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Why are women not promoted as quickly or as high as men? Why are women paid less than their male counterparts for similar roles and responsibilities? Why is bridging the gender gap so difficult? For instance, in European Union countries in 2020 women’s gross hourly earnings were on average 13% below those of men, and 2018 US Census Bureau data says women of all races earned, on average, just 82 cents for every dollar earned by men of all races. Gender disparities, though, are much more severe and pervasive, as stated in the latest UN Women report (bit.ly/3Kc7knX): “Gender inequalities and discrimination filter through every issue, whether a new pandemic or longstanding conflicts, deep-seated disparities in income or a lack of political voice. Women and girls confront additional risks and obstacles simply because they are women and girls.” Gender equality, in all aspects of women’s and men’s lives, is a democratic value and a prominent sustainable development goal in the United Nations (UN) Agenda 2030. Gendered statistical reasoning and gender statistics play a crucial role in informing policies and the efforts towards achieving equality, as well as in allocation of resources, and the potential to effectively contribute towards the protection and advancement of the rights of all women and girls. In this article we illustrate the importance of improving the measurement, monitoring, and prediction of gender gaps by exploring the potential of Bayesian networks.

When observational studies are used to establish the causal effects of treatments, the estimated effect is affected by treatment selection bias. The inverse propensity score weight (IPSW) is often used to deal with such bias. However, IPSW requires strong assumptions whose misspecifications and strategies to correct the misspecifications were rarely studied. We present a bootstrap bias correction of IPSW (BC-IPSW) to improve the performance of propensity score in dealing with treatment selection bias in the presence of failure to the ignorability and overlap assumptions. The approach was motivated by a real observational study to explore the potential of anticoagulant treatment for reducing mortality in patients with end-stage renal disease. The benefit of the treatment to enhance survival was demonstrated; the suggested BC-IPSW method indicated a statistically significant reduction in mortality for patients receiving the treatment. Using extensive simulations, we show that BC-IPSW substantially reduced the bias due to the misspecification of the ignorability and overlap assumptions. Further, we showed that IPSW is still useful to account for the lack of treatment randomization, but its advantages are stringently linked to the satisfaction of ignorability, indicating that the existence of relevant though unmeasured or unused covariates can worsen the selection bias.

A resampling technique for probability-proportional-to size sampling designs is proposed. It is essentially based on a special form of variable probability, without replacement sampling applied directly to the sample data, yet according to the pseudo-population approach. From a theoretical point of view, it is asymptotically correct: as both the sample size and the population size increase, under mild regularity conditions the proposed resampling design tends to coincide with the original sampling design under which sample data were collected. From a computational point of view, the proposed methodology is easy to be implemented and efficient, because it neither requires the actual construction of the pseudo-population nor any form of randomization to ensure integer weights and sizes. Empirical evidence based on a simulation study 1 indicates that the proposed resampling technique outperforms its two main competitors for confidence interval construction of various population parameters including quantiles.

The FENStatS Covid19 WR is a free spontaneous association of statistical experts from 14 European countries, united by concerns related to the current pan-infodemic and statistical challenges revealed by the Covid-19 havoc. The present short paper tracks when, how and why the WG has formed, illustrates our mission, aims and scope, describes the steps taken so far and outlines perspectives for future work.

The pursuance of gender equality has embraced a longstanding sta- tistical engendering process, to reflect women’s and men’s lives. In pursuing the 2030 Sustainability Development Goals (SDGs), the availability of high- quality gender-sensitive data has generated the current informative outburst. In the process, gender-sensitive data collection has departed from a mere dis- aggregation between men and women towards an unprecedented multifaceted informational spectrum. Methods for full exploiting gender-sensitive statis- tics, both standard and big data, though, faces some levels of criticality. The traditional descriptive linear combinations of a collection of simple indica- tors yields contradictory order results, whereas inference has so far privileged latent modelling only, holding several constraints. A novel statistical perspec- tive stems from recent developments of Multivariate Latent Markov Models (MLMMs), suitable to express a latent characteristic both in time and space. In addition to introducing covariates, on any measurement scales, not only in the structural model bul also the measurement one, MLMMs are innovative in so that they can handle a vast mass of data from very different sources. Thus they lead the way to an extensive investigation of the gender gap, account- ing for apparent contradictions in rankings and hence highlighting different paths, or “transition”, toward a more equitable society.

The number of samples is a major issue when estimating the mean herbage mass of grazed paddocks. The aim of this study was to assess the number of samples required for accurate visual estimation of mean herbage mass in relation to the herbage mass heterogeneity and size of paddocks. Data were collected across scales of space and time (273 sampling events) from paddocks on Campos grasslands in Uruguay, using the visual estimation technique. The mean herbage mass of the paddocks ranged from 270 to 6350 kg of dry matter (DM) per hectare with coefficient of variation (CV) of 0.13 to 1.26. Twenty-four events representing four levels of herbage mass hetero- geneity (CV = 0.3, 0.5, 0.7 and 1.0) × three levels of paddock size (small, 5–13 ha; medium, 41–67 ha; large, 100–140 ha) were chosen (two replicates per group), and analyzed for the probability that the estimation error exceeded 10% of the mean (10% error probability) using the bootstrap technique. The number of samples required for controlling the 10% error probability below 0.1 increased gradually from 50 to 150 per paddock as the CV increased from 0.3 to 0.7, then sharply to 350 until the CV increased to 1.0, with no effect of paddock size. Taking account of the distribution of CV (< 0.7 in nearly 80% of the events), we propose a general recommendation to take a minimum of 150 samples per paddock for accurate estimation of mean herbage mass in Campos grasslands irrespective of the size of paddocks.

Resampling methods are widely studied and increasingly employed in applied research and practice. When dealing with complex sampling designs, common resampling techniques require adjusting noninteger sampling weights in order to construct the so called “pseudopopulation” in order to perform the actual resampling. The practice of rounding, however, has been empirically shown to be harmful under general designs. In this paper, we present asymptotic results concerning, in particular, the practice of rounding resampling weights to the nearest integer, an approach that is commonly adopted by virtue of its reduced computational burden, as opposed to randomization‐based alternatives. We prove that such approach leads to nonconsistent estimation of the distribution function of the survey variable; we provide empirical evidence of the practical consequences of the nonconsistency when the point estimation of the variance of complex estimators is of interest.

Sampling a rare and clustered trait in a finite population is challenging: traditional sampling designs usually require a large sample size in order to obtain reasonably accurate estimates, resulting in a considerable investment of resources infront of the detection of a small number of cases. A notable example is the case of WHO’s tubercoulosis (TB) prevalence surveys, crucial for countries that bear a high TB burden, the prevalence of cases being still less than 1%. In the latest WHO guidelines, spatial patterns are not explicitly accounted for, with the risk of missing a large number of cases; moreover, cost and logistic constraints can pose further problems. After reviewing the methodology in use by WHO, the use of adaptive and sequential approaches is discussed as natural alternatives to overcome the limitations of the current practice. A small simulation study is presented to highlight possible advantages and limitations of these alternatives, and an integrated approach, combining both adaptive and sequential features in a single sampling strategy is discussed as a promising methodological perspective.

This paper concerns a Multivariate Latent Markov Model recently introduced in the literature for estimating latent traits in social sciences. Based on its ability of simultaneously dealing with longitudinal and spacial data, the model is proposed when the latent response variable is expected to have a time and space dynamic of its own, as an innovative alternative to popular methodologies such as the construction of composite indicators and structural equation modeling. The potentials of the proposed model and the added value with respect to the traditional weighted composition methodology, are illustrated via an empirical Gender Statistics exercise, focused on gender gap as the latent status to be measured and based on supranational o cial statistics for 30 European countries in the period 2010–2015.

In this paper, a class of resampling techniques for finite populations under $\pi $ps sampling design is introduced. The basic idea on which they rest is a two-step procedure consisting in: (i) constructing a “pseudo-population” on the basis of sample data; (ii) drawing a sample from the predicted population according to an appropriate resampling design. From a logical point of view, this approach is essentially based on the plug-in principle by Efron, at the “sampling design level”. Theoretical justifications based on large sample theory are provided. New approaches to construct pseudo populations based on various forms of calibrations are proposed. Finally, a simulation study is performed.

A collection of six novel bootstrap algorithms, applied to probability-proportional-to-size samples, is explored for variance estimation, confidence interval and p-value production. Developed according to bootstrap fundamentals such as the mimicking principle and the plug-in rule, these algorithms make use of an empirical bootstrap population informed by sampled units each with assigned weight. Starting from the natural choice of Horvitz–Thompson (HT)-type weights, improvements based on calibration to known population features are fostered. Focusing on the population total as the parameter to be estimated and on the distribution of the HT estimator as the target of bootstrap estimation, simulation results are presented with the twofold objective of checking practical implementation and of investigating the statistical properties of the bootstrap estimates supplied by the algorithms explored.

Recent gender literature shows a growing demand of sound statistical methods for analysing gender gaps, for capturing their complexity and for exploring the pattern of relationships among a collection of observable variables selected in order to disentangle the latent trait of gender equity. In this paper we consider parametric Hierarchical Marginal Models applying to binary and categorical data, as a promising statistical tool for gender studies. We explore the potential of Chain Graphical Models, by focusing on a special smooth sub-class of models known as Graphical Models of type II as recently developed (Nicolussi in Marginal parameterizations for conditional independence models and graphical models for categorical data, 2013) , i.e. an advanced methodology for untangling and highlighting any dependence/independence pattern between gender and a set of covariates of mixed nature, either categorical, ordinal or quantitative. With respect to traditional methodologies for treating categorical variables, such as Logistic Regression and Chi-Squared test for contingency table, the proposed model lead to a full multivariate analysis, allowing for isolating the effect of each dependent variable from all other response variables. At the same time, the resulting graph offers an immediate visual idea of the association pattern in the entire set of study variables. The empirical performance of the method is tested by using data from a recent survey about sexual harassment issues inside university, granted by the Equal Opportunities Committee of the University of Milano-Bicocca (Italy).

Summary The very expression Gender Statistics calls for a double interpretation. It accounts for the popular mix-up of statistical methodology with its typical products such as indexes, tables and graphs. At the same time it implies a broader and forward-looking perspective, which is inspired by the increasing demand of gender sensitive statistical information coming from society, official agencies, economy. Gender statistics stands as a proper independent field of statistics with its own objectives and a variety of applications in social, human and life science. Concurrently an emerging necessity of appropriate equipment of methods and dissemination tools is noticeable. The paper tracks the roots and the historical development of gender statistics, reviews critically the existing indexes and practice and outlines methodological needs and research prospects. Resume L'expression “Gender Statistics/Statistiques de Genres” suscite une double interpretation. Elle recouvre un melange de methodes statistiques courantes, dont les elements les plus representatifs sont des constructions d'indices, de tables et de graphes. En meme temps, la “Statistique de Genres” requiert une vision plus large, inspiree par la demande croissante, par les entreprises et les agences officielles, d'informations statistiques “sensibles” du point de vue des genres. La “Statistique de Genres”emerge ainsi comme un sujet independant, possedant ses propres objectifs et ses propres applications dans le domaine social et celui des sciences humaines en general. On assiste ainsi a l'apparition de methodes et d'outils de dissemination propres, dont cet article examine les origines et le developpement historique.

The effect of the practice of rounding non-integer weights in bootstrapping complex samples from finite populations is investigated by means of an extended simulation study. The extent to which rounding can interfere with basic Bootstrap principles as well as with the formal properties of the final Bootstrap estimates are evaluated. Indications and recommendations on application of this practice are discussed.

Writing papers is an essential part of the research process. Researchers have a professional obligation of disseminating their results, making them available for others to use to enhance common scientific knowledge. Besides the fun of sharing their own ideas and views, to publish is essential in order to actually have a scientific career. Although scientific writing certainly has its own conventions and standards, I suspect there is no a unique true recipe making the trick. As a matter of fact I do not have any. However my quite long time in the academic arena has given me a pretty clear idea about how I do and do not like things done. In this paper I will be giving my personal view and rules, in the hope that sharing my own experience would do some good to others as it did for me.

The problem of bootstrapping the estimator’s variance under a probability proportional to size design is examined. Focusing on the Horvitz-Thompson estimator, three πPS-bootstrap algorithms are introduced with the purpose of both simplifying available procedures and of improving efficiency. Results from a simulation study using both natural and artificial data are presented in order to empirically investigate the properties of the provided bootstrap variance estimators.

Resampling methods are often invoked in risk modelling when the stability of estimators of model parameters has to be assessed. The accuracy of variance estimates is crucial since the operational risk management affects strategies, decisions and policies. However, auxiliary variables and the complexity of the sampling design are seldom taken into proper account in variance estimation. In this paper bootstrap algorithms for finite population sampling are proposed in presence of an auxiliary variable and of complex samples. Results from a simulation study exploring the empirical performance of some bootstrap algorithms are presented.

Multiple Frame Survey has been originally proposed, according to an optimality approach, in order to persecute survey cost savings, especially in the case of a complete list available but expensive to sample. In the modern sampling practice it is frequent the case where a total and up-to-date list of units, to be used as sampling frame, is not available or it may not be built unless expensive or unfeasible screening of the target population. Instead, a set of lists singularly partial, usually overlapping, with union offering an adequate coverage of the target population, can be available. Thus the collection of the partial lists can be used as Multiple Frame. Literature about Multiple Frame estimation theory mainly concentrates over the Dual Frame case and it is only rarely concerned with the important practical issue of the variance estimation. By using a multiplicity approach a Single Frame estimator is proposed. The new estimator naturally applies to any number of frame and it is very simple so that its variance is given exactly and easily estimated.

Background\ud \ud An unprecedented number of nationwide tuberculosis (TB) prevalence surveys will be implemented between 2010 and 2015, to better estimate the burden of disease caused by TB and assess whether global targets for TB control set for 2015 are achieved. It is crucial that results are analysed using best-practice methods.\ud \ud \ud Objective\ud \ud To provide new theoretical and practical guidance on best-practice methods for the analysis of TB prevalence surveys, including analyses at the individual as well as cluster level and correction for biases arising from missing data.\ud \ud \ud Analytic methods\ud \ud TB prevalence surveys have a cluster sample survey design; typically 50-100 clusters are selected, with 400-1000 eligible individuals in each cluster. The strategy recommended by the World Health Organization (WHO) for diagnosing pulmonary TB in a nationwide survey is symptom and chest X-ray screening, followed by smear microscopy and culture examinations for those with an abnormal X-ray and/or TB symptoms. Three possible methods of analysis are described and explained. Method 1 is restricted to participants, and individuals with missing data on smear and/or culture results are excluded. Method 2 includes all eligible individuals irrespective of participation, through multiple missing value imputation. Method 3 is restricted to participants, with multiple missing value imputation for individuals with missing smear and/or culture results, and inverse probability weighting to represent all eligible individuals. The results for each method are then compared and illustrated using data from the 2007 national TB prevalence survey in the Philippines. Simulation studies are used to investigate the performance of each method.\ud \ud \ud Key findings\ud \ud A cluster-level analysis, and Methods 1 and 2, gave similar prevalence estimates (660 per 100,000 aged ≥ 10 years old), with a higher estimate using Method 3 (680 per 100,000). Simulation studies for each of 4 plausible scenarios show that Method 3 performs best, with Method 1 systematically underestimating TB prevalence by around 10%.\ud \ud \ud Conclusion\ud \ud Both cluster-level and individual-level analyses should be conducted, and individual-level analyses should be conducted both with and without multiple missing value imputation. Method 3 is the safest approach to correct the bias introduced by missing data and provides the single best estimate of TB prevalence at the population level.