Bias in linear model power and sample size calculation due to estimating noncentrality

Data analysts frequently calculate power and sample size for a planned study using mean and variance estimates from an initial trial. Hence power,or the sample size needed to achieve a fixed power, varies randomly. Such claculations can be very inaccurate in the General Linear Univeriate Model (GLUM). Biased noncentrality estimators and censored power calculations create inaccuracy. Censoring occurs if only certain outcomes of an initial trial lead to a power calculation. For example, a confirmatory study may be planned (and a sample size estimated) only following a significant resulte in the initial trial.

Computing accurate point estimates or confidence bounds of GLUM noncentrality, power, or sample size in the presence of censoring involves truncated noncentral F distributions. We recommed confidence bounds, whether or not censoring occurs. A power analysis of data from humans exposed to carbon monoxide demonstrates the substantial impact on samle size that may occur. The results highlight potential; biases and should aid study planning and interpretation.     

Participation in Voluntary Youth‐Serving Associations and Early Adult Voting Behavior*

Objective. We investigate adolescent membership in voluntary associations and whether participation in these activities influences voting behavior during early adulthood. Methods. Weighted logistic regression models predicting membership in voluntary associations and voting behavior were estimated using data from the National Educational Longitudinal Study of 1988–1994 (NELS). Results. Our findings suggest that membership in voluntary associations varies by race and socioeconomic status (SES). In addition, membership in organizations historically rooted in moral development and civic socialization positively predict voter‐registration status and whether or not young adults participated in the first national election that they were eligible to vote in, but this relationship is moderated by both race and SES. Conclusions. Our findings suggest that a large proportion of U.S. teenagers still participate in community‐based programs, many of which foster later civic participation, but that all youth do not equally benefit from participation.     

Creating places,relationships and education for refugee children in camps: Lessons learnt from the ‘The School of Peace’ educational model

This paper describes a unique model for building an afternoon school for refugee children sustained by volunteers and refugee teachers and based on humanistic intercultural values. The methodology is participatory including the whole school, from children to teachers to volunteers and managers. Central themes in the findings include a synergetic focus on creative placemaking, conflict negotiation and formal studies. This points to a theoretical connection between informal and formal studies. The findings teach us about the needs of refugee children. A methodological contribution is the use of arts-based methods to capture refugee children's lived experiences of school.     

Properties of doubly-truncated gamma variables

The truncated gamma distribution has been widely studied, primarily in life-testing and reliability settings. Most work has assumed an upper bound on the support of the random variable, i.e. the space of the distribution is (0,u). We consider a doubly-truncated gamma random variable restricted by both a lower (l) and upper (u) truncation point, both of which are considered known. We provide simple forms for the density, cumulative distribution function (CDF), moment generating function, cumulant generating function, characteristic function, and moments. We extend the results to describe the density, CDF, and moments of a doubly-truncated noncentral chi-square variable.     

School Context and the Effect of ESL Placement on Mexican‐Origin Adolescents' Achievement*

Objectives. Immigrant adolescents' academic achievement is crucial to our future economic stability, and Mexican‐origin linguistic minority youth in U.S. schools generally demonstrate lower levels of achievement. English as a Second Language (ESL) programs provide an institutional response to these students' needs, the effect of which may vary by the proportion of immigrant students in the school. Measures. Using propensity score matching and data from the Adolescent Health and Academic Achievement Study (AHAA) and the National Longitudinal Study of Adolescent Health (Add Health), we estimate the effect of ESL placement on Mexican‐origin achievement for first‐, second‐, and third‐generation adolescents separately in schools with many and few immigrant students. Results. The estimated effect of ESL placement varies by both immigrant concentration in the school and by students' generational status. Conclusions. We find that ESL enrollment may be protective for second‐generation Mexican‐origin adolescents in high immigrant concentration schools, and may prove detrimental for first‐generation adolescents in contexts with few other immigrant students.     

Determinants of the health and survival of the elderly: Suggestions from two different experiences — Italy and Israel

This study compares the health status and survival of the elderly in two countries, Italy and Israel. While both are developed Mediterranean countries, their degree of ageing, characteristic features of the elderly, health status and survival are different. The data are from two sample surveys and, for Israel, from a record linkage between survey and mortality data at five years remove. A preliminary analysis, using a multiple correspondence factorial analysis, highlighted a gradual change in living arrangements and socio-economic features as the population ages, which was only slightly associated with health conditions. In Israel, moreover, the Arab minority differs according to social conditions, living arrangements and health status. The determinants of health status and survival of the elderly in both countries were studied using as dependent variables; 1) self-perceived health status, 2) the frequency of medical examinations; 3) medical tests, for both countries and 4) (for Israel) deaths. Linear logistic models were constructed using, as explanatory variables, sex, age and living arrangements, a variable indicative of community level socio-economic and cultural conditions, two indicators describing individual socio-economic conditions and smoking habits. Thus it is possible to assess the impact of explanatory variables by comparing both subjective conditions and behaviour factors regarding medical care, with the unequivocal confirmation provided by death.     

Separability tests for high-dimensional,low-sample size multivariate repeated measures data

Longitudinal imaging studies have moved to the forefront of medical research due to their ability to characterize spatio-temporal features of biological structures across the lifespan. Valid inference in longitudinal imaging requires enough flexibility of the covariance model to allow reasonable fidelity to the true pattern. On the other hand, the existence of computable estimates demands a parsimonious parameterization of the covariance structure. Separable (Kronecker product) covariance models provide one such parameterization in which the spatial and temporal covariances are modeled separately. However, evaluating the validity of this parameterization in high dimensions remains a challenge. Here we provide a scientifically informed approach to assessing the adequacy of separable (Kronecker product) covariance models when the number of observations is large relative to the number of independent sampling units (sample size). We address both the general case, in which unstructured matrices are considered for each covariance model, and the structured case, which assumes a particular structure for each model. For the structured case, we focus on the situation where the within-subject correlation is believed to decrease exponentially in time and space as is common in longitudinal imaging studies. However, the provided framework equally applies to all covariance patterns used within the more general multivariate repeated measures context. Our approach provides useful guidance for high dimension, low-sample size data that preclude using standard likelihood-based tests. Longitudinal medical imaging data of caudate morphology in schizophrenia illustrate the approaches appeal.     

Probabilities for separating sets of order statistics

Consider a set of order statistics that arise from sorting samples from two different populations, each with their own, possibly different distribution functions. The probability that these order statistics fall in disjoint, ordered intervals and that of the smallest statistics, a certain number come from the first populations is given in terms of the two distribution functions. The result is applied to computing the joint probability of the number of rejections and the number of false rejections for the Benjamini-Hochberg false discovery rate procedure.     

Tenancy,Marriage, and the Boll Weevil Infestation, 1892–1930

In the early twentieth century, the cotton-growing regions of the U.S. South were dominated by families of tenant farmers. Tenant farming created opportunities and incentives for prospective tenants to marry at young ages. These opportunities and incentives especially affected African Americans, who had few alternatives to working as tenants. Using complete-count Census of Population data from 1900–1930 and Census of Agriculture data from 1889–1929, we find that increases in tenancy over time increased the prevalence of marriage among young African Americans. We then study how marriage was affected by one of the most notorious disruptions to southern agriculture at the turn of the century: the boll weevil infestation of 1892–1922. Using historical Department of Agriculture maps, we show that the boll weevil’s arrival reduced the share of farms worked by tenants as well as the share of African Americans who married at young ages. When the boll weevil infestation altered African Americans’ opportunities and incentives to marry, the share of African Americans who married young fell accordingly. Our results provide new evidence about the effect of economic and political institutions on demographic transformations.