This class covers quantitative analysis of uncertainty and risk for engineering applications. Fundamentals of probability, random processes, statistics, and decision analysis are covered, along with random variables and vectors, uncertainty propagation, conditional distributions, and second-moment analysis. System reliability is introduced. Other topics covered include Bayesian analysis and risk-based decision, estimation of distribution parameters, hypothesis testing, simple and multiple linear regressions, and Poisson and Markov processes. There is an emphasis placed on real-world applications to engineering problems.

Sixth grade math teacher Ana Posada shares a lesson on probability. Students do simulations of dependent and independent events using a goody bag of objects where they can document the differences between them.

Project Euclid's mission is to advance scholarly communication in the field of theoretical and applied mathematics and statistics. It provides access to independent and society journals publishing in these areas. Through the site users can view tables of contents and article abstracts and benefit from a system offering full-text searching, reference linking, and cross-linking to Math Reviews, Zentralblatt, and CrossRef. The site also offers monographs and conference proceedings in these fields.

Background The p value obtained from a significance test provides no information about the magnitude or importance of the underlying phenomenon. Therefore, additional reporting of effect size is often recommended. Effect sizes are theoretically independent from sample size. Yet this may not hold true empirically: non-independence could indicate publication bias. Methods We investigate whether effect size is independent from sample size in psychological research. We randomly sampled 1,000 psychological articles from all areas of psychological research. We extracted p values, effect sizes, and sample sizes of all empirical papers, and calculated the correlation between effect size and sample size, and investigated the distribution of p values. Results We found a negative correlation of r = −.45 [95% CI: −.53; −.35] between effect size and sample size. In addition, we found an inordinately high number of p values just passing the boundary of significance. Additional data showed that neither implicit nor explicit power analysis could account for this pattern of findings. Conclusion The negative correlation between effect size and samples size, and the biased distribution of p values indicate pervasive publication bias in the entire field of psychology.

P values represent a widely used, but pervasively misunderstood and fiercely contested method of scientific inference. Display items, such as figures and tables, often containing the main results, are an important source of P values. We conducted a survey comparing the overall use of P values and the occurrence of significant P values in display items of a sample of articles in the three top multidisciplinary journals (Nature, Science, PNAS) in 2017 and, respectively, in 1997. We also examined the reporting of multiplicity corrections and its potential influence on the proportion of statistically significant P values. Our findings demonstrated substantial and growing reliance on P values in display items, with increases of 2.5 to 14.5 times in 2017 compared to 1997. The overwhelming majority of P values (94%, 95% confidence interval [CI] 92% to 96%) were statistically significant. Methods to adjust for multiplicity were almost non-existent in 1997, but reported in many articles relying on P values in 2017 (Nature 68%, Science 48%, PNAS 38%). In their absence, almost all reported P values were statistically significant (98%, 95% CI 96% to 99%). Conversely, when any multiplicity corrections were described, 88% (95% CI 82% to 93%) of reported P values were statistically significant. Use of Bayesian methods was scant (2.5%) and rarely (0.7%) articles relied exclusively on Bayesian statistics. Overall, wider appreciation of the need for multiplicity corrections is a welcome evolution, but the rapid growth of reliance on P values and implausibly high rates of reported statistical significance are worrisome.

The chapters in their current form have been made available to students who used Python in my Decision Science course in Fall 2019 (the course I had to prep for. Most students used R, but this helped those who choose Python). It has also been used as reference for students and project partners who use Python but have not had any training on using Python for data management.

This work is still useful for those learning Python as a data analysis platform as well as those who need to convert R code into Python due to deployment needs or to take advantage of Python resources in other domains. While it was not used as a textbook, the material was used by students in my decision models course and in senior capstone course for those who choose to use Python instead of R. While it seemed to help, the students had more difficulty than students who used R.

The objectives of this course are as follows: Demonstrate an understanding of graphical representations of data and their interpretation; Demonstrate a competency in mathematical tools of decision making, including derivatives and analytical optimization; Demonstrate an understanding of descriptive statistics, hypothesis testing, and the theory of regression; Demonstrate competency in the use of software used in quantitative analysis, including Excel tools and statistical software. This textbook is organized to support you in these goals. The textbook is adapted from Contemporary Calculus, written by Dale Hoffman from Bellevue Community College and Business Calculus written by Shana Calaway from Shoreline Community College. New material is written by Margo Bergman from University of Washington Tacoma.

This open textbook covers common statistics used in agriculture research, including experimental design in plant breeding and genetics, as well as the analysis of variance, regression, and correlation.

Each of the books in the PBEA series comes with a section in its back matter titled "Applied Learning Activities" which includes additional content aligned to each chapter such as handouts and worksheets, csv files, code for statistical analysis in R, and recommended readings.

This course develops logical, empirically based arguments using statistical techniques and analytic methods. Elementary statistics, probability, and other types of quantitative reasoning useful for description, estimation, comparison, and explanation are covered. Emphasis is on the use and limitations of analytical techniques in planning practice.

As taught Spring Semester 2011.

The objective of this module is to introduce students to the practice of quantitative data analysis in the social sciences. The lecture component of the module will explore a variety of the most commonly used statistical methods; in the laboratory component, students will learn to apply these techniques to the analysis of social science data. Through assignments, students will have the opportunity to develop and test their own hypotheses and explanations on major research data sets. The module should provide a sound grasp of the possibilities, methods, and dangers inherent in quantitative social and political research.

Module Codes: M14121 (20 credits)

Suitable for study at: Postgraduate Level

Dr Mark Pickup, School of Politics and International Relations

Dr Mark Pickup is a specialist in Comparative politics, with a particular interest in public opinion and democratic representation within North American and European countries. His research focuses on political information, public opinion, the media, election campaigns and electoral institutions.

Dr Pickup is also a Visiting Fellow in the Department of Politics at the University of Oxford, where he runs the Oxford Polling Observatory website

We surveyed 807 researchers (494 ecologists and 313 evolutionary biologists) about their use of Questionable Research Practices (QRPs), including cherry picking statistically significant results, p hacking, and hypothesising after the results are known (HARKing). We also asked them to estimate the proportion of their colleagues that use each of these QRPs. Several of the QRPs were prevalent within the ecology and evolution research community. Across the two groups, we found 64% of surveyed researchers reported they had at least once failed to report results because they were not statistically significant (cherry picking); 42% had collected more data after inspecting whether results were statistically significant (a form of p hacking) and 51% had reported an unexpected finding as though it had been hypothesised from the start (HARKing). Such practices have been directly implicated in the low rates of reproducible results uncovered by recent large scale replication studies in psychology and other disciplines. The rates of QRPs found in this study are comparable with the rates seen in psychology, indicating that the reproducibility problems discovered in psychology are also likely to be present in ecology and evolution.

This activity helps students develop better understanding and stronger reasoning skills about distributions in terms of center and spread. Key words: center, spread, distribution

This course explores the detection and measurement of radio and optical signals encountered in communications, astronomy, remote sensing, instrumentation, and radar. Topics covered include: statistical analysis of signal processing systems, including radiometers, spectrometers, interferometers, and digital correlation systems; matched filters and ambiguity functions; communications channel performance; measurement of random electromagnetic fields, angular filtering properties of antennas, interferometers, and aperture synthesis systems; and radiative transfer and parameter estimation.

This activity uses simulation to help students understand sampling variability and reason about whether a particular samples result is unusual, given a particular hypothesis. By using first candies, then a web applet, and varying sample size, students learn that larger samples give more stable and better estimates of a population parameter and develop an appreciation for factors affecting sampling variability.

  Introductory Statistics is a non-calculus based, descriptive statistics course with applications. Topics include methods of collecting, organizing, and interpreting data; measures of central tendency, position, and variability for grouped and ungrouped data; frequency distributions and their graphical representations; introduction to probability theory, standard normal distribution, and areas under the curve. Course materials created by Fahmil Shah, content added to OER Commons by Victoria Vidal.

  Introductory Statistics is a non-calculus based, descriptive statistics course with applications. Topics include methods of collecting, organizing, and interpreting data; measures of central tendency, position, and variability for grouped and ungrouped data; frequency distributions and their graphical representations; introduction to probability theory, standard normal distribution, and areas under the curve. Course materials created by Fahmil Shah, content added to OER Commons by Victoria Vidal.

This textbook is an adaptation of the Research Methods in Psychology that is available on this site in US and Canadian editions. This New Zealand edition is an adaptation to the New Zealand context. The main changes are in Chapters 1 and 3 and the spelling, grammar, and terminology are changed throughout. This textbook is adopted at the University of Waikato in our 200-level research methods in psychology class.

Confirmation through competent replication is a founding principle of modern science. However, biomedical researchers are rewarded for innovation, and not for confirmation, and confirmatory research is often stigmatized as unoriginal and as a consequence faces barriers to publication. As a result, the current biomedical literature is dominated by exploration, which to complicate matters further is often disguised as confirmation. Only recently scientists and the public have begun to realize that high-profile research results in biomedicine can often not be replicated. Consequently, confirmation has become central stage in the quest to safeguard the robustness of research findings. Research which is pushing the boundaries of or challenges what is currently known must necessarily result in a plethora of false positive results. Thus, since discovery, the driving force of scientific progress, is unavoidably linked to high false positive rates and cannot support confirmatory inference, dedicated confirmatory investigation is needed for pivotal results. In this chapter I will argue that the tension between the two modes of research, exploration and confirmation, can be resolved if we conceptually and practically separate them. I will discuss the idiosyncrasies of exploratory and confirmatory studies, with a focus on the specific features of their design, analysis, and interpretation.

Review of Answering Questions with Data
https://drive.google.com/open?id=15lxoO1g39m6JICO7eKhiLR_pQqB4iOoJJtcylZJgp2E

This course has been designed to help students focus learning on specific areas of improvement. Unlike a typical college course where you would complete lessons in chronological order, this course allows you to focus on specific skills. Modules include: Arithmetic Review, Percents, Geometric Figures, Measurement, and Statistics