Computing the real solutions of Fleishman's equations for simulating non-normal data

Fleishman's power method is frequently used to simulate non-normal data with a desired skewness and kurtosis. Fleishman's method requires solving a system of nonlinear equations to find the third-order polynomial weights that transform a standard normal variable into a non-normal variable with desired moments. Most users of the power method seem unaware that Fleishman's equations have multiple solutions for typical combinations of skewness and kurtosis. Furthermore, researchers lack a simple method for exploring the multiple solutions of Fleishman's equations, so most applications only consider a single solution. In this paper, we propose novel methods for finding all real-valued solutions of Fleishman's equations. Additionally, we characterize the solutions in terms of differences in higher order moments. Our theoretical analysis of the power method reveals that there typically exists two solutions of Fleishman's equations that have noteworthy differences in higher order moments. Using simulated examples, we demonstrate that these differences can have remarkable effects on the shape of the non-normal distribution, as well as the sampling distributions of statistics calculated from the data. Some considerations for choosing a solution are discussed, and some recommendations for improved reporting standards are provided.     

Epistemological Development and Judgments and Reasoning About Teaching Methods

Children's, adolescents’, and adults’ (N = 96 7–8, 10–11, and 13–14-year-olds and university students) epistemological development and its relation to judgments and reasoning about teaching methods was examined. The domain (scientific or moral), nature of the topic (controversial or noncontroversial), and teaching method (direct instruction by lectures versus class discussions) were systematically varied. Epistemological development was assessed in the aesthetics, values, and physical truth domains. All participants took the domain, nature of the topic, and teaching method into consideration in ways that showed age-related variations. Epistemological development in the value domain alone was predictive of preferences for class discussions and a critical perspective on teacher-centered direct instruction, even when age was controlled in the analysis.     

Differences in creativity among homogeneous groups of students using the Torrance Test of creative Thinking and the Welsh Figure Preference Test.

Three intact groups of students in Grade 5 (n = 79) were grouped by ability on the Metropolitan Achievement Test and given the Torrance and Welsh tests used to assess creativity. Middle ability children scored higher on fluency, flexibility, and origence than the other two groups.     

Sex and developmental differences by complexity of functions of occupational aspirations of school children across ten years

The present longitudinal study examined the complexity of workers' functions for 65 children's occupational aspirations during a 10-yr. span beginning when the children were 7 yr. old and in Grade 2. Every two years through the senior year in high school, the children were interviewed, for a total of six interviews. Sex and developmental differences in occupational aspirations were examined with respect to the focus on Data, People, or Things. Girls (n=31) selected occupational aspirations requiring greater complexity in People functions throughout the study. From G;rades 2 to 8 boys chose occupations with greater complexity of Things and girls chose occupations with greater complexity of Data. Developmentally, all children chose increasingly more complex Data occupations from Grades 2 to 12. Occupational aspirations in high school showed a decrease in the complexity of workers' functions involving People and Things. These observations would be expected from social cognitive theory and the 1981 career development theory of Gottfredson.     

Children's,adolescents’, and adults’ judgments and reasoning about different methods of teaching values

This study investigated children's, adolescents’, and young adults’ judgments and reasoning about teaching two values (racial equality and patriotism) using methods that varied in provision for children's rational autonomy, active involvement, and choice. Ninety-six participants (7–8-, 10–11-, and 13–14-year-olds, and college students) evaluated four methods of teaching values in schools (Inculcation, Direct Teaching, Behavioral, and Discussion) for agents of two ages (3rd and 8th grade students), and in two contexts (student- vs. teacher-implemented methods). Older participants were more likely than younger participants (7–8-year-olds) to distinguish value education methods that stimulated children's rational thought processes and active involvement, and to coordinate factors such as the age of agents and the context of implementation in their judgments and reasoning.