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A Useful Pivotal Quantity
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| Pengarang | : | Panagiotis Toulis |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 272-274 |
| Abstrak | : | Consider n continuous random variables with joint density f that possibly dependson unknown parameters θ. If the negative of the logarithm of f is a positive homogenous function of degree p taking only positive values, then that function is distributed as a Gamma random variable with shape n/p and scale 2, and thus it is a pivotal quantity for θ. This provides a general method to construct pivotal quantities, which are widely applicable in statistical practice, such as hypothesis testing and confidence intervals. Here, we prove the aforementioned result and illustrate through examples. |
Convergence of Known Distributions to Limiting Normal or Non-normal Distributions: An Elementary Ratio Technique
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 265-271 |
| Abstrak | : | This article presents an elementary informal technique for deriving the convergence of known distributions to limiting normal or non-normal distributions. The presentation should be of interest to teachers and students of first year graduate level courses in probability and statistics. |
Bayes and MCMC for Undergraduates
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 259-264 |
| Abstrak | : | Students of statistics should be taught the ideas and methods that are widely used in practice and that will help them understand the world of statistics. Today, this means teaching them about Bayesian methods. In this article, I present ideas on teaching an undergraduate Bayesian course that uses Markov chain Monte Carlo and that can be a second course or, for strong students, a first course in statistics. |
Resolving a Multi-Million Dollar Contract Dispute With a Latin Square
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 249-258 |
| Abstrak | : | The City of New York negotiated a dispute over the performance of new garbage trucks purchased from a vehicle manufacturer. The dispute concerned the fulfillment of a specification in the purchase contract that the trucks load a minimum full-load of 12.5 tons of household refuse. On behalf of the City, but in cooperation with the manufacturer, the City's Department of Sanitation and consulting statisticians tested fulfillment of the contract specification, employing a Latin Square design for routing trucks. We present the classical analysis using a linear model and analysis of variance. We also show how fixed, mixed, and random effect models are useful in analyzing the results of the test. Finally, we take a Bayesian perspective to demonstrate how the information from the data overcomes the difference between the prior densities of the city and the manufacturer for the load capacities of the trucks to result in much closer posterior densities. This procedure might prove useful in similar negotiations. Supplementary material including the data and R code for computations in the article are available online. |
Coherent Hypothesis Testing
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 242-248 |
| Abstrak | : | Multiple hypothesis testing, an important quantitative tool to report the results of scientific inquiries, frequently leads to contradictory conclusions. For instance, in an analysis of variance (ANOVA) setting, the same dataset can lead one to reject the equality of two means, say μ1 = μ2, but at the same time to not reject the hypothesis that μ1 = μ2 = 0. These two conclusions violate the coherence principle introduced by Gabriel in Citation1969, and lead to results that are difficult to communicate, and, many times, embarrassing for practitioners of statistical methods. Although this situation is common in the daily life of statisticians, it is usually not discussed in courses of statistics. In this work, we enrich the teaching and discussion of this important topic by investigating through a few examples whether several standard test procedures are coherent or not. We also discuss the relationship between coherent tests and measures of support. Finally, we show how a Bayesian decision-theoretical framework can be used to build coherent tests. These approaches to coherence enlighten when such property is appealing in multiple testing and provide means of obtaining it. |
On the Use of the Concentration Function in Medical Fraud Assessment
| Pengarang | : | Tahir Ekin |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 236-241 |
| Abstrak | : | We propose a simple, but effective, tool to detect possible anomalies in the services prescribed by a health care provider (HP) compared to his/her colleagues in the same field and environment. Our method is based on the concentration function that is an extension of the Lorenz curve widely used in describing uneven distribution of wealth in a population. The proposed tool provides a graphical illustration of a possible anomalous behavior of the HPs and it can be used as a prescreening device for further investigations of potential medical fraud. |
All Data are Wrong, but Some are Useful? Advocating the Need for Data Auditing
| Pengarang | : | Djiwandodo Soedjati .J |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 231-235 |
| Abstrak | : | In a recent article from the Annals of Applied Statistics, Cox discussed the main phases of applied statistical research ranging from clarifying study objectives to final data analysis and interpreting results. As an incidental remark to these main phases, we advocate that beyond cleaning and preprocessing the data, it is a good practice to audit the data to determine if they can be trusted at all. A case study based on Ghanaian Official Fishery Statistics is used to illustrate this need, with Benford's law being the tool used to carrying out the data audit. Supplementary materials for this article are available online. |
Strategies for Success: Early-Stage Collaborating Biostatistics Faculty in an Academic Health Center
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 220-230 |
| Abstrak | : | Collaborative biostatistics faculty (CBF) are increasingly valued by academic health centers (AHCs) for their role in increasing success rates of grants and publications, and educating medical students and clinical researchers. Some AHCs have a biostatistics department that consists of only biostatisticians focused on methodological research, collaborative research, and education. Others may have a biostatistics unit within an interdisciplinary department, or statisticians recruited into clinical departments. Within each model, there is also variability in environment, influenced by the chair's background, research focus of colleagues, type of students taught, funding sources, and whether the department is in a medical school or school of public health. CBF appointments may be tenure track or nontenure, and expectations for promotion may vary greatly depending on the type of department, track, and the AHC. In this article, the authors identify strategies for developing early-stage CBFs in four domains: (1) Influence of department/environment, (2) Skills to develop, (3) Ways to increase productivity, and (4) Ways to document accomplishments. Graduating students and postdoctoral fellows should consider the first domain when choosing a faculty position. Early-stage CBFs will benefit by understanding the requirements of their environment early in their appointment and by modifying the provided progression grid with their chair and mentoring team as needed. Following this personalized grid will increase the chances of a satisfying career with appropriate recognition for academic accomplishments. |
Statistical Engineering: An Idea Whose Time Has Come?
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 209-219 |
| Abstrak | : | Several authors, including the American Statistical Association (ASA) guidelines for undergraduate statistics education Citation(American Statistical Association Undergraduate Guidelines Workgroup), have noted the challenges facing statisticians when attacking large, complex, and unstructured problems, as opposed to well-defined textbook problems. Clearly, the standard paradigm of selecting the one “correct” statistical method for such problems is not sufficient; a new paradigm is needed. Statistical engineering has been proposed as a discipline that can provide a viable paradigm to attack such problems, used in conjunction with sound statistical science. Of course, to develop as a true discipline, statistical engineering must be clearly defined and articulated. Further, a well-developed underlying theory is needed, one that would prove helpful in addressing such large, complex, and unstructured problems. The purpose of this expository article is to more clearly articulate the current state of statistical engineering, and make a case for why it merits further study by the profession as a means of addressing such problems. We conclude with a “call to action.” |
Sufficiency Revisited: Rethinking Statistical Algorithms in the Big Data Era
| Pengarang | : | Pande Radja Silalahi |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 71 (No. 3) |
| Halaman | : | 202-208 |
| Abstrak | : | The big data era demands new statistical analysis paradigms, since traditional methods often break down when datasets are too large to fit on a single desktop computer. Divide and Recombine (D&R) is becoming a popular approach for big data analysis, where results are combined over subanalyses performed in separate data subsets. In this article, we consider situations where unit record data cannot be made available by data custodians due to privacy concerns, and explore the concept of statistical sufficiency and summary statistics for model fitting. The resulting approach represents a type of D&R strategy, which we refer to as summary statistics D&R; as opposed to the standard approach, which we refer to as horizontal D&R. We demonstrate the concept via an extended Gamma–Poisson model, where summary statistics are extracted from different databases and incorporated directly into the fitting algorithm without having to combine unit record data. By exploiting the natural hierarchy of data, our approach has major benefits in terms of privacy protection. Incorporating the proposed modelling framework into data extraction tools such as TableBuilder by the Australian Bureau of Statistics allows for potential analysis at a finer geographical level, which we illustrate with a multilevel analysis of the Australian unemployment data. Supplementary materials for this article are available online. |