Principal Component Analysis of Mathematical Justification Skills Test Results on Probability for Eighth-Grade Students
Udjianna Sekteria Pasaribu (a), Rina Musannadah (b*), Nisa Fadlilah Fathul Ilmi (a)

a) Statistics Research Group, Department of Mathematics, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
b) Magister Program in Mathematics Teaching, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jalan Ganesha 10, Bandung 40132, Indonesia
*Corresponding Author: 24621014[at]mahasiswa.itb.ac.id

Abstract

Multivariate analysis can be used to examine the data and discover a variety of interpretations. Many education-related data sets need to be analyzed using more in-depth statistics. Student learning outcomes are an example of data in education. This study analyzed the mathematical justification skill test results using Principal Component Analysis (PCA). PCA is a type of multivariate statistical analysis that turns random variables that were once related to each other into new random variables that are not related to each other. These new variables are then called the Principal Components (PCs). Thirty-eighth-grade students from XXX junior high school were observed after being taught the same way: a guided discovery approach with the mathematical justification skills oriented. Four problems of mathematical justification are used on the test. The data used in this study are continuous quantitative data with an interval of [0, 15] for problems 1, 2, and 3 and an interval of [0, 19] for problem 4. PCA was performed after the data were transformed and met the assumptions of normality. The random variables that we transformed were the random variables for problems 1, 3, and 4. Based on the analysis, the Principal Component called the grade of students in determining the probability of an event, was chosen. The PC equation is PC1=0,006Problem1-0,0301Problem2-0,9995Problem3+0,0042Problem4. The Principal Component that was formed and can represent the absorption of data up to 97.12%. From this equation, question 3 has a reasonably significant coefficient in PC1. So, to test the mathematical reasoning skills of eighth-grade junior high school students on probability it is sufficient to pose a single question based on the criteria of PC1.

Keywords: Principal Component Analysis, Mathematical Justification Skill, Mathematical Justification Test

Topic: MATHEMATICS AND SCIENCE EDUCATIONS