A Mann–Whitney type effect measure of interaction for factorial designs

We propose a measure for interaction for factorial designs that is formulated in terms of a probability similar to the effect size of the Mann–Whitney test. It is shown how asymptotic confidence intervals can be obtained for the effect size and how a statistical test can be constructed. We further show how the test is related to the test proposed by Bhapkar and Gore [Sankhya A, 36:261–272 (1974)]. The results of a simulation study indicate that the test has good power properties and illustrate when the asymptotic approximations are adequate. The effect size is demonstrated on an example dataset.     

Extended scaled prediction variance optimality for modified central composite design

Robust parameter designs (RPDs) enable the experimenter to discover how to modify the design of the product to minimize the effect due to variation from noise sources. The aim of this article is to show how this amount of work can be reduced under modified central composite design (MCCD). We propose a measure of extended scaled prediction variance (ESPV) for evaluation of RPDs on MCCD. Using these measures, we show that we can check the error or bias associated with estimating the model parameters and suggest the values of α recommended for MCCS under minimum ESPV.     

Causal inferences on the effectiveness of complex social programs: Navigating assumptions,sources of complexity and evaluation design challenges

This paper explores avenues for navigating evaluation design challenges posed by complex social programs (CSPs) and their environments when conducting studies that call for generalizable, causal inferences on the intervention’s effectiveness. A definition is provided of a CSP drawing on examples from different fields, and an evaluation case is analyzed in depth to derive seven (7) major sources of complexity that typify CSPs, threatening assumptions of textbook-recommended experimental designs for performing impact evaluations. Theoretically-supported, alternative methodological strategies are discussed to navigate assumptions and counter the design challenges posed by the complex configurations and ecology of CSPs. Specific recommendations include: sequential refinement of the evaluation design through systems thinking, systems-informed logic modeling; and use of extended term, mixed methods (ETMM) approaches with exploratory and confirmatory phases of the evaluation. In the proposed approach, logic models are refined through direct induction and interactions with stakeholders. To better guide assumption evaluation, question-framing, and selection of appropriate methodological strategies, a multiphase evaluation design is recommended.     

Step-wise group screening with equal prior probabilities and no errors in observations

This paper introduces a screening procedure called step-wise group screening for isolating defective factors from a population consisting of defective (or important) and non-defective     

Performance of traditional f tests in repeated measures designs under covariance heterogeneity

This study investigates the performance of two traditional F tests, one for main effects and the other for interaction in repeated measures designs under several conditions of covariance heterogeneity. Overall, the test for interaction is more vulnerable than the one for main effects. Distortion in the level of significance is less serious for the case of equal group size.     

Confounding in mixed factorial experiments through isomorphisms

The derivation of a simpie mexhoa for confounding in mixed factorial experiments from an isomorphism of finite abelian groups is presented. The theoretical bases of confounding procedures that use modular arithmetic for such experiments are compared.     

Optimal design of complex experiments with qualitative factors of influence

A complex experiment with qualirarive factors influencing the outcome of the experiment can be seen as a general ANOVA setup. A design of such an experiment will be the assignment at which of the possible levels of the factors the actual experiment should be performed. In this paper optimal designs of such experiments will be characterized with respect to three different optimality criteria including the so called uniform optimality of a design. The possible applications of the main optimization result providing these characterizations can be used to more general experiments. The particular results on these generalizations will be indicated at the end of this paper.     

A Class of Sampling Two Units with Probability Proportional to Size

A class of sampling two units without replacement with inclusion probability proportional to size is proposed in this article. Many different well known probability proportional to size sampling designs are special cases from this class. The first and second inclusion probabilities of this class satisfy important properties and provide a non-negative variance estimator of the Horvitz and Thompson estimator for the population total. Suitable choice for the first and second inclusion probabilities from this class can be used to reduce the variance estimator of the Horvitz and Thompson estimator. Comparisons between different proportional to size sampling designs through real data and artificial examples are given. Examples show that the minimum variance of the Horvitz and Thompson estimator obtained from the proposed design is not attainable for the most cases at any of the well known designs.     

Step-wise group screening designs with errors in observations

The performance of step-wise group screening In terms of the expected number of runs and the expected number of incorrect decisions, Is considered. A method for obtaining optimal step-wise designs Is presented, for the cases in which the direction of each defective factor is assumed to be known a-priori and the observations are subject to error.     

Construction of minimum aberration blocked two-level regular factorial designs

ABSTRACT

In this article, we consider the construction of minimum aberration 2^{n ? k}: 2^p designs with respect to some existing combined wordlength patterns, where a 2^{n ? k}: 2^p design is a blocked two-level design with n treatment factors, 2^p blocks, and N = 2^q runs with q = n ? k. Two methods are proposed for two situations: n ? 2^{q ? p} ? 1 and n > N/2. These methods enable us to obtain some new minimum aberration 2^{n ? k}: 2^p designs from existing minimum aberration unblocked and blocked designs. Examples are included to illustrate the theory.