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Forbidden Knowledge and Specialized Training: A Versatile Solution for the Two Main Sources of Overfitting in Linear Regression
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| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 2) |
| Halaman | : | 160-168 |
| Abstrak | : | Overfitting in linear regression is broken down into two main causes. First, the formula for the estimator includes “forbidden knowledge” about training observations’ residuals, and it loses this advantage when deployed out-of-sample. Second, the estimator has “specialized training” that makes it particularly capable of explaining movements in the predictors that are idiosyncratic to the training sample. An out-of-sample counterpart is introduced to the popular “leverage” measure of training observations’ importance. A new method is proposed to forecast out-of-sample fit at the time of deployment, when the values for the predictors are known but the true outcome variable is not. In Monte Carlo simulations and in an empirical application using MRI brain scans, the proposed estimator performs comparably to Predicted Residual Error Sum of Squares (PRESS) for the average out-of-sample case and unlike PRESS, also performs consistently across different test samples, even those that differ substantially from the training set. |
Optimal and Fast Confidence Intervals for Hypergeometric Successes
| Pengarang | : | Jay Bartroff |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 2) |
| Halaman | : | 151-159 |
| Abstrak | : | We present an efficient method of calculating exact confidence intervals for the hypergeometric parameter representing the number of “successes,” or “special items,” in the population. The method inverts minimum-width acceptance intervals after shifting them to make their endpoints nondecreasing while preserving their level. The resulting set of confidence intervals achieves minimum possible average size, and even in comparison with confidence sets not required to be intervals it attains the minimum possible cardinality most of the time, and always within 1. The method compares favorably with existing methods not only in the size of the intervals but also in the time required to compute them. The available R package hyperMCI implements the proposed method. |
Bayesian-Frequentist Hybrid Inference in Applications with Small Sample Sizes
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 2) |
| Halaman | : | 143-150 |
| Abstrak | : | The Bayesian-frequentist hybrid model and associated inference can combine the advantages of both Bayesian and frequentist methods and avoid their limitations. However, except for few special cases in existing literature, the computation under the hybrid model is generally nontrivial or even unsolvable. This article develops a computation algorithm for hybrid inference under any general loss functions. Three simulation examples demonstrate that hybrid inference can improve upon frequentist inference by incorporating valuable prior information, and also improve Bayesian inference based on non-informative priors where the latter leads to biased estimates for the small sample sizes used in inference. The proposed method is illustrated in applications including a biomechanical engineering design and a surgical treatment of acral lentiginous melanoma. |
The Cauchy Combination Test under Arbitrary Dependence Structures
| Pengarang | : | Mingya Long |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 2) |
| Halaman | : | 134-142 |
| Abstrak | : | Combining individual p-values to perform an overall test is often encountered in statistical applications. The Cauchy combination test (CCT) (Journal of the American Statistical Association, 2020, 115, 393–402) is a powerful and computationally efficient approach to integrate individual p-values under arbitrary dependence structures for sparse signals. We revisit this test to additionally show that (i) the tail probability of the CCT can be approximated just as well when more relaxed assumptions are imposed on individual p-values compared to those of the original test statistics; (ii) such assumptions are satisfied by six popular copula distributions; and (iii) the power of the CCT is no less than that of the minimum p-value test when the number of p-values goes to infinity under some regularity conditions. These findings are confirmed by both simulations and applications in two real datasets, thus, further broadening the theory and applications of the CCT. |
How Do We Perform a Paired t-Test When We Don’t Know How to Pair?
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 2) |
| Halaman | : | 127-133 |
| Abstrak | : | We address the question of how to perform a paired t-test in situations where we do not know how to pair the data. Specifically, we discuss approaches for bounding the test statistic of the paired t-test in a way that allows us to recover the results of this test in some cases. We also discuss the relationship between the paired t-test and the independent samples t-test and what happens if we use the latter to approximate the former. Our results are informed by both theoretical results and a simulation study. |
The State of Play of Reproducibility in Statistics: An Empirical Analysis
| Pengarang | : | Xin Xiong |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 2) |
| Halaman | : | 115-126 |
| Abstrak | : | Reproducibility, the ability to reproduce the results of published papers or studies using their computer code and data, is a cornerstone of reliable scientific methodology. Studies where results cannot be reproduced by the scientific community should be treated with caution. Over the past decade, the importance of reproducible research has been frequently stressed in a wide range of scientific journals such as Nature and Science and international magazines such as The Economist. However, multiple studies have demonstrated that scientific results are often not reproducible across research areas such as psychology and medicine. Statistics, the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data, prides itself on its openness when it comes to sharing both computer code and data. In this article, we examine reproducibility in the field of statistics by attempting to reproduce the results in 93 published papers in prominent journals using functional magnetic resonance imaging (fMRI) data during the 2010–2021 period. Overall, from both the computer code and the data perspective, among all the 93 examined papers, we could only reproduce the results in 14 (15.1%) papers, that is, the papers provide both executable computer code (or software) with the real fMRI data, and our results matched the results in the paper. Finally, we conclude with some author-specific and journal-specific recommendations to improve the research reproducibility in statistics. |
The Probability Mass Function of the Kaplan–Meier Product–Limit Estimator
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 1) |
| Halaman | : | 102-110 |
| Abstrak | : | Kaplan and Meier’s Citation1958 article developed a nonparametric estimator of the survivor function from a right-censored dataset. Determining the size of the support of the estimator as a function of the sample size provides a challenging exercise for students in an advanced course in mathematical statistics. We devise two algorithms for calculating the support size and calculate the associated probability mass function for small sample sizes and particular probability distributions for the failure and censoring times. |
“Two Truths and a Lie” as a Class-Participation Activity
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | The American Statistician |
| Volume / Edisi | : | 77 (No. 1) |
| Halaman | : | 97-101 |
| Abstrak | : | We adapt the social game “Two truths and a lie” to a classroom setting to give an activity that introduces principles of statistical measurement, uncertainty, prediction, and calibration, while giving students an opportunity to meet each other. We discuss how this activity can be used in a range of different statistics courses. |
Learning from a State Professional Development Conference for Science Teachers: Beginning Secondary Science Teachers’ Experiences
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of Science Teacher Education |
| Volume / Edisi | : | 30 (No. 3-4) |
| Halaman | : | 409–428 |
| Abstrak | : | Although there is growing understanding of beginning secondary science teacher learning and development in the United States, little is known about their learning experiences at professional develop ment (PD) conferences. To increase knowledge in this area, this study investigated the experiences of 68 beginning secondary science teachers at a state conference for science teachers. Free-choice learn ing was the theoretical perspective in this qualitative study, and data consisted of surveys, written reflections, interviews, and classroom observations. Findings in the domains of conference experience, alignment, lifelong learning, and classroom implementation sug gested that the conference facilitated the beginning science teachers’ learning about inquiry, nature of science, and problem-based learn ing. Additionally, the data revealed that the conference served as a type of differentiated PD as the teachers selected sessions based on personal interests and relevance. Although the beginning teachers were eager to attend future conferences, their desire to present at future conferences was mitigated by their limited years of teaching experience. The participants’ positive experiences suggest that tea cher educators should encourage new science teachers to attend science teacher conferences, induction specialists should leverage existing conference structures, and policymakers and school division personnel should provide support for beginning teachers to attend conferences. Maximizing the potential of science teacher conferences could provide an efficient form of ongoing, differentiated PD for beginning teachers. |
Semi-quantitative Characterization of Secondary Science Teachers’ Use of Three-Dimensional Instruction
| Pengarang | : | - |
| Nama Majalah/Jurnal | : | Journal of Science Teacher Education |
| Volume / Edisi | : | 30 (No. 3-4) |
| Halaman | : | 379–408 |
| Abstrak | : | This quasi-experimental study evaluated middle- and high-school science teachers’ implementation of three-dimensional (3D) instruction as defined by the Next Generation Science Standards.Teachersparticipated in a long-term professional development (PD) program designed to increase their use of inquiry-based science instruction. We describe our semi-quantitative adaptation of the Educators Evaluating the Quality of Instructional Products: Science rubric version 2 (SQ-EQuIP) to facilitate the longitudinal evaluation of teacher practices with 3D instruction. SQ-EQuIP evaluations revealed that after two years, 80% of PD teachers implemen ted lessons where students were explicitly and coherently engaged in 3D learning, compared with 22% of comparison teachers. Further, in several cases lesson materials that should support student engagement in 3D learning were not implemented with fidelity. This discrepancy implies that PD developers must use the EQuIP not only to assess lesson or unit plans as intended by its creators, but to also evaluate the implementation of these materials from students’ perspective. The small sample size restricts claims of significance. However, observed trends between tea cher groups indicate long-established best practices designed to increase teacher use of inquiry-based practices may also positively impact teacher use of 3D instructional practices. |