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The relative bipolarisation literature features examples of indices which depend on the median of the distribution, including the renowned Foster–Wolfson index. This study shows that the use of the median in the design and computation of relative bipolarisation indices is both unnecessary and problematic. It is unnecessary because we can rely on existing well-behaved, median-independent indices. It is problematic because, as the study shows, median-dependent indices violate the basic transfer axioms of bipolarisation (defining spread and clustering properties), except when the median is unaffected by the transfers. The convenience of discarding the median from index computations is further illustrated with a numerical example in which median-independent indices rank distributions according to the basic transfer axioms while median-dependent indices do not.

Purpose – The goal of this chapter is to explore whether variation in the distribution of union members across the income distribution affects the role of unions in redistributive politics.

Design/methodology/approach – The conceptual part of the study provides a theoretical motivation for disaggregating organized labor by income. The empirical part uses European Social Survey data for 15 West European countries 2006–2008 to describe the composition of union membership by income across countries and to explore, in a preliminary fashion, the implications of where union members are located in the income distribution for social protection and redistribution.

Findings – In most countries, workers with incomes above the median are better organized than workers below the median and the income of the median union member exceeds the income of the median voter. The political implications of the overrepresentation of relatively well-off workers depend on the mechanism of preference aggregation within unions and the influence of unions in the policymaking process. While leaving a thorough examination of these issues for future research, we present descriptive regression results suggesting that the membership composition of unions by income is related to income inequality and redistribution but not social insurance.

Originality/value of paper – This is the first comparative study to map the distribution of union members across the income distribution and to examine the implications of compositional variation by income for redistributive politics.

Are the statements which we make true?…and, if they are true, how do we know that they are true? To address these two questions let us first note that this book is interested in two types of truth: mathematical truth and scientific truth. Mathematical truth applies to statements within a mathematical theory. A statement is true within a theory either if it is one of the axioms of the theory or if it can be deduced from the axioms of the theory (see Chapter 3). Scientific truth applies to statements about the real world. A statement about the real world is true if it corresponds to what happens in the real world. A theory about the real world is true if all of its statements correspond to what happens in the real world. Given a mathematical theory which is consistent (i.e. true within itself) or a specific statement which is true within the theory, we can enquire whether or not the theory or statement is true in relation to reality.

European Union (EU) as a whole has made modest short-term progress toward sustainable development goals (SDG). Only in one goal (ensuring healthy lives and promotion of well-being) out of 17, the progress was substantial. The most problematic goals, which show movements away from sustainable development objectives, are goals that are focused on building resilient infrastructure, promotion of inclusive, sustainable industrialization, fostering innovation, and the goal that takes urgent action to combat climate changes. The analysis between old and new EU members revealed that median new EU member has made bigger progress in the last five years. For 11 SDGs, the average score is lover for median new EU member compared to median old EU member. However, the last available level of the indicator is in general still more favorable for median old EU member compared to median new EU member.

The authors’ conclusions are based on mathematical derivations that are supported by computer simulations and three worked examples in applications of economics and finance. Finally, the authors provide a link to a computer program so that researchers can perform the analyses easily.

Based on a parameter estimation goal, the present work is concerned with determining the minimum sample size researchers should collect so their sample medians can be trusted as good estimates of corresponding population medians. The authors derive two solutions, using a normal approximation and an exact method.

The exact method provides more accurate answers than the normal approximation method. The authors show that the minimum sample size necessary for estimating the median using the exact method is substantially smaller than that using the normal approximation method. Therefore, researchers can use the exact method to enjoy a sample size savings.

In this paper, the a priori procedure is extended for estimating the population median under the skew normal settings. The mathematical derivation and with computer simulations of the exact method by using sample median to estimate the population median is new and a link to a free and user-friendly computer program is provided so researchers can make their own calculations.

This chapter explores differences in fringe, distant, and remote rural public library assets for asset-based community development (ABCD) and the relationships of those assets to geographic regions, governance structures, and demographics.

The author analyzes 2013 data from the Institute of Museum and Library Services (IMLS) and U.S. Department of Agriculture using nonparametric statistics and data mining random forest supervised classification algorithms.

There are statistically significant differences between fringe, distant, and remote library assets. Unexpectedly, median per capita outlets (along with service hours and staff) increase as distances from urban areas increase. The Southeast region ranks high in unemployment and poverty and low in median household income, which aligns with the Southeast’s low median per capita library expenditures, staff, hours, inventory, and programs. However, the Southeast’s relatively high percentage of rural libraries with at least one staff member with a Master of Library and Information Science promises future asset growth in those libraries. State and federal contributions to Alaska libraries propelled the remote Far West to the number one ranking in median per capita staff, inventory, and programs.

This study is based on IMLS library system-wide data and does not include rural library branches operated by nonrural central libraries.

State and federal contributions to rural libraries increase economic, cultural, and social capital creation in the most remote communities. On a per capita basis, economic capital from state and federal agencies assists small, remote rural libraries in providing infrastructure and services that are more closely aligned with libraries in more populated areas and increases library assets available for ABCD initiatives in otherwise underserved communities.

Even the smallest rural library can contribute to ABCD initiatives by connecting their communities to outside resources and creating new economic, cultural, and social assets.

Analyzing rural public library assets within their geographic, political, and demographic contexts highlights their potential contributions to ABCD initiatives.

This paper places what has happened to income inequality in rich countries over recent decades alongside trends in median and low incomes in real terms, taken as incomplete but valuable indicators of the evolution of living standards for “ordinary working families” and the poor. The findings demonstrate first just how varied country experiences have been, with some much more successful than others in generating rising real incomes around the middle and toward the bottom of the distribution. This variation is seen to be only modestly related to the extent to which income inequality rose, which itself is more varied across the rich countries than is often appreciated. The extent to which economic growth is transmitted to the middle and lower parts of the distribution is seen to depend on a range of factors of which inequality is only one. Sources of real income growth around the middle have also varied across countries, though transfers are consistently key toward the bottom. The diversity of rich country experiences should serve as an important corrective to a now-common “grand narrative” about inequality and stagnation based on the experience of the USA.

The purpose of this paper is to estimate that price appreciation for single‐family sales data for the complete population of deed recordings in one metro area using median comparisons is statistically more accurate in capturing local fluctuations than the repeat sale sample approach published by the Federal Housing Finance Agency. The median comparison method becomes the optimal method of choice due to its simplicity and ease in interpretation. The electronic access to court house records means that the complete population of data should be used to extract a community price trend in lieu of samples.

Local deed recordings for residential housing were compared to repeat sale results from the Federal Finance Housing Admin. The goal is to measure housing price appreciation.

Appreciation measured by local deed recordings captures house price variance better than repeat sales taken from mortgage applications.

A median to median comparison with local sales prices should be used in lieu of a national statistic using mortgage applications.

This project provides a more accurate method to assess price appreciation. Repeat sales are not appropriate especially in smaller metro areas.

Every individual and financial institution needs to know the value of its housing asset. The method shown is the best available.

The results have huge implications for the academic community where many regression equations are based on repeat sales.

In an effort to develop an audit quality (AQ) framework specific to the US audit market, the Public Company Accounting Oversight Board (PCAOB) recently issued a concept release proposing 28 audit quality indicators (AQIs) along three dimensions: audit professionals, audit process and audit results. Using AQIs initially proposed by the PCAOB, as well as AQIs suggested by prior literature, the authors solicit perceptions from junior-level (senior and staff) auditors to investigate the current state of practice along many of the AQIs relating to audit professionals and audit process.

In the study, 78 junior-level auditors responded to the survey.

An analysis of the responses suggests auditors engage in activities and audit firms promote conditions that at times improve, and at other times, reduce audit quality. The authors find that individual auditors’ perceptions differ across experience level, gender and audit firm size for certain AQIs.

The study is useful to the PCAOB because it provides insights to help assess the value of potential AQIs in differentiating AQ. The study is also useful to other regulators because it describes audit staff and seniors’ perceptions of apparent firm and auditor compliance with accounting and auditing standards. Practitioners should find this information useful in helping to identify possible root causes of audit deficiencies, a challenge put forth to firms by the PCAOB.

This study provides academia with evidence on AQ from practicing auditors, which informs existing and future research along. The study complements existing work by showing how individual auditor characteristics (experience and gender) at the junior levels may impact AQ in practice