Univariate Analysis and Normality Test Using SAS, Stata, and SPSS

Descriptive statistics provide important information about variables to be analyzed. Mean, median, and mode measure central tendency of a variable. Measures of dispersion include variance, standard deviation, range, and interquantile range (IQR). Researchers may draw a histogram, stem-and-leaf plot, or box plot to see how a variable is distributed. Statistical methods are based on various underlying assumptions. One common assumption is that a random variable is normally distributed. In many statistical analyses, normality is often conveniently assumed without any empirical evidence or test. But normality is critical in many statistical methods. When this assumption is violated, interpretation and inference may not be reliable or valid. The t-test and ANOVA (Analysis of Variance) compare group means, assuming a variable of interest follows a normal probability distribution. Otherwise, these methods do not make much sense. Figure 1 illustrates the standard normal probability distribution and a bimodal distribution. How can you compare means of these two random variables? There are two ways of testing normality (Table 1). Graphical methods visualize the distributions of random variables or differences between an empirical distribution and a theoretical distribution (e.g., the standard normal distribution). Numerical methods present summary statistics such as skewness and kurtosis, or conduct statistical tests of normality. Graphical methods are intuitive and easy to interpret, while numerical methods provide objective ways of examining normality

Ends of groups : a computational approach

We develop ways in which we can find the number of ends of automatic groups and groups with solvable word problem. In chapter 1, we provide an introduction to ends, splittings, and computa- tion in groups. We also remark that the `JSJ problem' for finitely presented groups is not solvable. In chapter 2, we prove some geometrical properties of Cayley graphs that underpin later computational results. In chapter 3, we study coboundaries (sets of edges which disconnect the Cayley graph), and show how Stallings' theorem gives us finite objects from which we can calculate splittings. In chapter 4, we draw the results of previous chapters together to prove that we can detect zero, two, or infinitely many ends in groups with `good' automatic structures. We also prove that given an automatic group or a group with solvable word problem, if the group splits over a finite subgroup, we can detect this, and explicitly calculate a finite subgroup over which it splits. In chapter 5 we give an exposition of Gerasimov's result that one- endedness can be detected in hyperbolic groups. In chapter 6, we give an exposition of Epstein's boundary construction for graphs. We prove that a testable condition for automatic groups implies that this boundary is uniformly path-connected, and also prove that infinitely ended groups do not have uniformly path-connected boundary. As a result we are able to sometimes detect one endedness (and thus solve the problem of how many ends the group has)

Applying and extending the theory of effective use in a business intelligence context

The benefits that organizations accrue from information systems depend on how effectively the systems are used. Yet despite the importance of knowing what it takes to use information systems effectively, little theory on the topic exists. One recent and largely untested exception is the theory of effective use (TEU). We report on a contextualization, extension, and test of TEU in the business intelligence (BI) context, a context of considerable importance in which researchers have called for such studies. We used a mixed-method, three-phase approach involving instrument development (n = 218), two-wave cross-sectional survey (n = 437), and three sets of follow-up interviews (n = 33). The paper contributes by (1) showing how TEU can be contextualized, operationalized, and extended, (2) demonstrating that many of TEU’s predictions hold in the BI context while also revealing ways to improve the theory, and (3) offering practical insights executives can draw on to improve use of BI in their organizations

Querying Geometric Figures Using a Controlled Language, Ontological Graphs and Dependency Lattices

Dynamic geometry systems (DGS) have become basic tools in many areas of geometry as, for example, in education. Geometry Automated Theorem Provers (GATP) are an active area of research and are considered as being basic tools in future enhanced educational software as well as in a next generation of mechanized mathematics assistants. Recently emerged Web repositories of geometric knowledge, like TGTP and Intergeo, are an attempt to make the already vast data set of geometric knowledge widely available. Considering the large amount of geometric information already available, we face the need of a query mechanism for descriptions of geometric constructions. In this paper we discuss two approaches for describing geometric figures (declarative and procedural), and present algorithms for querying geometric figures in declaratively and procedurally described corpora, by using a DGS or a dedicated controlled natural language for queries.Comment: 14 pages, 5 figures, accepted at CICM 201

Securing level 2 in mathematics (National Strategies: primary)

"The guidance identifies key areas of learning that children need to secure to attain level 2 in mathematics. While you will integrate the ideas from these materials into your ongoing planning, you could also use them to plan targeted support for particular groups of children. There is a double-page spread for each of the six areas of mathematics: • Counting, comparing and ordering numbers • Understanding addition and subtraction and their relationship • Using mental calculation strategies to solve problems involving addition and subtraction • Recognising and describing shapes • Understanding and using standard units and equipment to measure • Organising and interpreting data to answer questions" - Page 1

The Art of Science; An Exploration of Art Integration in a Science Classroom

This Practitioner Perspective examined how art integration in a science classroom affects student engagement and scientific understanding. The study took place over one school year in a 7th and 8th grade science classroom, with a total of 57 students and a focus group of eleven students. Collaboratively, the science teacher and a teaching artist designed purposeful integration of art into two science units and developed a culmination project where students connected their science learning throughout the year to a self portrait. Findings indicated that art integration increased engagement and understanding and allowed students to visually express their learning. However, supports may be needed for students who may not consider themselves artists or are hesitant to participate in the art integrated activities

Akin House Curriculum Development and Living History Programming

This unit plan is comprised of a variety of inquiry-based lessons that explore the culture and way of life of the Native Americans who occupied New England. After studying the Akin house documents, materials, and narratives, I chose to focus my unit on the land and the people who came before the Akin family so that students will learn the long-view of our rich New England history