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Statistical literacy, encompassing the interpretation and evaluation of statistical reports, is a skill developed in schools. However, the pedagogical approaches to statistical literacy skills have not been sufficiently investigated. This study investigated whether statistical literacy skills could be demonstrated through high school lessons. These lessons include a statistical literacy process, grounded in critical thinking principles, to facilitate students’ interpretation and evaluation of statistical reports. Additionally, a corresponding worksheet, aligning with this process, is included in the lessons to help students comprehend statistical reports. Seven 50-min lessons were conducted with 34 high school students, aged between 17 and 18 years, using this worksheet. Additionally, a statistical literacy skills test, designed to assess various statistical literacy skills within a short timeframe, was developed and administered at the beginning of the first lesson and at the end of the last lesson. The outcomes revealed that students were able to demonstrate some skills and effectively evaluate statistical reports. This study makes notable contributions by introducing a structured statistical literacy process and an associated skills assessment test. These tools can serve as valuable resources for students seeking to critically evaluate statistical reports and enable educators to gauge the extent of students’ acquisition. Supplementary materials for this article are available online.

For square contingency tables with ordered categories, Tomizawa, Biometrica J. 28 (1986), 387–393, considered the conditional point symmetry model. Kurakami et al ., J. Stat. Adv. Theory Appl. 17 (2017), 33–42, considered the another point symmetry and the reverse global symmetry model. The present paper proposes Kullback—Leibler information type measures to represent the degree of departure from each of the models. Also this paper shows a theorem that the measure for the another point symmetry model is equal to the sum of the measures for the reverse global symmetry model and for the conditional point symmetry model.

One of the first simulation-based introductory statistics curricula to be developed was the NSF-funded Change Agents for Teaching and Learning Statistics curriculum. True to its name, this curriculum is constantly undergoing change. This article describes the story of the curriculum as it has evolved at the University of Minnesota and offers insight into promising new future avenues for the curriculum to continue to affect radical, substantive change in the teaching and learning of statistics. Supplementary materials for this article are available online.

For a T -variate density function, the present paper defines the point-symmetry, quasi-point-symmetry of order k ( < T ), and the marginal point-symmetry of order k and gives the theorem that the density function is T -variate point-symmetric if and only if it is quasi-point-symmetric and marginal point-symmetric of order k . The theorem is illustrated for the multivariate normal density function.

Penalized spline estimator is one of the useful smoothing methods. To construct the estimator, having goodness of fit and smoothness, the smoothing parameter should be appropriately selected. The purpose of this paper is to select the smoothing parameter using the asymptotic property of the penalized splines. The new smoothing parameter selection method is established in the context of minimization asymptotic form of MISE of the penalized splines. The mathematical and the numerical properties of the proposed method are studied. First we organize the new method in univariate regression model. Next we extend to the additive models. A simulation study to confirm the efficiency of the proposed method is addressed.

Since its introduction by Hans Reichenbach, many philosophers have claimed to refute the idea – known as the common cause principle – that any surprising correlation between any two factors that do not directly influence one another is due to some common cause. For example, falsity of the principle is frequently inferred from falsifiability of Bell’s inequalities. The author demonstrates, however, that the situation is not so straightforward. There is more than one version of the principle formulated with the use of different variants of Reichenbach-inspired notions; their falsity still remains an open question. The book traces different formulations of the principle and provides proofs of a few pertinent theorems, settling the relevant questions in various probability spaces. In exploring mathematical and philosophical issues surrounding the principle, the book offers both philosophical insight and mathematical rigor.

Semiparametric regression models are very useful for time series analysis. They facilitate the detection of features resulting from external interventions. The complexity of semiparametric models poses new challenges for issues of nonparametric and parametric inference and model selection that frequently arise from time series data analysis. In this paper, we propose penalized least squares estimators which can simultaneously select significant variables and estimate unknown parameters. An innovative class of variable selection procedure is proposed to select significant variables and basis functions in a semiparametric model. The asymptotic normality of the resulting estimators is established. Information criteria for model selection are also proposed. We illustrate the effectiveness of the proposed procedures with numerical simulations.