Lecture

Two-way ANOVA and Chi-square Test

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In course

CS-411: Digital education

This course addresses the relationship between specific technological features and the learners' cognitive processes. It also covers the methods and results of empirical studies: do student actually learn due to technologies? In fall 2025, P. Dillenbourg w ...

Description

This lecture covers the application of two-way ANOVA to assess the impact of two categorical variables on a quantitative outcome, focusing on potential interaction effects. It also includes a demonstration using a dataset about cars. Additionally, the lecture introduces the chi-square test for analyzing the relationship between two categorical variables in contingency tables, serving as an alternative when ANOVA assumptions are not met. The instructor explains how to run these analyses, interpret the results, and check the assumptions, emphasizing the importance of model comparison and transformation when necessary.

Instructors (2)

Pierre Dillenbourg

A former teacher in elementary school, Pierre Dillenbourg graduated in educational science (University of Mons, Belgium). He started his research on learning technologies in 1984. In 1986, he has been on of the first in the world to apply machine learning to develop a self-improving teaching system. He obtained a PhD in computer science from the University of Lancaster (UK), in the domain of artificial intelligence applications for education. He has been assistant professor at the University of Geneva. He joined EPFL in 2002. He has been the director of Center for Research and Support on Learning and its Technologies, then academic director of Center for Digital Education, which implements the MOOC strategy of EPFL (over 2 million registrations). He is full professor in learning technologies in the School of Computer & Communication Sciences, where he is the head of the CHILI Lab: "Computer-Human Interaction for Learning & Instruction ». He is the director of the leading house DUAL-T, which develops technologies for dual vocational education systems (carpenters, florists,...). With EPFL colleagues, he launched in 2017 the Swiss EdTech Collider, an incubator with 80 start-ups in learning technologies. He (co-)-founded 4 start-ups, does consulting missions in the corporate world and joined the board of several companies or institutions. In 2018, he co-founded LEARN, the EPFL Center of Learning Sciences that brings together the local initiatives in educational innovation. He is a fellow of the International Society for Learning Sciences. He currently is the Associate Vice-President for Education at EPFL.

Patrick Jermann

After studies in Geneva (TECFA) and Pittsburgh (LRDC) I joined EPFL in 2003 to coordinate eLearning projects and conduct research in the field of Computer Supported Collaborative Learning (CSCL). Starting 2013 I am responsible for MOOCs production at the Center for Digital Education (CEDE).Former Associate Editor for the IEEE Transactions on Learning Technologies and former Member of the Editorial Board for the International Journal of Computer Supported Collaborative Learning (iJCSCL). Specialties: Interaction analysis, research methods, statistical methods, prototyping, software development, pedagogical design.

Official source

Ontological neighbourhood

Statistics

Statistical inference: Statistical hypothesis testing

Related concepts (29)

Analysis of variance

Analysis of variance (ANOVA) is a collection of statistical models and their associated estimation procedures (such as the "variation" among and between groups) used to analyze the differences among means. ANOVA was developed by the statistician Ronald Fisher. ANOVA is based on the law of total variance, where the observed variance in a particular variable is partitioned into components attributable to different sources of variation.

Contingency table

In statistics, a contingency table (also known as a cross tabulation or crosstab) is a type of table in a matrix format that displays the (multivariate) frequency distribution of the variables. They are heavily used in survey research, business intelligence, engineering, and scientific research. They provide a basic picture of the interrelation between two variables and can help find interactions between them.

Chi-squared test

A chi-squared test (also chi-square or χ2 test) is a statistical hypothesis test used in the analysis of contingency tables when the sample sizes are large. In simpler terms, this test is primarily used to examine whether two categorical variables (two dimensions of the contingency table) are independent in influencing the test statistic (values within the table). The test is valid when the test statistic is chi-squared distributed under the null hypothesis, specifically Pearson's chi-squared test and variants thereof.

Pearson's chi-squared test

Pearson's chi-squared test () is a statistical test applied to sets of categorical data to evaluate how likely it is that any observed difference between the sets arose by chance. It is the most widely used of many chi-squared tests (e.g., Yates, likelihood ratio, portmanteau test in time series, etc.) – statistical procedures whose results are evaluated by reference to the chi-squared distribution. Its properties were first investigated by Karl Pearson in 1900.

Chi-squared distribution

In probability theory and statistics, the chi-squared distribution (also chi-square or -distribution) with degrees of freedom is the distribution of a sum of the squares of independent standard normal random variables. The chi-squared distribution is a special case of the gamma distribution and is one of the most widely used probability distributions in inferential statistics, notably in hypothesis testing and in construction of confidence intervals.

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