nils-herrmann/clean_scirepeval huggingface dataset:
Teaching Statistics: A Bag of Tricks

Students in the sciences, economics, psychology, social sciences, and medicine take introductory statistics. Statistics is increasingly offered at the high school level as well. However, statistics can be notoriously difficult to teach as it is seen by many students as difficult and boring, if not irrelevant to their subject of choice. To help dispel these misconceptions, Gelman and Nolan have put together this fascinating and thought-provoking book. Based on years of teaching experience the book provides a wealth of demonstrations, examples and projects that involve active student participation. Part I of the book presents a large selection of activities for introductory statistics courses and combines chapters such as, 'First week of class', with exercises to break the ice and get students talking; then 'Descriptive statistics' , collecting and displaying data; then follows the traditional topics - linear regression, data collection, probability and inference. Part II gives tips on what does and what doesn't work in class: how to set up effective demonstrations and examples, how to encourage students to participate in class and work effectively in group projects. A sample course plan is provided. Part III presents material for more advanced courses on topics such as decision theory, Bayesian statistics and sampling.
You Can Load a Die, But You Can't Bias a Coin

Dice can be loaded—that is, one can easily alter a die so that the probabilities of landing on the six sides are dramatically unequal. However, it is not possible to bias a coin flip—that is, one cannot, for example, weight a coin so that it is substantially more likely to land “heads” than “tails” when flipped and caught in the hand in the usual manner. Coin tosses can be biased only if the coin is allowed to bounce or be spun rather than simply flipped in the air. We describe a student activity with dice and coins that gives empirical evidence to support this property, and we use this activity when we teach design of experiments and hypothesis testing in our introductory statistics courses. We explain this phenomenon by summarizing a physical argument made in earlier literature.
Voting, Fairness, and Political Representation

W e want our political system to represent the voters and treat them fairly. At the simplest procedural level, this means givinga vote to all citizens and deciding elections based on majority or plurality rule. In practice, however, we are not all represented equally by the government, and as longas there is political disagreement there willbe some dissatisfaction. It would be appealing to have a mathematical definition of the amount that citizens are "represented." Unfortunately, different measures of representation can clash with each other, as we discuss with examples from national elections in the United States.
Statistical Computing and Graphics Let's Practice What We Preach: Turning Tables into Graphs

Statisticians recommend graphical displays but often use tables to present their own research results. Could graphs do better? We study the question by going through the tables in a recent issue of the Journal of the American Statistical Association . We show how it is possible to improve the presentationsusing graphs that actually take up less space than the original tables. We nd a particularly effective tool to be multiple repeated line plots, with comparisons of interest connected by lines and separate comparisons isolated on different plots.
How Much does a Vote Count? Voting Power, Coalitions, and the Electoral College

In an election, the probability that a single voter is decisive is affected by the electoral system, that is, the rule for aggregating votes into a single outcome. Under the assumption that all votes are equally likely (i.e., random voting), we prove that the average probability of a vote being decisive is maximized under a popular-vote (or simple majority) rule and is lower under any coalition system, such as the U.S. Electoral College system, no matter how complicated. Forming a coalition increases the decisive vote probability for the voters within a coalition, but the aggregate e®ect of coalitions is to decrease the average decisiveness of the population of voters. We then review results on voting power in an electoral college system. Under the random voting assumption, it is well known that the voters with the highest probability of decisiveness are those in large states. However, we show using empirical estimates of the closeness of historical U.S. Presidential elections that voters in small states have been advantaged because the random voting model overestimates the frequencies of close elections in the larger states. Finally, we estimate the average probability of decisiveness for all U.S. Presidential elections from 1960 to 2000 under three possible electoral systems: popular vote, electoral vote, and winner-take-all within Congressional districts. We find that the average probability of decisiveness is about the same under all three systems.
Models, assumptions and model checking in ecological regressions

Ecological regression is based on assumptions that are untestable from aggregate data. However, these assumptions seem more questionable in some applications than in others. There has been some research on implicit models of individual data underlying aggregate ecological regression modelling. We discuss ways in which these implicit models can be checked from aggregate data. We also explore the differences in applications of ecological regressions in two examples: estimating the effect of radon on lung cancer in the United States and estimating voting patterns for different ethnic groups in New York City.
Poststratification Without Population Level Information on the Poststratifying Variable With Application to Political Polling

We investigate the construction of more precise estimates of a collection of population means using information about a related variable in the context of repeated sample surveys. The method is illustrated using poll results concerning presidential approval rating (our related variable is political party identification). We use poststratification to construct these improved estimates, but because we do not have population level information on the poststratifying variable, we construct a model for the manner in which the poststratifier develops over time. In this manner, we obtain more precise estimates without making possibly untenable assumptions about the dynamics of our variable of interest, the presidential approval rating.
Bayesian Inference with Probability Matrix Decomposition Models

Probability Matrix Decomposition models may be used to model observed binary associations between two sets of elements. More specifically, to explain observed associations between two elements, it is assumed that B latent Bernoulli variables are realized for each element and that these variables are subsequently mapped into an observed data point according to a prespecified deterministic rule. In this paper, we present a fully Bayesian analysis for the PMD model making use of the Gibbs sampler. This approach is shown to yield three distinct advantages: (a) in addition to posterior mean estimates it yields (1 — α)% posterior intervals for the parameters, (b) it allows for an investigation of hypothesized indeterminacies in the model's parameters and for the visualization of the best possible reduction of the posterior distribution in a low-dimensional space, and (c) it allows for a broad range of goodness-of-fit tests, making use of the technique of posterior predictive checks. To illustrate the approach, we applied the PMD model to opinions of respondents of different countries concerning the possibility of contracting AIDS in a specific situation.
A method for quantifying artefacts in mapping methods illustrated by application to headbanging.

Maps of disease rates (and other quantities) often must contend with variance associated with variable population sizes and low incidence within spatial units. These characteristics can lead to substantial statistical noise that can mask underlying spatial variation. As Gelman and Price illustrated, most conventional mapping methods fail to address this problem, and in fact can introduce statistical artefacts; mapped quantities can show spatial patterns even when there are no spatial patterns in the underlying parameter of interest. Kafadar evaluated the performance of the headbanging algorithm for spatial smoothing (Tukey and Tukey, Hansen) for eliminating small scale variation and preserving edge structure. Here we perform a simulation study to investigate the artefacts of maps smoothed by unweighted and weighted headbanging. We find substantial artefacts that depend on the spatial structure of the statistical variation (for example, the spatial pattern of sample sizes) and on the details of the spatial distribution of geographic units. The methods used here could readily be adapted to study other spatial smoothers; we choose headbanging because (i) it is an important method used in practice, and (ii) its heavily computational nature is naturally studied using simulation (in contrast to the analytical methods used by Gelman and Price).
Type S error rates for classical and Bayesian single and multiple comparison procedures

SummaryIn classical statistics, the significance of comparisons (e. g., θ1–θ2) is calibrated using the Type 1 error rate, relying on the assuption that the true difference is zero, which makes no sense in many applications. We set up a more relevant framework in which a true comparison can be positive or negative, and, based on the data, you can state “θ1 > θ2 with confidence,”“θ2 > θ1 with confidence,” or “no claim with confidence.” We focus on the Type S (for sign) error, which occurs when you claim “θ1 > θ2 with confidence” when θ2 > θ1 (or vice-versa). We compute the Type S error rates for classical and Bayesian confidence statements and find that classical Type S error rates can be extremely high (up to 50%). Bayesian confidence statements are conservative in the sense that claims based on 95% posterior intervals have Type S error rates between 0 and 2.5%. For multiple comparison situations, the conclusions are similar.
Simulation Modeling for Cost Estimation

What do a group of statisticians have to contribute to the subject of good costing practices, and in particular the United States Postal Service (USPS) costing methodology? Credible cost estimates require the collection of high quality information as component inputs. Deciding what information to collect lies in the province of the economist, but exactly how to collect that information, when to collect it, how much of it to collect, as well as a significant part of the overall evaluation of the quality of the information itself, lies in the province of the
Should we take measurements at an intermediate design point?

It is well known that, for estimating a linear treatment effect with constant variance, the optimal design divides the units equally between the two extremes of the design space. If the dose-response relation may be nonlinear, however, intermediate measurements may be useful in order to estimate the effects of partial treatments. We consider the decision of whether to gather data at an intermediate design point: do the gains from learning about nonlinearity outweigh the loss in efficiency in estimating the linear effect? Under reasonable assumptions about nonlinearity, we find that, unless sample size is very large, the design with no interior measurements is best, because with moderate total sample sizes, any nonlinearity in the dose-response will be difficult to detect. We discuss in the context of a simplified version of the problem that motivated this work-a study of pest-control treatments intended to reduce asthma symptoms in children.
Bayesian probabilistic extensions of a deterministic classification model

SummaryThis paper extends deterministic models for Boolean regression within a Bayesian framework. For a given binary criterion variable Y and a set of k binary predictor variables X1,...,Xk, a Boolean regression model is a conjunctive (or disjunctive) logical combination consisting of a subset S of the X variables, which predicts Y. Formally, Boolean regression models include a specification of a k-dimensional binary indicator vector (θ1,...,θk) with θj = 1 iff Xj∈S. In a probabilistic extension, a parameter π is added which represents the probability of the predicted value ŷi and the observed value yi differing (for any observation i). Within a Bayesian framework, a posterior distribution of the parameters (θl,...,θk, π) is looked for. The advantages of such a Bayesian approach include a proper account of the uncertainty in the model estimates and various possibilities for model checking (using posterior predictive checks). We illustrate this method with an example using real data.
Analysis of Large-Scale Social Surveys 1

Large-scale social surveys are an important source of information for a wide range of topics. In analyzing such surveys, it is important to be aware of the complexity of the sampling design and the data adjustments that are used by survey organizations, including weighting to adjust for diierences between sample and population and imputation to ll in missing responses. For estimating population means and proportions, the analyst should calculate weighted averages, using survey weights. In regression analysis, it is best to include, among the predictors, the variables that are used in the design and the weighting. Hierarchical models can be used to obtain inferences for small subpopulations. In general, analyzing survey data as if they had been obtained through simple random sampling can result in biased point estimates and underestimated standard errors. These calculations can often be adjusted reasonably well by using design eeects reported in the survey documentation or in previous analyses. For more involved analysis, it is advisable to use statistical packages that are speciically designed to correctly handle complex survey data.
Evaluating Standards for Protecting Aquatic Life in Washington ' s Surface Water Quality Standards Temperature Criteria Draft Discussion Paper and Literature Summary

This paper is admirable in that it presents a general framework that allows the user to focus on the pharmacokinetic modeling rather than on the computational and statistical details of estimation. The authors set up a reasonable-seeming model and obtain a good t to the pain-relief data with plausible parameter values, while accounting for the kind of complications that typically arise in clinical trials. We would like to focus on the following features of this work: (1) analysis of the missing data (dropouts), (2) the pharmacokinetic model, (3) checking the t of the model, (4) modeling and display of individual variation, and (5) extrapolation to other dosing strategies. Analysis of the dropouts Although the analysis of dropouts appears to be a major complication in the analysis (and is certainly a problem of general interest in this eld; see, e.g., Ten Have et al., 1997), it is, we believe, a minor concern in this particular example. As noted in the article, the pain relief level just preceding dropout was 0 (no pain relief) in nearly all the cases. Considering the design of the study (with dropouts allowed to switch to an eeective analgesic), it seems reasonable to impute pain relief scores of 0 for the responses that were unobserved because of dropout. Our Figure 1 shows the aggregate results for the completed dataset (including both observed and imputed responses). In addition to the imputation, we have altered Figure 1 of the article by separating the \dose = 0" respondents into three groups corresponding to the three diierent experiments. We believe that our Figure 1, with imputations included, gives We thank the National Science Foundation for grant DMS-9404305 and Young Investigator award DMS-9457824; the Research Council of Katholieke Universiteit Leuven for fellowship F/96/9; and Lewis Sheiner for providing the data and model predictions for the ketorolac analysis.
Diagnostic checks for discrete data regression models using posterior predictive simulations

Model checking with discrete data regressions can be difficult because the usual methods such as residual plots have complicated reference distributions that depend on the parameters in the model. Posterior predictive checks have been proposed as a Bayesian way to average the results of goodness‐of‐fit tests in the presence of uncertainty in estimation of the parameters. We try this approach using a variety of discrepancy variables for generalized linear models fitted to a historical data set on behavioural learning. We then discuss the general applicability of our findings in the context of a recent applied example on which we have worked. We find that the following discrepancy variables work well, in the sense of being easy to interpret and sensitive to important model failures: structured displays of the entire data set, general discrepancy variables based on plots of binned or smoothed residuals versus predictors and specific discrepancy variables created on the basis of the particular concerns arising in an application. Plots of binned residuals are especially easy to use because their predictive distributions under the model are sufficiently simple that model checks can often be made implicitly. The following discrepancy variables did not work well: scatterplots of latent residuals defined from an underlying continuous model and quantile–quantile plots of these residuals.
Bridges between Deterministic and Probabilistic Models for Binary Data

For the analysis of binary data, various deterministic models have been proposed, which are generally simpler to fit and easier to understand than probabilistic models. We claim that corresponding to any deterministic model is an implicit stochastic model in which the deterministic model fits imperfectly, with errors occurring at random. In the context of binary data, we consider two error models in the first model, all predictions are equally likely to be in error; in the second model, the probability of error depends on the model prediction. We show how to fit these models using a stochastic modification of deterministic optimization schemes. The advantages of fitting the stochastic models explicitly (rather than implicitly, by simply fitting a deterministic model and accepting the occurrence of errors) include quantification of uncertainty in the deterministic model's parameter estimates, better estimation of the true model error rate, and the ability to check the fit of the model nontrivially. We illustrate with a simple theoretical example of item response data and with empirical examples from archaeology and the psychology of choice.
All maps of parameter estimates are misleading.

Maps are frequently used to display spatial distributions of parameters of interest, such as cancer rates or average pollutant concentrations by county. It is well known that plotting observed rates can have serious drawbacks when sample sizes vary by area, since very high (and low) observed rates are found disproportionately in poorly-sampled areas. Unfortunately, adjusting the observed rates to account for the effects of small-sample noise can introduce an opposite effect, in which the highest adjusted rates tend to be found disproportionately in well-sampled areas. In either case, the maps can be difficult to interpret because the display of spatial variation in the underlying parameters of interest is confounded with spatial variation in sample sizes. As a result, spatial patterns occur in adjusted rates even if there is no spatial structure in the underlying parameters of interest, and adjusted rates tend to look too uniform in areas with little data. We introduce two models (normal and Poisson) in which parameters of interest have no spatial patterns, and demonstrate the existence of spatial artefacts in inference from these models. We also discuss spatial models and the extent to which they are subject to the same artefacts. We present examples from Bayesian modelling, but, as we explain, the artefacts occur generally.
Optimal design for a study of butadiene toxicokinetics in humans.

The derivation of the optimal design for an upcoming toxicokinetic study of butadiene in humans is presented. The specific goal of the planned study is to obtain a precise estimate of butadiene metabolic clearance for each study subject, together with a good characterization of its population variance. We used a two-compartment toxicokinetic model, imbedded in a hierarchical population model of variability, in conjunction with a preliminary set of butadiene kinetic data in humans, as a basis for design optimization. Optimization was performed using Monte Carlo simulations. Candidate designs differed in the number and timing of exhaled air samples to be collected. Simulations indicated that only 10 air samples should be necessary to obtain a coefficient of variation of 15% for the estimated clearance rate, if the timing of those samples is properly chosen. Optimal sampling times were found to closely bracket the end of exposure. This efficient design will allow the recruitment of more subjects in the study, in particular to match prescribed levels of accuracy in the estimate of the population variance of the butadiene metabolic rate constant. The techniques presented here have general applicability to the design of human and animal toxicology studies.
Corrigendum: Characterizing a joint probability distribution by conditionals

With regard to the theorem in the paper, the second part is, in general, false, and the proof, given in Section 4.2, is in error. Dr K. W. Ng and Professor A. P. Dawid have pointed out the following simple counter-example for two binary random variables x,, x2: P(0, 0) = 0.3, P(0, 1) = 0.2, P(1, 0) = 0.2 and P(1, 1) = 0.3. This joint density is uniquely specified by P(xl 1x2) and P(xl), in contradiction to the second part of the stated theorem.
Analysis of Local Decisions Using Hierarchical Modeling, Applied to Home Radon Measurement and Remediation

This paper examines the decision problems associated with measurement and remediation of environmental hazards, using the example of indoor radon (a carcinogen) as a case study. Innovative methods developed here include (1) the use of results from a previous hierarchical statistical analysis to obtain probability distributions with local variation in both predictions and uncertainties, (2) graphical methods to display the aggregate consequences of decisions by individuals and (3) alternative parameterizations for individual variation in the dollar value of a given reduction in risk. We perform cost-benefit analyses for a variety of decision strategies, as a function of home types and geography, so that measurement and remediation can be recommended where it is most effective. We also briefly discuss the sensitivity of policy recommendations and outcomes to uncertainty in inputs. For the home radon example, we estimate that if the recommended decision rule were applied to all houses in the United States, it would be possible to save the same number of lives as with the current official recommendations for about 40% less cost.
Some Issues in Monitoring Convergence of Iterative Simulations

In this paper, we discuss some recent results and open questions concerning monitoring convergence of iterative simulations. We begin by discussing the various approaches to convergence assessment proposed in the literature, grouping the methods according to their underlying principles. We then discuss how MCMC simulations can be constructed so that convergence monitoring is simpliied. Finally, we discuss some new convergence assessment ideas that are the focus of current work.