Edgeworth expansion and the bootstrap for stratified sampling without replacement from a finite population

An Edgeworth expansion for a linear combination of stratum means in stratified sampling without replacement from a finite population is derived. The expansion is applied to a bootstrap proposed for this context to show that the bootstrap captures the second-order term of the expansion.     

Participatory video analysis in disability research

This article sets out critical framing as an analytical approach in participatory video by which people investigate and analyze a topic through arts-based engagement, storyboarding, and collaborative editing. Participatory video as an action research method in self-advocacy has been discussed elsewhere. Here, the author examines critical framing and the role of generative themes in participatory analysis by describing a case study in which adults with developmental disabilities explored the dimensions of sexual health through participatory video. The author proposes that critical framing provides a more nuanced approach to participatory analysis. Credibility and trustworthiness with data triangulation and overall findings are also described.     

Folded over non-orthogonal designs

In this article, we use the notion of minimal dependent sets (MDS) to introduce MDS-resolution and MDS-aberration as criteria for comparing non-orthogonal foldover designs, and discuss the ideas and their usefulness. We also develop a fast isomorphism check that uses a cyclic matrix defined on the design before it is folded over. By doing so, the speed of the check for comparing two isomorphic designs is increased relative to merely applying an isomorphism check to the foldover design. This relative difference becomes greater as the design size increases. Finally, we use the isomorphism check to obtain a catalog of minimum MDS-aberration designs for some useful n$n$ and k$k$ and discuss an algorithm for obtaining “good” larger designs.     

An isomorphism check for two-level fractional factorial designs

Two fractional factorial designs are isomorphic if one can be obtained from the other by reordering the treatment combinations, relabelling the factor levels and relabelling the factors. By defining a word-pattern matrix, we are able to create a new isomorphism check which is much faster than existing checks for certain situations. We combine this with a new, extremely fast, sufficient condition for non-isomorphism to avoid checking certain cases. We then create a faster search algorithm by combining the Bingham and Sitter [1999. Minimum aberration fractional factorial split-plot designs. Technometrics 41, 62–70] search algorithm, the isomorphism check algorithm of Clark and Dean [2001. Equivalence of fractional factorial designs. Statist. Sinica 11, 537–547] with our proposed isomorphism check. The algorithm is used to extend the known set of existing non-isomorphic 128-run two-level regular designs with resolution ?4$?4$ to situations with 12, 13, 14, 15 and 16 factors, 256- and 512-run designs with resolution ?5$?5$ and ?17$?17$ factors and 1024-run even designs with resolution ?6$?6$ and ?18$?18$ factors.     

Designing fractional factorial split-plot experiments with few whole-plot factors

Summary.  When it is impractical to perform the experimental runs of a fractional factorial design in a completely random order, restrictions on the randomization can be imposed. The resulting design is said to have a split-plot, or nested, error structure. Similarly to fractional factorials, fractional factorial split-plot designs can be ranked by using the aberration criterion. Techniques that generate the required designs systematically presuppose unreplicated settings of the whole-plot factors. We use a cheese-making experiment to demonstrate the practical relevance of designs with replicated settings of these factors. We create such designs by splitting the whole plots according to one or more subplot effects. We develop a systematic method to generate the required designs and we use the method to create a table of designs that is likely to be useful in practice.     

Imputation for missing values and corresponding variance estimation

Imputation is commonly used to compensate for missing data in surveys. We consider the general case where the responses on either the variable of interest y or the auxiliary variable x or both may be missing. We use ratio imputation for y when the associated x is observed and different imputations when x is not observed. We obtain design-consistent linearization and jackknife variance estimators under uniform response. We also report the results of a simulation study on the efficiencies of imputed estimators, and relative biases and efficiencies of associated variance estimators.     

Participatory video: toward a method,advocacy and voice (MAV) framework

Using the new conceptual framework of participatory visual media as method, advocacy and voice (MAV), the author explores an action research study using an exemplar in which advocates from the disability community created and distributed a series of videos about love and sexuality as a critical human rights issue in the disability community. The author proposes that conceptualizing these three areas as overlapping, rather than being mutually exclusive, offers an integrated way of understanding collaborative media practices that are community-based and action-oriented. Methodological, practical and ethical considerations are also addressed regarding collaborative-based research that involves public distribution.