Robust Statistics

In lieu of an abstract, here is the entry\u27s first paragraph: Robust statistics are procedures that maintain nominal Type I error rates and statistical power in the presence of violations of the assumptions that underpin parametric inferential statistics. Since George Box coined the term in 1953, research on robust statistics has centered on the assumption of normality, although the violation of other parametric assumptions (e.g., homogeneity of variance) has their own implications for the accuracy of parametric procedures. This entry looks at the importance of robust statistics in educational and social science research and explains the robustness argument. It then describes robust descriptive statistics, their inferential extensions, and two common resampling procedures that are robust alternatives to classic parametric methods

The cyclic sieving phenomenon: a survey

The cyclic sieving phenomenon was defined by Reiner, Stanton, and White in a 2004 paper. Let X be a finite set, C be a finite cyclic group acting on X, and f(q) be a polynomial in q with nonnegative integer coefficients. Then the triple (X,C,f(q)) exhibits the cyclic sieving phenomenon if, for all g in C, we have # X^g = f(w) where # denotes cardinality, X^g is the fixed point set of g, and w is a root of unity chosen to have the same order as g. It might seem improbable that substituting a root of unity into a polynomial with integer coefficients would have an enumerative meaning. But many instances of the cyclic sieving phenomenon have now been found. Furthermore, the proofs that this phenomenon hold often involve interesting and sometimes deep results from representation theory. We will survey the current literature on cyclic sieving, providing the necessary background about representations, Coxeter groups, and other algebraic aspects as needed.Comment: 48 pages, 3 figures, the sedcond version contains numerous changes suggested by colleagues and the referee. To appear in the London Mathematical Society Lecture Note Series. The third version has a few smaller change

Defining the outcomes of community care: the perspectives of older people with dementia and their carers

There is growing recognition of the need for outcome measures which reflect the aims of services for people with dementia. The development and application of existing outcome measures has often marginalised people with dementia. ‘Experts’ and carers have been viewed as primary sources when identifying relevant outcomes or domains of quality of life, and proxy respondents have often been responsible for rating outcomes on the resulting measures. This paper reports a small consultation with people with dementia and their carers to identify the desired outcomes of community care. While there was considerable overlap in the outcomes identified by people with dementia and their carers, a number of limitations of relying solely on carers as proxy respondents were identified. A key outcome, which has been relatively neglected in previous work, was maximising a sense of autonomy. A range of outcomes related to the ways in which services are delivered were also identified. Future evaluative studies should encompass both quality-of-life outcomes and service-process outcomes (the impacts of the ways in which services are delivered) in addition to other outcome measures relevant to the aims and objectives of the service

Perceived orientation, spatial layout and the geometry of pictures

The purpose is to discuss the role of geometry in determining the perception of spatial layout and perceived orientation in pictures viewed at an angle. This discussion derives from Cutting's (1988) suggestion, based on his analysis of some of the author's data (Goldstein, 1987), that the changes in perceived orientation that occur when pictures are viewed at an angle can be explained in terms of geometrically produced changes in the picture's virtual space

PROTECTING SHELL EGGS BETWEEN PACKING PLANT AND SUPERMARKET

Studies the importance of factors affecting eggshell damage such as type of pack, age of laying hen and season of year.Agribusiness,

Measured Steady-State Performance of Water Vapor Jets for Use in Space Vehicle Attitude Control Systems

Measurements have been made in a vacuum environment to determine the steady-state performance of several nozzles having thrusts up to 1000 dynes for use in space vehicle attitude control systems. Water vapor was used as a propellant. The results indicate that the trend of the variation of specific impulse and thrust coefficient with expansion ratio is predicted by calculations based on one-dimensional isentropic flow. The level of these quantities, however, is dependent upon the nozzle diameter. The specific impulse, for example, varies from about 30 percent to 80 percent of the theoretical value as the nozzle thrust is increased from about 10 to 1000 dynes