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).

The mechanical and inflammatory low back pain (MIL) index: development and validation

Abstract Background The purpose of this study was the development of a valid and reliable “Mechanical and Inflammatory Low Back Pain Index” (MIL) for assessment of non-specific low back pain (NSLBP). This 7-item tool assists practitioners in determining whether symptoms are predominantly mechanical or inflammatory. Methods Participants (n = 170, 96 females, age = 38 ± 14 years-old) with NSLP were referred to two Spanish physiotherapy clinics and completed the MIL and the following measures: the Roland Morris Questionnaire (RMQ), SF-12 and “Backache Index” (BAI) physical assessment test. For test-retest reliability, 37 consecutive patients were assessed at baseline and three days later during a non-treatment period. Face and content validity, practical characteristics, factor analysis, internal consistency, discriminant validity and convergent validity were assessed from the full sample. Results A total of 27 potential items that had been identified for inclusion were subsequently reduced to 11 by an expert panel. Four items were then removed due to cross-loading under confirmatory factor analysis where a two-factor model yielded a good fit to the data (χ2 = 14.80, df = 13, p = 0.37, CFI = 0.98, and RMSEA = 0.029). The internal consistency was moderate (α = 0.68 for MLBP; 0.72 for ILBP), test-retest reliability high (ICC = 0.91; 95%CI = 0.88-0.93) and discriminant validity good for either MLBP (AUC = 0.74) and ILBP (AUC = 0.92). Convergent validity was demonstrated through similar but weak correlations between the ILBP and both the RMQ and BAI (r = 0.34, p < 0.001) and the MLBP and BAI (r = 0.38, p < 0.001). Conclusions The MIL is a valid and reliable clinical tool for patients with NSLBP that discriminates between mechanical and inflammatory LBP. Keywords: Low back pain; Psychometrics properties; Pain measurement; Screening tool; Inflammatory; Mechanical

A statistical model for combustion resonance from a DI diesel engine with applications

Introduced in this paper is a Bayesian model for isolating the resonant frequency from combustion chamber resonance. The model shown in this paper focused on characterising the initial rise in the resonant frequency to investigate the rise of in-cylinder bulk temperature associated with combustion. By resolving the model parameters, it is possible to determine: the start of pre-mixed combustion, the start of diffusion combustion, the initial resonant frequency, the resonant frequency as a function of crank angle, the in-cylinder bulk temperature as a function of crank angle and the trapped mass as a function of crank angle. The Bayesian method allows for individual cycles to be examined without cycle-averaging|allowing inter-cycle variability studies. Results are shown for a turbo-charged, common-rail compression ignition engine run at 2000 rpm and full load.

The mathematical modelling of cheese ripening

A mathematical model is developed for the ripening of cheese. Such models may assist predicting final cheese quality using measured initial composition. The main constituent chemical reactions are described with ordinary differential equations. Numerical solutions to the model equations are found using Matlab. Unknown parameter values have been fitted using experimental data available in the literature. The results from the numerical fitting are in good agreement with the data. Statistical analysis is performed on near infrared data provided to the MISG. However, due to the inhomogeneity and limited nature of the data, not many conclusions can be drawn from the analysis. A simple model of the potential changes in acidity of cheese is also considered. The results from this model are consistent with cheese manufacturing knowledge, in that the pH of cheddar cheese does not significantly change during ripening.

Arabic translation, adaptation and modification of the dialysis symptom index for chronic kidney disease stages four and five

Background Symptom burden in chronic kidney disease (CKD) is poorly understood. To date, the majority of research focuses on single symptoms and there is a lack of suitable multidimensional symptom measures. The purpose of this study was to modify, translate, cross-culturally adapt and psychometrically analyse the Dialysis Symptom Index (DSI). Methods The study methods involved four phases: modification, translation, pilot-testing with a bilingual non-CKD sample and then psychometric testing with the target population. Content validity was assessed using an expert panel. Inter-rater agreement, test-retest reliability and Cronbach’s alpha coefficient were calculated to demonstrate reliability of the modified DSI. Discriminative and convergent validity were assessed to demonstrate construct validity. Results Content validity index during translation was 0.98. In the pilot study with 25 bilingual students a moderate to perfect agreement (Kappa statistic = 0.60-1.00) was found between English and Arabic versions of the modified DSI. The main study recruited 433 patients CKD with stages 4 and 5. The modified DSI was able to discriminate between non-dialysis and dialysis groups (p < 0.001) and demonstrated convergent validity with domains of the Kidney Disease Quality of Life short form. Excellent test-retest and internal consistency (Cronbach’s α = 0.91) reliability were also demonstrated. Conclusion The Arabic version of the modified DSI demonstrated good psychometric properties, measures the multidimensional nature of symptoms and can be used to assess symptom burden at different stages of CKD. The modified instrument, renamed the CKD Symptom Burden Index (CKD-SBI), should encourage greater clinical and research attention to symptom burden in CKD.

Numeracy and statistical reasoning on entering university

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on mathematics anxiety. Gnaldi (2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning, basic numeracy skills, mathematics background and attitudes towards statistics. This work reports on some key relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Numeracy counts in the statistical reasoning equation

The relationship between mathematics and statistical reasoning frequently receives comment (Vere-Jones 1995, Moore 1997); however most of the research into the area tends to focus on maths anxiety. Gnaldi (Gnaldi 2003) showed that in a statistics course for psychologists, the statistical understanding of students at the end of the course depended on students’ basic numeracy, rather than the number or level of previous mathematics courses the student had undertaken. As part of a study into the development of statistical thinking at the interface between secondary and tertiary education, students enrolled in an introductory data analysis subject were assessed regarding their statistical reasoning ability, basic numeracy skills and attitudes towards statistics. This work reports on the relationships between these factors and in particular the importance of numeracy to statistical reasoning.

Experimental and statistical investigation of Australian native plants for second-generation biodiesel production

This work explores the potential of Australian native plants as a source of second-generation biodiesel for internal combustion engines application. Biodiesels were evaluated from a number of non-edible oil seeds which are grow naturally in Queensland, Australia. The quality of the produced biodiesels has been investigated by several experimental and numerical methods. The research methodology and numerical model developed in this study can be used for a broad range of biodiesel feedstocks and for the future development of renewable native biodiesel in Australia.

Development of a hybrid pollution index for heavy metals in marine and estuarine sediments

Heavy metal pollution of sediments is a growing concern in most parts of the world, and numerous studies focussed on identifying contaminated sediments by using a range of digestion methods and pollution indices to estimate sediment contamination have been described in the literature. The current work provides a critical review of the more commonly used sediment digestion methods and identifies that weak acid digestion is more likely to provide guidance on elements that are likely to be bioavailable than other traditional methods of digestion. This work also reviews common pollution indices and identifies the Nemerow Pollution Index as the most appropriate method for establishing overall sediment quality. Consequently, a modified Pollution Index that can lead to a more reliable understanding of whole sediment quality is proposed. This modified pollution index is then tested against a number of existing studies and demonstrated to give a reliable and rapid estimate of sediment contamination and quality.

Cross-cultural adaptation, reliability and validity of the Turkish version of the spine functional index

Background The Spine Functional Index (SFI) is a patient reported outcome measure with sound clinimetric properties and clinical viability for the determination of whole-spine impairment. To date, no validated Turkish version is available. The purpose of this study is to cross-culturally adapted the SFI for Turkish-speaking patients (SFI-Tk) and determine the psychometric properties of reliability, validity and factor structure in a Turkish population with spine musculoskeletal disorders. Methods The SFI English version was culturally adapted and translated into Turkish using a double forward and backward method according to established guidelines. Patients (n = 285, cervical = l29, lumbar = 151, cervical and lumbar region = 5, 73% female, age 45 ± 1) with spine musculoskeletal disorders completed the SFI-Tk at baseline and after a seven day period for test-retest reliability. For criterion validity the Turkish version of the Functional Rating Index (FRI) was used plus the Neck Disability Index (NDI) for cervical patients and the Oswestry Disability Index (ODI) for back patients. Additional psychometric properties were determined for internal consistency (Chronbach’s α), criterion validity and factor structure. Results There was a high degree of internal consistency (α = 0.85, item range 0.80-0.88) and test-retest reliability (r = 0.93, item range = 0.75-0.95). The factor analysis demonstrated a one-factor solution explaining 24.2% of total variance. Criterion validity with the ODI was high (r = 0.71, p < 0.001) while the FRI and NDI were fair (r = 0.52 and r = 0.58, respectively). The SFI-Tk showed no missing responses with the ‘half-mark’ option used in 11.75% of total responses by 77.9% of participants. Measurement error from SEM and MDC90 were respectively 2.96% and 7.12%. Conclusions The SFI-Tk demonstrated a one-factor solution and is a reliable and valid instrument. The SFI-Tk consists of simple and easily understood wording and may be used to assess spine region musculoskeletal disorders in Turkish speaking patients.

Case Studies in Bayesian Statistical Modelling and Analysis

Provides an accessible foundation to Bayesian analysis using real world models This book aims to present an introduction to Bayesian modelling and computation, by considering real case studies drawn from diverse fields spanning ecology, health, genetics and finance. Each chapter comprises a description of the problem, the corresponding model, the computational method, results and inferences as well as the issues that arise in the implementation of these approaches. Case Studies in Bayesian Statistical Modelling and Analysis: •Illustrates how to do Bayesian analysis in a clear and concise manner using real-world problems. •Each chapter focuses on a real-world problem and describes the way in which the problem may be analysed using Bayesian methods. •Features approaches that can be used in a wide area of application, such as, health, the environment, genetics, information science, medicine, biology, industry and remote sensing. Case Studies in Bayesian Statistical Modelling and Analysis is aimed at statisticians, researchers and practitioners who have some expertise in statistical modelling and analysis, and some understanding of the basics of Bayesian statistics, but little experience in its application. Graduate students of statistics and biostatistics will also find this book beneficial.

Statistical, electrical and mathematical analysis of water treed cross-linked polyethylene cable insulation

This work examined a new method of detecting small water filled cracks in underground insulation ('water trees') using data from commecially available non-destructive testing equipment. A testing facility was constructed and a computer simulation of the insulation designed in order to test the proposed ageing factor - the degree of non-linearity. This was a large industry-backed project involving an ARC linkage grant, Ergon Energy and the University of Queensland, as well as the Queensland University of Technology.

The YOU CALL-WE CALL randomized clinical trial: Impact of a multimodal support intervention after a mild stroke

Background Comparison of a multimodal intervention WE CALL (study initiated phone support/information provision) versus a passive intervention YOU CALL (participant can contact a resource person) in individuals with first mild stroke. Methods and Results This study is a single-blinded randomized clinical trial. Primary outcome includes unplanned use of health services (participant diaries) for adverse events and quality of life (Euroquol-5D, Quality of Life Index). Secondary outcomes include planned use of health services (diaries), mood (Beck Depression Inventory II), and participation (Assessment of Life Habits [LIFE-H]). Blind assessments were done at baseline, 6, and 12 months. A mixed model approach for statistical analysis on an intention-to-treat basis was used where the group factor was intervention type and occasion factor time, with a significance level of 0.01. We enrolled 186 patients (WE=92; YOU=94) with a mean age of 62.5±12.5 years, and 42.5% were women. No significant differences were seen between groups at 6 months for any outcomes with both groups improving from baseline on all measures (effect sizes ranged from 0.25 to 0.7). The only significant change for both groups from 6 months to 1 year (n=139) was in the social domains of the LIFE-H (increment in score, 0.4/9±1.3 [95% confidence interval, 0.1–0.7]; effect size, 0.3). Qualitatively, the WE CALL intervention was perceived as reassuring, increased insight, and problem solving while decreasing anxiety. Only 6 of 94 (6.4%) YOU CALL participants availed themselves of the intervention. Conclusions Although the 2 groups improved equally over time, WE CALL intervention was perceived as helpful, whereas YOU CALL intervention was not used.

Commentary on the article by Swanenburg et al. ‘Validity and reliability of a German version of the Neck Disability Index (NDI-G)’

We commend Swanenburg et al. (2013) on translation, development, and clinimetric analysis of the NDI-G. However, the dual-factor structure with factor analysis and the high level of internal consistency (IC) highlighted in their discussion were not emphasized in the abstract or conclusion. These points may imply some inconsistencies with the final conclusions since determination of stable point estimates with the study's small sample are exceedingly difficult.