scholarly journals Some Statistical Methods for Random Process Data from Seismology and Neurophysiology

Author(s):  
David R. Brillinger
2020 ◽  
Vol 122 (14) ◽  
pp. 1-32
Author(s):  
Norma Ming ◽  
Alec I. Kennedy

Background/Context Amidst the complex and fast-paced demands in schools and classrooms, identifying what most deserves educators’ attention can pose a challenge. Indicators help focus attention by highlighting key features that signal important outcomes or opportunities to take action or learn. Purpose Informed by multiple literatures, we offer a conceptual framework that elaborates on the connection between an indicator's development and use. Specifically, the framework proposes that how to develop indicators depends on the answers to several questions about how they will be used: the intended use (why), timing (when), content (on what), and threshold (how much). Research Design To explore this conceptual framework, we present two cases on the construction and use of indicators for continuous improvement in the San Francisco Unified School District. In the first case, we applied statistical process control (SPC) theory to create control charts that visualize district-level outliers on student achievement outcomes to examine potential causes of variation among schools. In the second case, we combined SPC with more basic statistical methods to develop indicators highlighting areas of potential promise across multiple measures and student subgroups within a school. In our exploration of the two case studies, we present the statistical methods applied to construct the indicator, an example of the visualizations created, and descriptions of how central office leaders interpreted and used the results. We document how the intended use informed the indicators’ design, and the ramifications of those decisions for educators’ subsequent use of the indicators for improvement. Conclusions and Recommendations In learning from these cases, we highlight the importance of constructing indicators from the perspective of their intended use and linked with specific conditions and potential actions. This requires including more useful process data in the development of those indicators, as well as more follow-up analysis of the effectiveness of the actions taken based on those indicators, contrasted against alternative actions. We also underscore the importance of developing indicators that distinguish between the need for systemic versus targeted improvement efforts, based on SPC. We believe that combining approaches across disciplines and methodologies holds great promise for the development and use of indicators for continuous improvement in education.


1998 ◽  
Vol 65 (2) ◽  
pp. 398-409 ◽  
Author(s):  
S. F. Masri ◽  
A. W. Smyth ◽  
M.-I. Traina

A relatively simple and straightforward procedure is presented for representing non-stationary random process data in a compact probabilistic format which can be used as excitation input in multi-degree-of-freedom analytical random vibration studies. The method involves two main stages of compaction. The first stage is based on the spectral decomposition of the covariance matrix by the orthogonal Karhunen-Loeve expansion. The dominant eigenvectors are subsequently least-squares fitted with orthogonal polynomials to yield an analytical approximation. This compact analytical representation of the random process is then used to derive an exact closed-form solution for the nonstationary response of general linear multi-degree-of-freedom dynamic systems. The approach is illustrated by the use of an ensemble of free-field acceleration records from the 1994 Northridge earthquake to analytically determine the covariance kernels of the response of a two-degree-of-freedom system resembling a commonly encountered problem in the structural control field. Spectral plots of the extreme values of the rms response of representative multi-degree-of-freedom systems under the action of the subject earthquake are also presented. It is shown that the proposed random data-processing method is not only a useful data-archiving and earthquake feature-extraction tool, but also provides a probabilistic measure of the average statistical characteristics of earthquake ground motion corresponding to a spatially distributed region. Such a representation could be a valuable tool in risk management studies to quantify the average seismic risk over a spatially extended area.


2019 ◽  
Vol 94 ◽  
pp. 147-155 ◽  
Author(s):  
Wanjun Liu ◽  
Runze Li ◽  
Marc A. Zimmerman ◽  
Maureen A. Walton ◽  
Rebecca M. Cunningham ◽  
...  

1978 ◽  
Vol 48 ◽  
pp. 7-29
Author(s):  
T. E. Lutz

This review paper deals with the use of statistical methods to evaluate systematic and random errors associated with trigonometric parallaxes. First, systematic errors which arise when using trigonometric parallaxes to calibrate luminosity systems are discussed. Next, determination of the external errors of parallax measurement are reviewed. Observatory corrections are discussed. Schilt’s point, that as the causes of these systematic differences between observatories are not known the computed corrections can not be applied appropriately, is emphasized. However, modern parallax work is sufficiently accurate that it is necessary to determine observatory corrections if full use is to be made of the potential precision of the data. To this end, it is suggested that a prior experimental design is required. Past experience has shown that accidental overlap of observing programs will not suffice to determine observatory corrections which are meaningful.


2014 ◽  
Vol 17 (1) ◽  
pp. 4-16
Author(s):  
Jade H. Coston ◽  
Corine Myers-Jennings

To better prepare the professionals and scholars of tomorrow in the field of communication sciences and disorders (CSD), a research project in which undergraduate students collected and analyzed language samples of child-parent dyads is presented. Student researchers gained broad and discipline-specific inquiry skills related to the ethical conduct of research, the literature review process, data collection using language assessment techniques, language sample analysis, and research dissemination. Undergraduate students majoring in CSD developed clinical research knowledge, skills, and dispositions necessary for future graduate level study and professional employment. In addition to the benefits of student growth and development, language samples collected through this project are helping to answer research questions regarding communicative turn-taking opportunities within the everyday routines of young children, the effects of turn-taking interactions on language development, and the construct validity of language sampling analysis techniques.


2008 ◽  
Vol 67 (2) ◽  
pp. 71-83 ◽  
Author(s):  
Yolanda A. Métrailler ◽  
Ester Reijnen ◽  
Cornelia Kneser ◽  
Klaus Opwis

This study compared individuals with pairs in a scientific problem-solving task. Participants interacted with a virtual psychological laboratory called Virtue to reason about a visual search theory. To this end, they created hypotheses, designed experiments, and analyzed and interpreted the results of their experiments in order to discover which of five possible factors affected the visual search process. Before and after their interaction with Virtue, participants took a test measuring theoretical and methodological knowledge. In addition, process data reflecting participants’ experimental activities and verbal data were collected. The results showed a significant but equal increase in knowledge for both groups. We found differences between individuals and pairs in the evaluation of hypotheses in the process data, and in descriptive and explanatory statements in the verbal data. Interacting with Virtue helped all students improve their domain-specific and domain-general psychological knowledge.


1973 ◽  
Vol 18 (11) ◽  
pp. 562-562
Author(s):  
B. J. WINER
Keyword(s):  

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