Previous work on statistical power has discussed mainly single-level designs or 2-level balanced designs with random effects. Although balanced experiments are common, in practice balance cannot always be achieved. Work on class size is one example of unbalanced designs. This study provides methods for power analysis in 2-level unbalanced designs…

Social characteristics that differ by place of residence are consequential for health. To study implications of this among older adults in rural vs. urban China, this study employs data from the Beijing municipality, a region that has witnessed growth and gaps in development. Life and active life expectancy is assessed using a multistate life…

Background: This study was originally prepared for the African Inter-Ministerial Conference on Literacy (September 2007) with the objective of analysing the costs of successful adult literacy programmes run both by government ministries, as well as international and national non-governmental organisations. Objectives: This study aims to increase…

In evaluating the relationship between two measures across different groups (i.e., in evaluating "differential validity") it is necessary to examine differences in correlation coefficients and in regression lines. Ordinary least squares (OLS) regression is the standard method for fitting lines to data, but its criterion for optimal fit…

An application of the contingent valuation method (CVM) for estimating the economic value of a regional public library service is described, and some of the key methodological issues surrounding CVM and other stated preference techniques are discussed with reference to library use and funding contexts. Given the range of valuations that can result…

Recent missing data studies have argued in favor of an "inclusive analytic strategy" that incorporates auxiliary variables into the estimation routine, and Graham (2003) outlined methods for incorporating auxiliary variables into structural equation analyses. In practice, the auxiliary variables often have missing values, so it is reasonable to…

As you have read in the previous "After the Bell" column, water harvesting is a process of diverting and collecting rainwater. One of the main reasons to harvest rainwater is to reduce the demand on local sources of water. The objective of the harvesting procedure is to gather water from a weather event that is usually lost as runoff and either…

A complex technology-based problem in visualization and computation for students in calculus is presented. Strategies are shown for its solution and the opportunities for students to put together sequences of concepts and skills to build for success are highlighted. The problem itself involves placing an object under water in order to actually see…

The mathematics for finding and plotting the locations of stars and constellations are available in many books on astronomy, but the steps involve mystifying and fragmented equations, calculations, and terminology. This paper will introduce an entirely new unified and cohesive technique that is easy to understand by mathematicians, and simple…

We solve two problems that arise when constructing picture frames using only a table saw. First, to cut a cove running the length of a board (given the width of the cove and the angle the cove makes with the face of the board) we calculate the height of the blade and the angle the board should be turned as it is passed over the blade. Second, to…

The effectiveness of problem solving as a learning tool is often diminished because students typically use only an algorithmic approach to get to the answer. We discuss a way of encouraging students to reflect on the solution to their problem by requiring them--after they have arrived at their solution--to draw solution maps. A solution map…

It has been proposed that causal power (defined as the probability with which a candidate cause would produce an effect in the absence of any other background causes) can be intuitively computed from cause-effect covariation information. Estimation of power is assumed to require a special type of counterfactual probe question, worded to remove…

The chemistry of dissolved inorganic carbon in seawater is reviewed and used to predict the potential effect of rising levels of carbon dioxide in the atmosphere. In agreement with more detailed treatments, we find that calcium carbonate (aragonite) may become unsaturated in cold surface seawater by the year 2100 C.E., resulting in the destruction…

The problems of hypothesis testing and interval estimation of the squared multiple correlation coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to…

In educational tests, subscores are often generated from a portion of the items in a larger test. Guidelines based on mean squared error are proposed to indicate whether subscores are worth reporting. Alternatives considered are direct reports of subscores, estimates of subscores based on total score, combined estimates based on subscores and…