Exploring the association between self-efficacy and future utility beliefs in mathematics: A practical tutorial on correspondence analysis.

It has long been understood that there exists a strong association between a student's belief in the future utility of mathematics and their self-efficacy in mathematics. This study re-examines this association by studying these variables based on data collected from a sample of 21,444 ninth-grade students who participated in the 2009 High School Longitudinal Study (HSLS09). The nature of the association between future utility beliefs of students in mathematics and self-efficacy of students in mathematics is explored visually using the simple correspondence analysis technique. The main feature that will be utilised from this technique is a two-dimensional graphical display, referred to as a correspondence plot. By studying the HSLS09 data, the first two axes of such a plot summarised nearly 99% of the statistically significant association that exists between a student's beliefs in the future utility of mathematics and their mathematics self-efficacy. It is shown visually that students who strongly believe in the future importance of studying mathematics also perform strongly in the subject, while those who do not believe that there is any future utility from studying mathematics do not perform well at it. This study, therefore, suggests that mathematics ability is associated with a student's perception of its future importance.

Manipulating the Alpha Level Cannot Cure Significance Testing.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable.

Application of Correspondence Analysis to Graphically Investigate Associations Between Foods and Eating Locations.

This paper presents the application of correspondence analysis (CA) for investigating associations using confidence regions (CRs) with a focus on facilitating mining the data and hypothesis generation. We study the relationship between locations and "less-healthy" food consumption by UK teenagers. CA allows for a quick visual inspection of the various association structures that exist between the categories of cross-classified variables in large datasets derived with varying study designs. The hypotheses generated by the visual display can then be independently tested using suitable regression models. CA makes use of readily available software tools and of robust statistical tests amenable to interpretation.

Modelling Trends in Ordered Correspondence Analysis Using Orthogonal Polynomials.

The core of the paper consists of the treatment of two special decompositions for correspondence analysis of two-way ordered contingency tables: the bivariate moment decomposition and the hybrid decomposition, both using orthogonal polynomials rather than the commonly used singular vectors. To this end, we will detail and explain the basic characteristics of a particular set of orthogonal polynomials, called Emerson polynomials. It is shown that such polynomials, when used as bases for the row and/or column spaces, can enhance the interpretations via linear, quadratic and higher-order moments of the ordered categories. To aid such interpretations, we propose a new type of graphical display-the polynomial biplot.

Zinc starvation induces a stress response in Saccharomyces cerevisiae that is mediated by the Msn2p and Msn4p transcriptional activators.

During the production of wine and beer, the yeast Saccharomyces cerevisiae can encounter an environment that is deficient in zinc, resulting in a 'sluggish' or a 'stuck' ferment. It has been shown that the Zap1p-transcription factor induces the expression of a regulon in response to zinc deficiency; however, it was evident that a separate regulon was also activated during zinc deficiency in a Zap1p-independent manner. This study discovered the Msn2p and Msn4p (Msn2/4p) transcriptional activator proteins to be an additional control mechanism inducing the stress response during zinc deficiency. Promoter sequence analysis identified the stress-response element (STRE) motif, recognized by Msn2/4p, and was significantly enriched in the promoters of genes induced by zinc deficiency. An investigation using genome-wide analyses revealed a distinct regulon consisting of STRE-containing genes whose zinc-responsive expression was abolished in an msn2 msn4 double mutant. An STRE-driven lacZ reporter construct confirmed that expression of the genes within this regulon was perturbed by the deletion of MSN2 and MSN4 and also implicated Hog1p as a contributing factor. This research provides a better understanding of the molecular mechanisms involved in the yeast response to zinc deficiency during fermentation.