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Lecture

Statistics Essentials: The t-test

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 t-test, a statistical method used to assess the effect of a categorical variable on a quantitative outcome. It includes topics such as data set illustration, mean and standard deviation calculation, hypothesis testing, normality and variance assumptions, and alternative tests like Welch's t-test and Wilcoxon-Mann-Whitney test.

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, Mathematical statistics

Related concepts (32)

Student's t-test

A t-test is a type of statistical analysis used to compare the averages of two groups and determine if the differences between them are more likely to arise from random chance. It is any statistical hypothesis test in which the test statistic follows a Student's t-distribution under the null hypothesis. It is most commonly applied when the test statistic would follow a normal distribution if the value of a scaling term in the test statistic were known (typically, the scaling term is unknown and therefore a nuisance parameter).

Alternative hypothesis

In statistical hypothesis testing, the alternative hypothesis is one of the proposed proposition in the hypothesis test. In general the goal of hypothesis test is to demonstrate that in the given condition, there is sufficient evidence supporting the credibility of alternative hypothesis instead of the exclusive proposition in the test (null hypothesis). It is usually consistent with the research hypothesis because it is constructed from literature review, previous studies, etc.

Test statistic

A test statistic is a statistic (a quantity derived from the sample) used in statistical hypothesis testing. A hypothesis test is typically specified in terms of a test statistic, considered as a numerical summary of a data-set that reduces the data to one value that can be used to perform the hypothesis test. In general, a test statistic is selected or defined in such a way as to quantify, within observed data, behaviours that would distinguish the null from the alternative hypothesis, where such an alternative is prescribed, or that would characterize the null hypothesis if there is no explicitly stated alternative hypothesis.

Null hypothesis

In scientific research, the null hypothesis (often denoted H0) is the claim that no relationship exists between two sets of data or variables being analyzed. The null hypothesis is that any experimentally observed difference is due to chance alone, and an underlying causative relationship does not exist, hence the term "null". In addition to the null hypothesis, an alternative hypothesis is also developed, which claims that a relationship does exist between two variables.

Z-test

A Z-test is any statistical test for which the distribution of the test statistic under the null hypothesis can be approximated by a normal distribution. Z-tests test the mean of a distribution. For each significance level in the confidence interval, the Z-test has a single critical value (for example, 1.96 for 5% two tailed) which makes it more convenient than the Student's t-test whose critical values are defined by the sample size (through the corresponding degrees of freedom).

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