In this paper we develop a framework to study the dependence structure of scrambled {(t,m,s)}-nets. It relies on values denoted by {C_{b}({\boldsymbol{k}};P_{n})}, which are related to how many distinct pairs of points from {P_{n}} lie in the same elementary {{\boldsymbol{k}}}-interval in base b. These values quantify the equidistribution properties of {P_{n}} in a more informative way than the parameter t. They also play a key role in determining if a scrambled set {\widetilde{P}_{n}} is negative lower orthant dependent (NLOD). Indeed, this property holds if and only if {C_{b}({\boldsymbol{k}};P_{n})\leq 1} for all {{\boldsymbol{k}}\in\mathbb{N}^{s}}, which in turn implies that a scrambled digital {(t,m,s)}-net in base b is NLOD if and only if {t=0}. Through numerical examples we demonstrate that these {C_{b}({\boldsymbol{k}};P_{n})} values are a powerful tool to compare the quality of different {(t,m,s)}-nets, and to enhance our understanding of how scrambling can improve the quality of deterministic point sets.
In this paper we develop a framework to study the dependence structure of scrambled point sets, with a focus on scrambled digital (t, m, s)-nets. Our main result shows that, if for all (k1, . . . , ks) ∈ N s the total number of distinct pairs from a given point set that come from the same elementary (k1, . . . , ks)-interval is less than what is expected with random sampling, then after scrambling the point set will be negative lower/upper orthant dependent (NLOD/NUOD). Using this we obtain that a scrambled digital (t, m, s)-net is NLOD/NUOD if and only if t = 0 and that the first n points of a scrambled (0, s)-sequence are always NLOD/NUOD. Finally, we explore the possibility of using our framework to differentiate the quality of point sets that have the same value for the parameter t but show obvious differences.
Integrating educational assessment tools such as the Motivated Strategies for Learning Questionnaire (MSLQ) into university classrooms can help students and faculty gain insight into areas of strength and challenge for students. The present study adapted and integrated the MSLQ into a set of first-year communication courses for Faculty of Arts students at the University of Waterloo. This adaptation allowed us to better situate the scale within the writing and communication course context. Through exploratory and confirmatory analysis, a shortened questionnaire (MSLQ-AF) with 6 subscales (motivation, academic self-confidence, performance anxiety, critical thinking, planning for optimal learning, and peer learning) was created. MSLQ-AF proved to have stable factor structure, adequate and stable internal consistency, and construct validity (correlation with grades), when assessed across four samples spanning four university terms. We discuss the role of this new scale in helping students transition into university.
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