Bases such as 5 and 12 provide the same structural place value benefits as base 10. However, when numbers less than one are concerned, base 10 provides friendly decimals for the most common fractions of half, quarter, three-quarters. Base 5 is not user friendly at all in this regard. Base 12 would provide nice dozenimals(?) for the same…

The Bernoulli polynomials are generalized and some properties of the resulting generalizations are presented.

A general cubic equation ax[cubed] + bx[squared] + cx + d = 0 where a , b , c , d [is a member of R], a [not equal to] 0 has three roots with two possibilities--either all three roots are real or one root is real and the remaining two roots are imaginary. Dealing with the second possibility this paper attempts to give the geometrical locations of…

Reciprocal determinism is a central premise of Bandura's (1986) social cognitive theory. Studies of the relationship between self-beliefs and performance tend to draw on this or related theories and usually endorse the notion of reciprocal determinism at a substantive-theoretical level. However, attempts to model this postulated mutual influence…

For a number of conceptually and practically important reasons, reporting of effect size estimates, confidence intervals, and power in parameter estimation is increasingly being recognized as the preferred approach in social science research. Unfortunately, this practice has not yet been widely adopted in the rehabilitation or general counseling…

The rationale underlying factor analysis applies to continuous and categorical variables alike; however, the models and estimation methods for continuous (i.e., interval or ratio scale) data are not appropriate for item-level data that are categorical in nature. The authors provide a targeted review and synthesis of the item factor analysis (IFA)…

A novel assignment exercise is described, in which students use a dictionary to estimate the size of their vocabulary. This task was developed for an introductory statistics service course, although it can be modified for use in survey sampling courses. The exercise can be used to simultaneously assess a range of core statistics skills: sample…

Background/Hypothesis: The degree of attention directed to a stimulus and the presence of anisometric representations can alter the perception of the magnitude of a stimulus. We wanted to learn if normal right-handed subjects' estimates of distance traveled are influenced by the right-left direction or hemispace of movements. Methods: We had…

This article presents a way of computing a surface integral when the vector field of the integrand is a curl field. Presented in some advanced calculus textbooks such as [1], the technique, as the author experienced, is simple and applicable. The computation is based on Stokes' theorem in 3-space calculus, and thus provides not only a means to…

The problem of motorbike feathering has been analysed by writing the angular momentum theorem for non-inertial reference systems. The acceleration, for which the ideal line joining the median points of the axles of the two wheels makes an angle [theta] with the horizontal, has been calculated neglecting air friction and considering that the…

Previous work has suggested that eye movements may be necessary for accurate enumeration beyond the subitization range of about 4 items. This study determined the frequency of eye movements normally made during enumeration, their relationship to response times, and whether they are required for accurate performance. This was achieved by monitoring…

The composite direct product (CDP) model is a multiplicative model for multitrait-multimethod (MTMM) designs. It is extended to incomplete MTMM correlation matrices where some trait-method combinations are not available. Rules for omitting trait-method combinations without resulting in an indeterminate model are also suggested. Maximum likelihood…

A picture of a 95% confidence interval (CI) implicitly contains pictures of CIs of all other levels of confidence, and information about the "p"-value for testing a null hypothesis. This article discusses pictures, taken from interactive software, that suggest several ways to think about the level of confidence of a CI,…

A method for estimating criterion validity of scales with homogeneous components is outlined. It accomplishes point and interval estimation of interrelationship indices between composite scores and criterion variables and is useful for testing hypotheses about criterion validity of measurement instruments. The method can also be used with missing…

At the heart of the debate about the place of standard arithmetic algorithms is the practice of teaching subtraction through decomposition. One welcome feature of the national numeracy strategy in both its initial and current incarnations has been the introduction of a focus upon a variety of mental strategies supported by jottings. In this…