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.

Assessing a statistical inquiry

As statistical education becomes more firmly embedded in the school curriculum and its value across the curriculum is recognised, attention moves from knowing procedures, such as calculating a mean or drawing a graph, to understanding the purpose of a statistical investigation in decision making in many disciplines. As students learn to complete the stages of an investigation, the question of meaningful assessment of the process arises. This paper considers models for carrying out a statistical inquiry and, based on a four-phase model, creates a developmental squence that can be used for the assessment of outcomes from each of the four phases as well as for the complete inquiry. The developmental sequence is based on the SOLO model, focussing on the "observed" outcomes during the inquiry process.

Combining HPLC-DAD and ICP-MS data for improved analysis of complex samples: Classification of the root samples from Cortex moutan

A combined data matrix consisting of high performance liquid chromatography–diode array detector (HPLC–DAD) and inductively coupled plasma-mass spectrometry (ICP-MS) measurements of samples from the plant roots of the Cortex moutan (CM), produced much better classification and prediction results in comparison with those obtained from either of the individual data sets. The HPLC peaks (organic components) of the CM samples, and the ICP-MS measurements (trace metal elements) were investigated with the use of principal component analysis (PCA) and the linear discriminant analysis (LDA) methods of data analysis; essentially, qualitative results suggested that discrimination of the CM samples from three different provinces was possible with the combined matrix producing best results. Another three methods, K-nearest neighbor (KNN), back-propagation artificial neural network (BP-ANN) and least squares support vector machines (LS-SVM) were applied for the classification and prediction of the samples. Again, the combined data matrix analyzed by the KNN method produced best results (100% correct; prediction set data). Additionally, multiple linear regression (MLR) was utilized to explore any relationship between the organic constituents and the metal elements of the CM samples; the extracted linear regression equations showed that the essential metals as well as some metallic pollutants were related to the organic compounds on the basis of their concentrations

Adult total wellness: group differences based on sitting time and physical activity level

Background An increasing body of evidence associates a high level of sitting time with poor health outcomes. The benefits of moderate to vigorous-intensity physical activities to various aspects of health are now well documented; however, individuals may engage in moderate-intensity physical activity for at least 30 minutes on five or more days of the week and still exhibit a high level of sitting time. This purpose of this study was to examine differences in total wellness among adults relative to high/low levels of sitting time combined with insufficient/sufficient physical activity (PA). The construct of total wellness incorporates a holistic approach to the body, mind and spirit components of life, an approach which may be more encompassing than some definitions of health. Methods Data were obtained from 226 adult respondents (27 ± 6 years), including 116 (51%) males and 110 (49%) females. Total PA and total sitting time were assessed with the International Physical Activity Questionnaire (IPAQ) (short-version). The Wellness Evaluation of Lifestyle Inventory was used to assess total wellness. An analysis of covariance (ANCOVA) was utilised to assess the effects of the sitting time/physical activity group on total wellness. A covariate was included to partial out the effects of age, sex and work status (student or employed). Cross-tabulations were used to show associations between the IPAQ derived high/low levels of sitting time with insufficient/sufficient PA and the three total wellness groups (i.e. high level of wellness, moderate wellness and wellness development needed). Results The majority of the participants were located in the high total sitting time and sufficient PA group. There were statistical differences among the IPAQ groups for total wellness [F (2,220) = 32.5 (p <0.001)]. A Chi-square test revealed a significant difference in the distribution of the IPAQ categories within the classification of wellness [χ2 (N = 226) = 54.5, p < .001]. One-hundred percent (100%) of participants who self-rated as high total sitting time/insufficient PA were found in the wellness development needed group. In contrast, 72% of participants who were located in the low total sitting time/sufficient PA group were situated in the moderate wellness group. Conclusion Many participants who meet the physical activity guidelines, in this sample, sit for longer periods of time than the median Australian sitting time. An understanding of the effects of the enhanced PA and reduced sitting time on total wellness can add to the development of public health initiatives. Keywords: IPAQ; The Wellness Evaluation of Lifestyle (WEL); Sedentary lifestyle

Combined NIR/MIR analysis: A novel method for the classification of complex substances such as Illicium verum Hook. F. and its adulterants

A novel combined near- and mid-infrared (NIR and MIR) spectroscopic method has been researched and developed for the analysis of complex substances such as the Traditional Chinese Medicine (TCM), Illicium verum Hook. F. (IVHF), and its noxious adulterant, Iuicium lanceolatum A.C. Smith (ILACS). Three types of spectral matrix were submitted for classification with the use of the linear discriminant analysis (LDA) method. The data were pretreated with either the successive projections algorithm (SPA) or the discrete wavelet transform (DWT) method. The SPA method performed somewhat better, principally because it required less spectral features for its pretreatment model. Thus, NIR or MIR matrix as well as the combined NIR/MIR one, were pretreated by the SPA method, and then analysed by LDA. This approach enabled the prediction and classification of the IVHF, ILACS and mixed samples. The MIR spectral data produced somewhat better classification rates than the NIR data. However, the best results were obtained from the combined NIR/MIR data matrix with 95–100% correct classifications for calibration, validation and prediction. Principal component analysis (PCA) of the three types of spectral data supported the results obtained with the LDA classification method.

Structure matters: Adoption of structured classification Approach in the context of cognitive presence classification

Within online learning communities, receiving timely and meaningful insights into the quality of learning activities is an important part of an effective educational experience. Commonly adopted methods – such as the Community of Inquiry framework – rely on manual coding of online discussion transcripts, which is a costly and time consuming process. There are several efforts underway to enable the automated classification of online discussion messages using supervised machine learning, which would enable the real-time analysis of interactions occurring within online learning communities. This paper investigates the importance of incorporating features that utilise the structure of on-line discussions for the classification of "cognitive presence" – the central dimension of the Community of Inquiry framework focusing on the quality of students' critical thinking within online learning communities. We implemented a Conditional Random Field classification solution, which incorporates structural features that may be useful in increasing classification performance over other implementations. Our approach leads to an improvement in classification accuracy of 5.8% over current existing techniques when tested on the same dataset, with a precision and recall of 0.630 and 0.504 respectively.

Statistical literacy social media project for the masses

This article examines a social media assignment used to teach and practice statistical literacy with over 400 students each semester in large-lecture traditional, fully online, and flipped sections of an introductory-level statistics course. Following the social media assignment, students completed a survey on how they approached the assignment. Drawing from the authors’ experiences with the project and the survey results, this article offers recommendations for developing social media assignments in large courses that focus on the interplay between the social media tool and the implications of assignment prompts.

Assistive classification for improving the efficiency of avian species richness surveys

Avian species richness surveys, which measure the total number of unique avian species, can be conducted via remote acoustic sensors. An immense quantity of data can be collected, which, although rich in useful information, places a great workload on the scientists who manually inspect the audio. To deal with this big data problem, we calculated acoustic indices from audio data at a one-minute resolution and used them to classify one-minute recordings into five classes. By filtering out the non-avian minutes, we can reduce the amount of data by about 50% and improve the efficiency of determining avian species richness. The experimental results show that, given 60 one-minute samples, our approach enables to direct ecologists to find about 10% more avian species.

Image processing and classification procedure for the analysis of Australian frog vocalisations

Frog species have been declining worldwide at unprecedented rates in the past decades. There are many reasons for this decline including pollution, habitat loss, and invasive species [1]. To preserve, protect, and restore frog biodiversity, it is important to monitor and assess frog species. In this paper, a novel method using image processing techniques for analyzing Australian frog vocalisations is proposed. An FFT is applied to audio data to produce a spectrogram. Then, acoustic events are detected and isolated into corresponding segments through image processing techniques applied to the spectrogram. For each segment, spectral peak tracks are extracted with selected seeds and a region growing technique is utilised to obtain the contour of each frog vocalisation. Based on spectral peak tracks and the contour of each frog vocalisation, six feature sets are extracted. Principal component analysis reduces each feature set down to six principal components which are tested for classification performance with a k-nearest neighbor classifier. This experiment tests the proposed method of classification on fourteen frog species which are geographically well distributed throughout Queensland, Australia. The experimental results show that the best average classification accuracy for the fourteen frog species can be up to 87%.

Acoustic classification of Australian anurans using syllable features

Acoustic classification of anurans (frogs) has received increasing attention for its promising application in biological and environment studies. In this study, a novel feature extraction method for frog call classification is presented based on the analysis of spectrograms. The frog calls are first automatically segmented into syllables. Then, spectral peak tracks are extracted to separate desired signal (frog calls) from background noise. The spectral peak tracks are used to extract various syllable features, including: syllable duration, dominant frequency, oscillation rate, frequency modulation, and energy modulation. Finally, a k-nearest neighbor classifier is used for classifying frog calls based on the results of principal component analysis. The experiment results show that syllable features can achieve an average classification accuracy of 90.5% which outperforms Mel-frequency cepstral coefficients features (79.0%).

Acoustic feature extraction using perceptual wavelet packet decomposition for frog call classification

Frog protection has become increasingly essential due to the rapid decline of its biodiversity. Therefore, it is valuable to develop new methods for studying this biodiversity. In this paper, a novel feature extraction method is proposed based on perceptual wavelet packet decomposition for classifying frog calls in noisy environments. Pre-processing and syllable segmentation are first applied to the frog call. Then, a spectral peak track is extracted from each syllable if possible. Track duration, dominant frequency and oscillation rate are directly extracted from the track. With k-means clustering algorithm, the calculated dominant frequency of all frog species is clustered into k parts, which produce a frequency scale for wavelet packet decomposition. Based on the adaptive frequency scale, wavelet packet decomposition is applied to the frog calls. Using the wavelet packet decomposition coefficients, a new feature set named perceptual wavelet packet decomposition sub-band cepstral coefficients is extracted. Finally, a k-nearest neighbour (k-NN) classifier is used for the classification. The experiment results show that the proposed features can achieve an average classification accuracy of 97.45% which outperforms syllable features (86.87%) and Mel-frequency cepstral coefficients (MFCCs) feature (90.80%).

Application of image processing techniques for frog call classification

Frogs have received increasing attention due to their effectiveness for indicating the environment change. Therefore, it is important to monitor and assess frogs. With the development of sensor techniques, large volumes of audio data (including frog calls) have been collected and need to be analysed. After transforming the audio data into its spectrogram representation using short-time Fourier transform, the visual inspection of this representation motivates us to use image processing techniques for analysing audio data. Applying acoustic event detection (AED) method to spectrograms, acoustic events are firstly detected from which ridges are extracted. Three feature sets, Mel-frequency cepstral coefficients (MFCCs), AED feature set and ridge feature set, are then used for frog call classification with a support vector machine classifier. Fifteen frog species widely spread in Queensland, Australia, are selected to evaluate the proposed method. The experimental results show that ridge feature set can achieve an average classification accuracy of 74.73% which outperforms the MFCCs (38.99%) and AED feature set (67.78%).

Acoustic features for multi-level classification of Australian frogs

Over past few decades, frog species have been experiencing dramatic decline around the world. The reason for this decline includes habitat loss, invasive species, climate change and so on. To better know the status of frog species, classifying frogs has become increasingly important. In this study, acoustic features are investigated for multi-level classification of Australian frogs: family, genus and species, including three families, eleven genera and eighty five species which are collected from Queensland, Australia. For each frog species, six instances are selected from which ten acoustic features are calculated. Then, the multicollinearity between ten features are studied for selecting non-correlated features for subsequent analysis. A decision tree (DT) classifier is used to visually and explicitly determine which acoustic features are relatively important for classifying family, which for genus, and which for species. Finally, a weighted support vector machines (SVMs) classifier is used for the multi- level classification with three most important acoustic features respectively. Our experiment results indicate that using different acoustic feature sets can successfully classify frogs at different levels and the average classification accuracy can be up to 85.6%, 86.1% and 56.2% for family, genus and species respectively.

A Bayesian Framework for the Assessment of Vision-based Weed and Fruit Detection and Classification Algorithms

This paper proposes new metrics and a performance-assessment framework for vision-based weed and fruit detection and classification algorithms. In order to compare algorithms, and make a decision on which one to use fora particular application, it is necessary to take into account that the performance obtained in a series of tests is subject to uncertainty. Such characterisation of uncertainty seems not to be captured by the performance metrics currently reported in the literature. Therefore, we pose the problem as a general problem of scientific inference, which arises out of incomplete information, and propose as a metric of performance the(posterior) predictive probabilities that the algorithms will provide a correct outcome for target and background detection. We detail the framework through which these predicted probabilities can be obtained, which is Bayesian in nature. As an illustration example, we apply the framework to the assessment of performance of four algorithms that could potentially be used in the detection of capsicums (peppers).

Statistical modelling and power analysis for detecting trends in total suspended sediment loads

The export of sediments from coastal catchments can have detrimental impacts on estuaries and near shore reef ecosystems such as the Great Barrier Reef. Catchment management approaches aimed at reducing sediment loads require monitoring to evaluate their effectiveness in reducing loads over time. However, load estimation is not a trivial task due to the complex behaviour of constituents in natural streams, the variability of water flows and often a limited amount of data. Regression is commonly used for load estimation and provides a fundamental tool for trend estimation by standardising the other time specific covariates such as flow. This study investigates whether load estimates and resultant power to detect trends can be enhanced by (i) modelling the error structure so that temporal correlation can be better quantified, (ii) making use of predictive variables, and (iii) by identifying an efficient and feasible sampling strategy that may be used to reduce sampling error. To achieve this, we propose a new regression model that includes an innovative compounding errors model structure and uses two additional predictive variables (average discounted flow and turbidity). By combining this modelling approach with a new, regularly optimised, sampling strategy, which adds uniformity to the event sampling strategy, the predictive power was increased to 90%. Using the enhanced regression model proposed here, it was possible to detect a trend of 20% over 20 years. This result is in stark contrast to previous conclusions presented in the literature. (C) 2014 Elsevier B.V. All rights reserved.