Measuring and Comparing Student Performance: A New Technique for Assessing Directional Associations

Abstract

Measuring and comparing student performance have been topics of much interest for educators and psychologists. Particular attention has traditionally been paid to the design of experimental studies and careful analyses of observational data. Classical statistical techniques, such as fitting regression lines, have traditionally been utilized and far-reaching policy guidelines offered. In the present paper, we argue in favour of a novel technique, which is mathematical in nature, and whose main idea relies on measuring distance of the actual bivariate data from the class of all monotonic (increasing in the context of this paper) patterns. The technique sharply contrasts the classical approach of fitting least-squares regression lines to actual data, which usually follow non-linear and even non-monotonic patterns, and then assessing and comparing their slopes based on the Pearson correlation coefficient, whose use is justifiable only when patterns are (approximately) linear. We describe the herein suggested distance-based technique in detail, show its benefits, and provide a step-by-step implementation guide. Detailed graphical and numerical illustrations elucidate our theoretical considerations throughout the paper. The index of increase, upon which the technique is based, can also be used as a summary index for the LOESS and other fitted regression curves.

Assessing Transfer Functions in Control Systems

“…The Lomax distribution is absolutely continuous, and thus the cdf F (x) of X is also absolutely continuous, as required by condition (C1). Its pdf is 7) and the density-quantile function is…”

“…as closely as desired by choosing a sufficiently large n. Namely, we have the statement I 0 n (g) → I(g) when n → ∞, (1.4) whose numerical explorations can be found in Chen and Zitikis (2017), and Chen et al (2018).…”

Estimating the index of increase via balancing deterministic and random data

“…In addition, supported by the examples of Anscombe (1973) on potential pitfalls when using the classical correlation coefficient, Chen and Zitikis (2017) argue in favour of using the index of increase, as defined by Davydov and Zitikis (2017), for assessing non-monotonicity of scatterplots. Chen and Zitikis (2017) apply this approach to analyze and compare student performance in subjects such as mathematics, reading and spelling, and illustrate their reasoning on data provided by Thorndike and Thorndike-Christ (2010). One of the methods discussed by Chen and Zitikis (2017) deals with scatterplots representing finite populations, in which case large-sample estimation is not possible.…”

Machine Learning-Based App for Self-Evaluation of Teacher-Specific Instructional Style and Tools

“…It is important to note that actual exam scores are not linear functions of other exam and test scores [8], and they do not follow some other simple well-defined form (e.g., logistic, probit, power law, log-linear, etc.). Because of that, we do not use classical regression models based on specific assumptions about the model.…”