available for effluent disposal. • The dosing regime for effluent disposal can play a significant role in the prevention of salt accumulation in the case of poorly draining sites. Though intermittent dosing was not considered satisfactory for the removal of the clogging mat layer, it has positive attributes in the context of removal of accumulated salts in the soil.

A Systematic review of a statistical vacuum circuit breaker model for condition monitoring

Vacuum circuit breaker (VCB) overvoltage failure and its catastrophic failures during shunt reactor switching have been analyzed through computer simulations for multiple reignitions with a statistical VCB model found in the literature. However, a systematic review (SR) that is related to the multiple reignitions with a statistical VCB model does not yet exist. Therefore, this paper aims to analyze and explore the multiple reignitions with a statistical VCB model. It examines the salient points, research gaps and limitations of the multiple reignition phenomenon to assist with future investigations following the SR search. Based on the SR results, seven issues and two approaches to enhance the current statistical VCB model are identified. These results will be useful as an input to improve the computer modeling accuracy as well as the development of a reignition switch model with point-on-wave controlled switching for condition monitoring

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.