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We investigate various methods for testing whether two groups of curves are statistically significantly different, with the motivation to apply the techniques to the analysis of data arising from designed experiments. We propose a set of tests based on pairwise differences between individual curves. Our objective is to compare the power and robustness of a variety of tests, including a collection of permutation tests, a test based on the functional principal components scores, the adaptive Neyman test and the functional F test. We illustrate the application of these tests in the context of a designed 2^4 factorial experiment with a case study using data provided by NASA. We apply the methods for comparing curves to this factorial data by dividing the data into two groups by each effect (A, B, . . . , ABCD) in turn. We carry out a large simulation study investigating the power of the tests in detecting contamination, location, and shift effects on unimodal and monotone curves. We conclude that the permutation test using the mean of the pairwise differences in L1 norm has the best overall power performance and is a robust test statistic applicable in a wide variety of situations. The advantage of using a permutation test is that it is an exact, distribution-free test that performs well overall when applied to functional data. This test may be extended to more than two groups by constructing test statistics based on averages of pairwise differences between curves from the different groups and, as such, is an important building-block for larger experiments and more complex designs.

We investigate various methods for testing whether two groups of curves are statistically significantly different, with the motivation to apply the techniques to the analysis of data arising from designed experiments. We propose a set of tests based on pairwise differences between individual curves. Our objective is to compare the power and robustness of a variety of tests, including a collection of permutation tests, a test based on the functional principal components scores, the adaptive Neyman test and the functional F test. We illustrate the application of these tests in the context of a designed 2^4 factorial experiment with a case study using data provided by NASA. We apply the methods for comparing curves to this factorial data by dividing the data into two groups by each effect (A, B, . . . , ABCD) in turn. We carry out a large simulation study investigating the power of the tests in detecting contamination, location, and shift effects on unimodal and monotone curves. We conclude that the permutation test using the mean of the pairwise differences in L1 norm has the best overall power performance and is a robust test statistic applicable in a wide variety of situations. The advantage of using a permutation test is that it is an exact, distribution-free test that performs well overall when applied to functional data. This test may be extended to more than two groups by constructing test statistics based on averages of pairwise differences between curves from the different groups and, as such, is an important building-block for larger experiments and more complex designs.

Dyadic data analysis methods are underutilized in child and youth care, where much of the practice relies on relationships with individuals and groups. In this exploratory study, a dyadic data analysis approach was used to study the interdependence amongst client-counsellor dyads in a voluntary counselling setting. Ten counsellors and thirty-six clients from a Canadian voluntary counselling agency participated in this study. Counselling sessions ranged from two to 20 sessions. Clients completed a session rating scale, a measure of the therapeutic alliance. In addition, clients and counsellors completed an outcome rating scale and personal change questions. A one-with-many design was used to explore the similarity between client-counsellor dyads, the degree of consensus, assimilation, and uniqueness as well as the level of reciprocity for perceived client well-being. Multi-level modeling was used to partition the variance on the outcome rating scale to account for sources of non-independence in client-counsellor dyads, and the indirect relationships between multiple clients working with the same counsellor. Implications of the study and recommendations for future research are discussed. / Graduate

Reliability characteristics of new devices are usually demonstrated by life testing. When lifetime data are sparse, as is often the case with highly reliable devices, expensive devices, and devices for which accelerated life testing is not feasible, reliability models that are based on a combination of degradation and lifetime data represent an important practical approach. This thesis presents reliability models based on the combination of degradation and lifetime data or degradation data alone, with and without the presence of covariates. Statistical inference methods associated with the models are also developed. / The degradation process is assumed to follow a Wiener process. Failure is defined as the first passage of this process to a fixed barrier. The degradation data of a surviving item are described by a truncated Wiener process and lifetimes follow an inverse Gaussian distribution. Models are developed for three types of data structures that are often encountered in reliability studies, terminal point data (a combination of degradation and lifetime data) and mixed data (an extended case of terminal point data); conditional degradation data; and covariate data. / Maximum likelihood estimators (MLEs) are derived for the parameters of each model. Inferences about the parameters are based on asymptotic properties of the MLEs and on the likelihood ratio method. An analysis of deviance is presented and approximate pivotal quantities are derived for the drift and variance parameters. Predictive density functions for the lifetime and the future degradation level of either a surviving item or a new item are obtained using empirical Bayes methods. Case examples are given to illustrate the applications of the models.

Large data sets are difficult to analyze. Visualization has been proposed to assist exploratory data analysis (EDA) as our visual systems can process signals in parallel to quickly detect patterns. Nonetheless, designing an effective visual analytic tool remains a challenge. This challenge is partly due to our incomplete understanding of how common visualization techniques are used by human operators during analyses, either in laboratory settings or in the workplace. This thesis aims to further understand how visualizations can be used to support EDA. More specifically, we studied techniques that display multiple levels of visual information resolutions (VIRs) for analyses using a range of methods. The first study is a summary synthesis conducted to obtain a snapshot of knowledge in multiple-VIR use and to identify research questions for the thesis: (1) low-VIR use and creation; (2) spatial arrangements of VIRs. The next two studies are laboratory studies to investigate the visual memory cost of image transformations frequently used to create low-VIR displays and overview use with single-level data displayed in multiple-VIR interfaces. For a more well-rounded evaluation, we needed to study these techniques in ecologically-valid settings. We therefore selected the application domain of web session log analysis and applied our knowledge from our first three evaluations to build a tool called Session Viewer. Taking the multiple coordinated view and overview + detail approaches, Session Viewer displays multiple levels of web session log data and multiple views of session populations to facilitate data analysis from the high-level statistical to the low-level detailed session analysis approaches. Our fourth and last study for this thesis is a field evaluation conducted at Google Inc. with seven session analysts using Session Viewer to analyze their own data with their own tasks. Study observations suggested that displaying web session logs at multiple levels using the overview + detail technique helped bridge between high-level statistical and low-level detailed session analyses, and the simultaneous display of multiple session populations at all data levels using multiple views allowed quick comparisons between session populations. We also identified design and deployment considerations to meet the needs of diverse data sources and analysis styles.

This research investigates the spectral reflectance characteristics of soil and vegetation using multi-angular and single view hyperspectral data. The question of the thesis is ???How much information can be obtained from multi-angular hyperspectral remote sensing in comparison with single view angle hyperspectral remote sensing of soil and vegetation???? This question is addressed by analysing multi-angular and single view angle hyperspectral remote sensing using data from the field, airborne and space borne hyperspectral sensors. Spectral mapping, spectral indices and Functional Data Analysis (FDA) are used to analyse the data. Spectral mapping has been successfully used to distinguish features of soil and cotton with hyperspectral data. Traditionally, spectral mapping is based on collecting endmembers of pure pixels and using these as training areas for supervised classification. There are, however, limitations in the use of these algorithms when applied to multi-angular images, as the reflectance of a single ground unit will differ at each angle. Classifications using six-class endmembers identified using single angle imagery were assessed using multi-angular Compact High Resolution Imaging Spectrometer (CHRIS) imagery, as well as a set of vegetation indices. The results showed no significant difference between the angles. Low nutrient content in the soil produced lower vegetation index values, and more nutrients increased the index values. This research introduces FDA as an image processing tool for multi-angular hyperspectral imagery of soil and cotton, using basis functions for functional principal component analysis (fPCA) and functional linear modelling. FDA has advantages over conventional statistical analysis because it does not assume the errors in the data are independent and uncorrelated. Investigations showed that B-splines with 20-basis functions was the best fit for multi-angular soil spectra collected using the spectroradiometer and the satellite mounted CHRIS. Cotton spectra collected from greenhouse plants using a spectrodiometer needed 30-basis functions to fit the model, while 20-basis functions were sufficient for cotton spectra extracted from CHRIS. Functional principal component analysis (fPCA) of multi-angular soil spectra show the first fPCA explained a minimum of 92.5% of the variance of field soil spectra for different azimuth and zenith angles and 93.2% from CHRIS for the same target. For cotton, more than 93.6% of greenhouse trial and 70.6% from the CHRIS data were explained by the first fPCA. Conventional analysis of multi-angular hyperspectral data showed significant differences exist between soil spectra acquired at different azimuth and zenith angles. Forward scan direction of zenith angle provides higher spectral reflectance than backward direction. However, most multi-angular hyperspectral data analysed as functional data show no significant difference from nadir, except for small parts of the wavelength of cotton spectra using CHRIS. There is also no significant difference for soil spectra analysed as functional data collected from the field, although there was some difference for soil spectra extracted from CHRIS. Overall, the results indicate that multi-angular hyperspectral data provides only a very small amount of additional information when used for conventional analyses.

This study investigated the discrimination between sources of the semi-precious mineral, nephrite, by a targeted microanalytical determination of the elemental composition, including the trace elements. Nephrite specimens were collected from two significant nephrite sources in New Zealand, namely the Westland and Wakatipu fields, and combined with donated specimens from the Southland field to complete a representative collection of New Zealand nephrite. A small number of nephrite specimens were donated from the South Westland nephrite field and from foreign sources. Representative fragments of these specimens were analysed by electron microprobe analysis (EMPA) for major elements and by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) for trace elements. The data obtained by the analytical procedure were treated within a compositional data (CoDa) framework of statistical analysis that focuses on the relative sizes of the components in the data set. The data were transformed under the guidelines of the CoDa framework, where appropriate, and the transformed data were treated with standard statistical methods for exploratory data analysis, dimension reduction and discriminant analysis. Advances were made to the Hotelling’s method for comparison of multivariate means by incorporating a permutation evaluation step. This permutation method removes the requirement for multivariate normality, and it also allows comparisons to be made when there are many more variables than observations, as is often the case when objects are being characterized using elemental data. The strategy used in this study showed that it is possible to discriminate between sources of nephrite at both an intra- and inter-source level within New Zealand. In addition, an exploratory investigation showed that New Zealand nephrite could be differentiated from the few nephrite specimens from foreign sources that were available for comparison. Recommendations are made for the protection of the New Zealand nephrite resource and for casework, based on the results obtained in this study.

This study investigated the discrimination between sources of the semi-precious mineral, nephrite, by a targeted microanalytical determination of the elemental composition, including the trace elements. Nephrite specimens were collected from two significant nephrite sources in New Zealand, namely the Westland and Wakatipu fields, and combined with donated specimens from the Southland field to complete a representative collection of New Zealand nephrite. A small number of nephrite specimens were donated from the South Westland nephrite field and from foreign sources. Representative fragments of these specimens were analysed by electron microprobe analysis (EMPA) for major elements and by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) for trace elements. The data obtained by the analytical procedure were treated within a compositional data (CoDa) framework of statistical analysis that focuses on the relative sizes of the components in the data set. The data were transformed under the guidelines of the CoDa framework, where appropriate, and the transformed data were treated with standard statistical methods for exploratory data analysis, dimension reduction and discriminant analysis. Advances were made to the Hotelling’s method for comparison of multivariate means by incorporating a permutation evaluation step. This permutation method removes the requirement for multivariate normality, and it also allows comparisons to be made when there are many more variables than observations, as is often the case when objects are being characterized using elemental data. The strategy used in this study showed that it is possible to discriminate between sources of nephrite at both an intra- and inter-source level within New Zealand. In addition, an exploratory investigation showed that New Zealand nephrite could be differentiated from the few nephrite specimens from foreign sources that were available for comparison. Recommendations are made for the protection of the New Zealand nephrite resource and for casework, based on the results obtained in this study.

This study investigated the discrimination between sources of the semi-precious mineral, nephrite, by a targeted microanalytical determination of the elemental composition, including the trace elements. Nephrite specimens were collected from two significant nephrite sources in New Zealand, namely the Westland and Wakatipu fields, and combined with donated specimens from the Southland field to complete a representative collection of New Zealand nephrite. A small number of nephrite specimens were donated from the South Westland nephrite field and from foreign sources. Representative fragments of these specimens were analysed by electron microprobe analysis (EMPA) for major elements and by laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) for trace elements. The data obtained by the analytical procedure were treated within a compositional data (CoDa) framework of statistical analysis that focuses on the relative sizes of the components in the data set. The data were transformed under the guidelines of the CoDa framework, where appropriate, and the transformed data were treated with standard statistical methods for exploratory data analysis, dimension reduction and discriminant analysis. Advances were made to the Hotelling’s method for comparison of multivariate means by incorporating a permutation evaluation step. This permutation method removes the requirement for multivariate normality, and it also allows comparisons to be made when there are many more variables than observations, as is often the case when objects are being characterized using elemental data. The strategy used in this study showed that it is possible to discriminate between sources of nephrite at both an intra- and inter-source level within New Zealand. In addition, an exploratory investigation showed that New Zealand nephrite could be differentiated from the few nephrite specimens from foreign sources that were available for comparison. Recommendations are made for the protection of the New Zealand nephrite resource and for casework, based on the results obtained in this study.