A simple test for equally likely random responses in a sequence of bernoulli trials

A simple versatile combinatorial test is given for the null hypothesis that the two kinds of responses in a sequence of binary random variables are both equiprobable and randomly distributed. It is sensitive to a preponderance of either kind of response in either of two pre-selected halves of the positions of the sequence, e.g., the right half vs. the left, or the center vs. both ends. It combines the nice features of being, on the one hand, relatively assumption free and easy to apply and, on the other hand, sensitive to basic patterns underlying a poor fit of the empirical distribution to a theoretical model.     

Are Interactional Behaviors Exhibited When the Self-Reported Health Question is Asked Associated with Health Status?

The self-reported health question summarizes information about health status across several domains of health and is widely used to measure health because it predicts mortality well. We examine whether interactional behaviors produced by respondents and interviewers during the self-reported health question-answer sequence reflect complexities in the respondent’s health history. We observed more problematic interactional behaviors during question-answer sequences in which respondents reported worse health. Furthermore, these behaviors were more likely to occur when there were inconsistencies in the respondent’s health history, even after controlling for the respondent’s answer to the self-reported health question, cognitive ability, and sociodemographic characteristics. We also found that among respondents who reported “excellent” health, and to a lesser extent among those who reported their health was “very good,” problematic interactional behaviors were associated with health inconsistencies. Overall, we find evidence that the interactional behaviors exhibited during the question-answer sequence are associated with the respondent’s health status.     

Single machine scheduling with non-availability interval and optional job rejection

This paper studies the single machine scheduling problem with availability constraints and optional job rejection. We consider the non-resumable and resumable variants, and show that the problems remain ordinary NP-hard, even with the rejection possibility extension, by presenting pseudo-polynomial dynamic-programming (DP) solutions. We also present an enhanced running time implementation of the algorithm of Kellerer and Strusevich (Algorithmica 57(4):769–795, 2010) for the resumable scenario without job rejection. This solution is adapted to efficiently solve the machine non-availability problem with a floating interval and the problem of two competing agents on a single machine, with and without optional job rejection. Numerical experiments support the efficiency of our DP implementation.