Statnote 10: the two-way analysis of variance

The two-way design has been variously described as a matched-sample F-test, a simple within-subjects ANOVA, a one-way within-groups ANOVA, a simple correlated-groups ANOVA, and a one-factor repeated measures design! This confusion of terminology is likely to lead to problems in correctly identifying this analysis within commercially available software. The essential feature of the design is that each treatment is allocated by randomization to one experimental unit within each group or block. The block may be a plot of land, a single occasion in which the experiment was performed, or a human subject. The ‘blocking’ is designed to remove an aspect of the error variation and increase the ‘power’ of the experiment. If there is no significant source of variation associated with the ‘blocking’ then there is a disadvantage to the two-way design because there is a reduction in the DF of the error term compared with a fully randomised design thus reducing the ‘power’ of the analysis.

Statnote 9: The one-way analysis of variance (random effects model)

There is an alternative model of the 1-way ANOVA called the 'random effects' model or ‘nested’ design in which the objective is not to test specific effects but to estimate the degree of variation of a particular measurement and to compare different sources of variation that influence the measurement in space and/or time. The most important statistics from a random effects model are the components of variance which estimate the variance associated with each of the sources of variation influencing a measurement. The nested design is particularly useful in preliminary experiments designed to estimate different sources of variation and in the planning of appropriate sampling strategies.

Statnote 30 : The one-way analysis of variance (ANOVA):fixed effects model

In Statnote 9, we described a one-way analysis of variance (ANOVA) ‘random effects’ model in which the objective was to estimate the degree of variation of a particular measurement and to compare different sources of variation in space and time. The illustrative scenario involved the role of computer keyboards in a University communal computer laboratory as a possible source of microbial contamination of the hands. The study estimated the aerobic colony count of ten selected keyboards with samples taken from two keys per keyboard determined at 9am and 5pm. This type of design is often referred to as a ‘nested’ or ‘hierarchical’ design and the ANOVA estimated the degree of variation: (1) between keyboards, (2) between keys within a keyboard, and (3) between sample times within a key. An alternative to this design is a 'fixed effects' model in which the objective is not to measure sources of variation per se but to estimate differences between specific groups or treatments, which are regarded as 'fixed' or discrete effects. This statnote describes two scenarios utilizing this type of analysis: (1) measuring the degree of bacterial contamination on 2p coins collected from three types of business property, viz., a butcher’s shop, a sandwich shop, and a newsagent and (2) the effectiveness of drugs in the treatment of a fungal eye infection.

Evidence of the heterogeneous market hypothesis using wavelet multi -resolution analysis

In finance literature many economic theories and models have been proposed to explain and estimate the relationship between risk and return. Assuming risk averseness and rational behavior on part of the investor, the models are developed which are supposed to help in forming efficient portfolios that either maximize (minimize) the expected rate of return (risk) for a given level of risk (rates of return). One of the most used models to form these efficient portfolios is the Sharpe's Capital Asset Pricing Model (CAPM). In the development of this model it is assumed that the investors have homogeneous expectations about the future probability distribution of the rates of return. That is, every investor assumes the same values of the parameters of the probability distribution. Likewise financial volatility homogeneity is commonly assumed, where volatility is taken as investment risk which is usually measured by the variance of the rates of return. Typically the square root of the variance is used to define financial volatility, furthermore it is also often assumed that the data generating process is made of independent and identically distributed random variables. This again implies that financial volatility is measured from homogeneous time series with stationary parameters. In this dissertation, we investigate the assumptions of homogeneity of market agents and provide evidence for the case of heterogeneity in market participants' information, objectives, and expectations about the parameters of the probability distribution of prices as given by the differences in the empirical distributions corresponding to different time scales, which in this study are associated with different classes of investors, as well as demonstrate that statistical properties of the underlying data generating processes including the volatility in the rates of return are quite heterogeneous. In other words, we provide empirical evidence against the traditional views about homogeneity using non-parametric wavelet analysis on trading data, The results show heterogeneity of financial volatility at different time scales, and time-scale is one of the most important aspects in which trading behavior differs. In fact we conclude that heterogeneity as posited by the Heterogeneous Markets Hypothesis is the norm and not the exception.

Evaluating a School Community Linked Physical Activity Intervention Programme: a Multi-level Analysis.

Previous research has highlighted the importance of positive physical activity (PA) behaviors during childhood to promote sustained active lifestyles throughout the lifespan (Telama et al. 2005; 2014). It is in this context that the role of schools and teachers in facilitating PA education is promoted. Research suggests that teachers play an important role in the attitudes of children towards PA (Figley 1985) and schools may be an efficient vehicle for PA provision and promotion (McGinnis, Kanner and DeGraw, 1991; Wechsler, Deveraux, Davis and Collins, 2000). Yet despite consensus that schools represent an ideal setting from which to ‘reach’ young people (Department of Health and Human Services, UK, 2012) there remains conceptual (e.g. multi-component intervention) and methodological (e.g. duration, intensity, family involvement) ambiguity regarding the mechanisms of change claimed by PA intervention programmes. This may, in part, contribute to research findings that suggest that PA interventions have had limited impact on children’s overall activity levels and thereby limited impact in reducing children’s metabolic health (Metcalf, Henley & Wilkin, 2012). A marked criticism of the health promotion field has been the focus on behavioural change while failing to acknowledge the impact of context in influencing health outcomes (Golden & Earp, 2011). For years, the trans-theoretical model of behaviour change has been ‘the dominant model for health behaviour change’ (Armitage, 2009); this model focusses primarily on the individual and the psychology of the change process. Arguably, this model is limited by the individual’s decision-making ability and degree of self-efficacy in order to achieve sustained behavioural change and does not take account of external factors that may hinder their ability to realise change. Similar to the trans-theoretical model, socio-ecological models identify the individual at the focal point of change but also emphasises the importance of connecting multiple impacting variables, in particular, the connections between the social environment, the physical environment and public policy in facilitating behavioural change (REF). In this research, a social-ecological framework was used to connect the ways a PA intervention programme had an impact (or not) on participants, and to make explicit the foundational features of the programme that facilitated positive change. In this study, we examined the evaluation of a multi-agency approach to a PA intervention programme which aimed to increase physical activity, and awareness of the importance of physical activity to key stage 2 (age 7-12) pupils in three UK primary schools. The agencies involved were the local health authority, a community based charitable organisation, a local health administrative agency, and the city school district. In examining the impact of the intervention, we adopted a process evaluation model in order to better understand the mechanisms and context that facilitated change. Therefore, the aim of this evaluation was to describe the provision, process and impact of the intervention by 1) assessing changes in physical activity levels 2) assessing changes in the student’s attitudes towards physical activity, 3) examining student’s perceptions of the child size fitness equipment in school and their likelihood of using the equipment outside of school and 4) exploring staff perceptions, specifically the challenges and benefits, of facilitating equipment based exercise sessions in the school environment. Methodology, Methods, Research Instruments or Sources Used Evaluation of the intervention was designed as a matched-control study and was undertaken over a seven-month period. The school-based intervention involved 3 intervention schools (n =436; 224 boys) and one control school (n=123; 70 boys) in a low socioeconomic and multicultural urban setting. The PA intervention was separated into two phases: a motivation DVD and 10 days of circuit based exercise sessions (Phase 1) followed by a maintenance phase (Phase 2) that incorporated a PA reward program and the use of specialist kid’s gym equipment located at each school for a period of 4 wk. Outcome measures were measured at baseline (January) and endpoint (July; end of academic school year) using reliable and valid self-report measures. The children’s attitudes towards PA were assessed using the Children’s Attitudes towards Physical Activity (CATPA) questionnaire. The Physical Activity Questionnaire for Children (PAQ-C), a 7-day recall questionnaire, was used to assess PA levels over a school week. A standardised test battery (Fitnessgram®) was used to assess cardiovascular fitness, body composition, muscular strength and endurance, and flexibility. After the 4 wk period, similar kid’s equipment was available for general access at local community facilities. The control school did not receive any of the interventions. All physical fitness tests and PA questionnaires were administered and collected prior to the start of the intervention (January) and following the intervention period (July) by an independent evaluation team. Evaluation testing took place at the individual schools over 2-3 consecutive days (depending on the number of children to be tested at the school). Staff (n=19) and student perceptions (n = 436) of the child sized fitness equipment were assessed via questionnaires post-intervention. Students completed a questionnaire to assess enjoyment, usage, ease of use and equipment assess and usage in the community. A questionnaire assessed staff perceptions on the delivery of the exercise sessions, classroom engagement and student perceptions. Conclusions, Expected Outcomes or Findings Findings showed that both the intervention (16.4%) and control groups increased their PAQ-C score by post-intervention (p < 0.05); with the intervention (17.8%) and control (21.3%) boys showing the greatest increase in physical activity levels. At post-intervention, there was a 5.5% decline in the intervention girls’ attitudes toward PA in the aesthetic subdomains (p = 0.009); whereas the control boys had an increase in positive attitudes in the health domain (p = 0.003). No significant differences in attitudes towards physical activity were observed in any other domain for either group at post-intervention (p > 0.05). The results of the equipment questionnaire, 96% of the children stated they enjoyed using the equipment and would like to use the equipment again in the future; however at post-intervention only 27% reported using the equipment outside of school in the last 7 days. Students identified the ski walker (34%) and cycle (32%) as their favorite pieces of equipment; with the single joint exercises such as leg extension and bicep/tricep machine (<3%) as their least favorite. Key themes from staff were that the equipment sessions were enjoyable, a novel activity, children felt very grown-up, and the activity was linked to a real fitness experience. They also expressed the need for more support to deliver the sessions and more time required for each session. Findings from this study suggest that a more integrated approach within the various agencies is required, particularly more support to increase teachers pedagogical content knowledge in physical activity instruction which is age appropriate. Future recommendations for successful implementation include sufficient time period for all students to access and engage with the equipment; increased access and marketing of facilities to parents within the local community, and professional teacher support strategies to facilitate the exercise sessions.

Multi-residue analysis of 39 pesticides in surface waters of Ria de Aveiro

A multi-residue gas chromatography-mass spectrometry method was developed in order to evaluate the presence of 39 pesticides of different chemical families (organophosphorus, triazines, imidazole, organochlorine), as well as some of their transformation products, in surface water samples from Ria de Aveiro. Ria de Aveiro is an estuarine coastal lagoon, located in the northern west region of Portugal, which receives inputs from agriculture, urban and industrial activities. The analytical method was developed and validated according international guidelines and showed good linearity, with correlation coefficients higher than 0.9949 for all compounds, adequate precision and accuracy, and high sensitivity. Pesticides were chosen from the priority pollutants list of the Directive 2008/105/EC of the European Parliament and of the Council (on environmental quality standards in the field of water policy), or were selected due their common use in agricultural practices. Some of these 39 pesticides are, or are suspected to be, endocrine disruptor compounds (EDCs), being capable of altering the endocrine system of wildlife and humans, causing form malfunction and ultimately health problems. Even those pesticides which are not EDCs, are known to be awfully toxic and have a recognised impact in human health. The aquatic environment is particularly susceptible to pollution due to intentional and accidental release of chemicals to water [3]. Pesticide contamination of surface water is a national issue as it is often used as drinking water. This concern is especially important in rural agricultural areas where population uses small private water supplies, regularly without any laboratory surveillance. The study was performed in seven sampling points and the results showed a considerable concern pesticide contamination of all samples.

Multi-scale analysis of active landslides using two-pass differential interferometry

Landslides are common features of the landscape of the north-central Apennine mountain range and cause frequent damage to human facilities and infrastructure. Most of these landslides move periodically with moderate velocities and, only after particular rainfall events, some accelerate abruptly. Synthetic aperture radar interferometry (InSAR) provides a particularly convenient method for studying deforming slopes. We use standard two-pass interferometry, taking advantage of the short revisit time of the Sentinel-1 satellites. In this paper we present the results of the InSAR analysis developed on several study areas in central and Northern Italian Apennines. The aims of the work described within the articles contained in this paper, concern: i) the potential of the standard two-pass interferometric technique for the recognition of active landslides; ii) the exploration of the potential related to the displacement time series resulting from a two-pass multiple time-scale InSAR analysis; iii) the evaluation of the possibility of making comparisons with climate forcing for cognitive and risk assessment purposes. Our analysis successfully identified more than 400 InSAR deformation signals (IDS) in the different study areas corresponding to active slope movements. The comparison between IDSs and thematic maps allowed us to identify the main characteristics of the slopes most prone to landslides. The analysis of displacement time series derived from monthly interferometric stacks or single 6-day interferograms allowed the establishment of landslide activity thresholds. This information, combined with the displacement time series, allowed the relationship between ground deformation and climate forcing to be successfully investigated. The InSAR data also gave access to the possibility of validating geographical warning systems and comparing the activity state of landslides with triggering probability thresholds.

Aplicação do modelo Tucker-3 para a análise da biodegradação de diesel

Tucker-3 model offers several advantages for analysis of environmental data but its interpretation is still challenging. A Tucker-3 model was applied to a biodegradation experiment involving a large number of overlapped chromatographic peaks and a temporal variation. The Tucker-3 model allowed the data to be decomposed in two processes: evaporation and biodegradation. The results suggest that linear hydrocarbons were those biodegraded first and demonstrate that the data analysis can be simplified by interpreting the elements of the core array. The approach discussed in this work can be applied in similar problems involving multi-way data in other areas of chemistry.

Precision-recall operating characteristic (P-ROC) curves in imprecise environments

Traditionally, machine learning algorithms have been evaluated in applications where assumptions can be reliably made about class priors and/or misclassification costs. In this paper, we consider the case of imprecise environments, where little may be known about these factors and they may well vary significantly when the system is applied. Specifically, the use of precision-recall analysis is investigated and compared to the more well known performance measures such as error-rate and the receiver operating characteristic (ROC). We argue that while ROC analysis is invariant to variations in class priors, this invariance in fact hides an important factor of the evaluation in imprecise environments. Therefore, we develop a generalised precision-recall analysis methodology in which variation due to prior class probabilities is incorporated into a multi-way analysis of variance (ANOVA). The increased sensitivity and reliability of this approach is demonstrated in a remote sensing application.

Multi-criteria spatial decision analysis for demarcation of greenway: A case study of the city of Rio Claro, São Paulo, Brazil

Concern regarding hydrological resources has been a theme of growing importance in Brazil, associating the development of new management policies and maintenance of natural areas related to rivers. An efficient way to maintain natural areas around rivers has been the development of greenways, and some cites have already adopted specific legislation in this respect. Following this growing evolution in the treatment of hydrological resources, this study was carried out to demarcate a greenway along the Corumbatai River in the state of São Paulo, Using multi-criteria analysis in a GIS environment. First, thematic maps were elaborated based on Landsat 7 satellite, aerial photographs and digital topographic base, Supported by field activities. With the use of multi-criteria analysis, for which ad hoe consultations were conducted to attribute weights to the thematic maps, a suitability map was elaborated for the allocation of the greenway. Sites that should be included in the greenway were also selected, such as areas appropriate for leisure activities, and ecologically important areas. Based on the suitability map, a pathway analysis was done, connecting the relevant points of interest, thus generating a greenway that runs along the Corumbatai River, with the aim of contributing to the conservation of this important hydrological resource. (c) 2007 Elsevier B.V. All rights reserved.