An approximation to the distribution of the sample variance

A simple three-moment approximation is introduced for the distribution of the sample variance. Comparisons are given with other approximations discussed by Tan and Wong (1977) and with an approximation developed very recently by Mudholkar and Trivedi (1981).     

Maximum Test versus Adaptive Tests for the Two-Sample Location Problem

For the non-parametric two-sample location problem, adaptive tests based on a selector statistic are compared with a maximum and a sum test, respectively. When the class of all continuous distributions is not restricted, the sum test is not a robust test, i.e. it does not have a relatively high power across the different possible distributions. However, according to our simulation results, the adaptive tests as well as the maximum test are robust. For a small sample size, the maximum test is preferable, whereas for a large sample size the comparison between the adaptive tests and the maximum test does not show a clear winner. Consequently, one may argue in favour of the maximum test since it is a useful test for all sample sizes. Furthermore, it does not need a selector and the specification of which test is to be performed for which values of the selector. When the family of possible distributions is restricted, the maximin efficiency robust test may be a further robust alternative. However, for the family of t distributions this test is not as powerful as the corresponding maximum test.     

Teaching History That Functions for Daily Living

As the development of active, democratic citizens has become, arguably, the primary purpose of social studies education, the model of instruction in citizenship education varies significantly. Although current models of citizenship education typically foster a sense of societal conformity and law-obeyance to the exclusion of social change, this article illustrates how elementary school students engaged in the critical examination of a pertinent social issue and guided the direction of a social action plan devised to overcome the injustice of bullying. The focus of this article is to illustrate how one fourth-grade teacher harnessed her students’ enthusiasm and interest in activism through an inquiry-based, interdisciplinary social action unit devised to solve elementary school bullying. A detailed, step-by-step narrative of the unit is described.     

A Multi-Method Evaluation of the Teen Pregnancy Hotline in Taiwan

The present study examines the outputs and qualities of the thirteen teen pregnancy service hotlines in Taiwan that were funded by the Children’s Bureau in 2004 and 2005. The evaluation was made through agency visits, focus groups, document reviews, call-in tests and the use of a management information system. The results show that the average number of calls was low, and one agency did not receive any calls during the time period examined. The quality of services varied, and the advice provided by the hotline staff was influenced by the value orientation of the agencies. Most callers were adult women, and the major services they received were information and emotional support. The service characteristics were heavily affected by the goals and routine tasks of the agencies as certain agencies applied their existing services to the program without assessing their fitness to the needs of the potential clients. Suggestions for service improvement are provided, including an islandwide hotline to be set up and operated by a single agency with high accountability. Implications for program monitoring and documentation, staff training and knowledge-sharing, and service advertisement and promotion are also discussed.     

Adaptive bootstrap tests and its competitors in the c-sample scale problem

This paper deals with a study of different types of tests for the two-sided c-sample scale problem. We consider the classical parametric test of Bartlett [M.S. Bartlett, Properties of sufficiency and statistical tests, Proc. R. Stat. Soc. Ser. A. 160 (1937), pp. 268–282] several nonparametric tests, especially the test of Fligner and Killeen [M.A. Fligner and T.J. Killeen, Distribution-free two-sample tests for scale, J. Amer. Statist. Assoc. 71 (1976), pp. 210–213], the test of Levene [H. Levene, Robust tests for equality of variances, in Contribution to Probability and Statistics, I. Olkin, ed., Stanford University Press, Palo Alto, 1960, pp. 278–292] and a robust version of it introduced by Brown and Forsythe [M.B. Brown and A.B. Forsythe, Robust tests for the equality of variances, J. Amer. Statist. Assoc. 69 (1974), pp. 364–367] as well as two adaptive tests proposed by Büning [H. Büning, Adaptive tests for the c-sample location problem – the case of two-sided alternatives, Comm. Statist.Theory Methods. 25 (1996), pp. 1569–1582] and Büning [H. Büning, An adaptive test for the two sample scale problem, Nr. 2003/10, Diskussionsbeiträge des Fachbereich Wirtschaftswissenschaft der Freien Universität Berlin, Volkswirtschaftliche Reihe, 2003]. which are based on the principle of Hogg [R.V. Hogg, Adaptive robust procedures. A partial review and some suggestions for future applications and theory, J. Amer. Statist. Assoc. 69 (1974), pp. 909–927]. For all the tests we use Bootstrap sampling strategies, too. We compare via Monte Carlo Methods all the tests by investigating level α and power β of the tests for distributions with different strength of tailweight and skewness and for various sample sizes. It turns out that the test of Fligner and Killeen in combination with the bootstrap is the best one among all tests considered.     

A Caution on Comparisons

Abstract

The family is the foundation of our society. By learning about family life in other countries, we learn about our own lives and we realize that we all belong to one big family—the family of mankind. … [Studying families of the world] could help us to get closer to people in distant countries and support the knowledge that “we are one.” — Liv Ullmann, UNICEF Goodwill Ambassador