Representative embodiments of a method for grouping participants in an activity include the steps of: (i) defining a grouping policy; (ii) storing, in a database, participant records that include a participant identifier, a characteristic associated with the participant, and/or an identifier for a participant's handheld device; (iii) defining groupings based on the policy and characteristics of the participants relating to the policy and to the activity; and (iv) communicating the groupings to the handheld devices to establish the groups.
In various embodiments, online discussions in connection with an eductional resource are improved by analyzing annotations made by students assigned to a discussion group to identify high-quality annotations likely to generate responses and stimulate discussion threads and by making the identified annotations visibile to students not assigned to the discussion group.
Researchers who generate data often optimize efficiency and robustness by choosing stratified over simple random sampling designs. Yet, all theories of inference proposed to justify matching methods are based on simple random sampling. This is all the more troubling because, although these theories require exact matching, most matching applications resort to some form of ex post stratification (on a propensity score, distance metric, or the covariates) to find approximate matches, thus nullifying the statistical properties these theories are designed to ensure. Fortunately, the type of sampling used in a theory of inference is an axiom, rather than an assumption vulnerable to being proven wrong, and so we can replace simple with stratified sampling, so long as we can show, as we do here, that the implications of the theory are coherent and remain true. Properties of estimators based on this theory are much easier to understand and can be satisfied without the unattractive properties of existing theories, such as assumptions hidden in data analyses rather than stated up front, asymptotics, unfamiliar estimators, and complex variance calculations. Our theory of inference makes it possible for researchers to treat matching as a simple form of preprocessing to reduce model dependence, after which all the familiar inferential techniques and uncertainty calculations can be applied. This theory also allows binary, multicategory, and continuous treatment variables from the outset and straightforward extensions for imperfect treatment assignment and different versions of treatments.