Geometry of Linear Correlation Coefficient
B H Priyanto*1, K I A Suhada2

1,2Statistics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10 Bandung, 40132, Indonesia
*budihp.itb[at]students.itb.ac.id
budihp.itb[at]gmail.com

Abstract

Abstract The idea of this study is the fact that (1) the linear correlation coefficients that are statistically significant based on the t-test statistic, first, the sign of significance does not indicate the magnitude of the intensity (strength) of the relationship between test items and the indicators constructed by the tested items- and, second, the sign of significance also does not guarantee that the test items have a similar direction to the direction of the indicator- (2) the angle between the tested items and the indicator (correlation angle) and the linear correlation coefficient are two equivalent measures- and (3) there is a close relationship between the linear correlation coefficient and the average distance between the two variables. Therefore, to determine the test items that form the research indicators, the researcher should consider the correlation angle and the average distance between the indicators and the selected test items.

Keywords: Keywords correlation angle, linear correlation coefficient, t-test statistic, test items, indicator.

Topic: Mathematics Education