We present empirical data showing that the relative frequency with which a verb normally appears in a syntactic construction predicts young children's ability to remember and repeat sentences instantiating that construction. Children aged 2;10-5;8 years were asked to repeat grammatical and ungrammatical sentential complement sentences (e.g., "I…

The authors argue that a robust version of Cohen's effect size constructed by replacing population means with 20% trimmed means and the population standard deviation with the square root of a 20% Winsorized variance is a better measure of population separation than is Cohen's effect size. The authors investigated coverage probability for…

This paper is a personal exploration of where the ideas of "distribution" that we are trying to develop in students come from and are leading to, how they fit together, and where they are important and why. We need to have such considerations in the back of our minds when designing learning experiences. The notion of "distribution" as a lens…

In Bayesian statistics, the choice of the prior distribution is often controversial. Different rules for selecting priors have been suggested in the literature, which, sometimes, produce priors that are difficult for the students to understand intuitively. In this article, we use a simple heuristic to illustrate to the students the rather…

Research Services calculates enrollment projections on an annual basis. These projections are presented each year at the district's Pupil Population Estimating Conference. For this year's projections, two years of trend data (2006-07 and 2007-08) were used to project student enrollment for 2008-09. Projections are provided by individual grade…

Meehl's taxometric method was developed to distinguish categorical and continuous constructs. However, taxometric output can be difficult to interpret because expected results for realistic data conditions and differing procedural implementations have not been derived analytically or studied through rigorous simulations. By applying bootstrap…

The range of response options has been shown to influence the answers given in self-report instruments that measure behaviors ranging from television viewing to sexual partners. The current research extends this line of inquiry to 36 quantitative items extracted from a biographical inventory used in personnel selection. A total of 92…

Direct provision of public services can alter the balance of resources across income groups. We focus on the issues arising when taking account of the impact of publicly provided education services across the income distribution. We combine OECD information on spending per student in particular levels of the education system with micro data from…

This paper presents facts and figures of the international higher education. Facts reveal that the UK sells more brainpower per capita than anywhere else in the world. The UK has 1% of the world's population but undertakes 5% of the world's scientific research and produces 14% of the world's most highly cited papers (Universities UK 2010). More…

The logic and uses of test equating are discussed, including three methods of test equating. The focus is on the conceptual underpinnings of each test equating method, rather than on the mathematics of the procedures. Additional consideration is given to the assumptions of each method and its respective strengths and weaknesses. A commonly…

Sampling error refers to variability that is unique to the sample. If the sample is the entire population, then there is no sampling error. A related point is that sampling error is a function of sample size, as a hypothetical example illustrates. As the sample statistics more and more closely approximate the population parameters, the sampling…

A new and unified approach to test equating is described that is based on log-linear models for smoothing score distributions and on the kernel method of nonparametric density estimation. The new method contains both linear and standard equipercentile methods as special cases and can handle several important equating data collection designs. An…

Central limit theorem (CLT) is considered an important topic in statistics, because it serves as the basis for subsequent learning in other crucial concepts such as hypothesis testing and power analysis. There is an increasing popularity in using dynamic computer software for illustrating CLT. Graphical displays do not necessarily clear up…

This paper explains the underlying assumptions of the sampling distribution and its role in significance testing. To compute statistical significance, estimates of population parameters must be obtained so that only one sampling distribution is defined. A sampling distribution is the underlying distribution of a statistic. Sampling distributions…

Previous research examining the effects of reducing the number of score groups used in the matching criterion of the Mantel-Haenszel procedure, when screening for differential item functioning, has produced ambiguous results. The goal of this study was to resolve the ambiguity by examining the problem with a simulated data set. The main results…