Mediaspace scheduled maintenance: Aug 25, 2026 07:00 - 12:00 AM. During this time, videos will be temporarily unavailable. Check status updates.

Lecture

Multi-factor ANOVA

In course

MSE-213: Probability and statistics for materials science

The course establishes the concepts of statistical analysis, probability theory, and data analysis. This includes standard statistical tests, correlation analysis and experimental design. It introduces computational statistical methods to analyse large dat ...

Description

This lecture covers the concept of Multi-factor ANOVA, focusing on analyzing the variance explained by multiple factors and their interactions. The instructor explains how to build models to predict outcomes based on different factor levels and how to interpret the results using F-values. The lecture also delves into the significance of factor interactions and provides practical hints on decomposing the total sum of squares. Through examples and formulas, students learn how to apply Multi-factor ANOVA in real-world scenarios.

This video is available exclusively on Mediaspace for a restricted audience. Please log in to MediaSpace to access it if you have the necessary permissions.

Watch on Mediaspace

Official source

Related concepts (32)

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.

F-test

An F-test is any statistical test in which the test statistic has an F-distribution under the null hypothesis. It is most often used when comparing statistical models that have been fitted to a data set, in order to identify the model that best fits the population from which the data were sampled. Exact "F-tests" mainly arise when the models have been fitted to the data using least squares. The name was coined by George W. Snedecor, in honour of Ronald Fisher. Fisher initially developed the statistic as the variance ratio in the 1920s.

F-distribution

In probability theory and statistics, the F-distribution or F-ratio, also known as Snedecor's F distribution or the Fisher–Snedecor distribution (after Ronald Fisher and George W. Snedecor), is a continuous probability distribution that arises frequently as the null distribution of a test statistic, most notably in the analysis of variance (ANOVA) and other F-tests. The F-distribution with d1 and d2 degrees of freedom is the distribution of where and are independent random variables with chi-square distributions with respective degrees of freedom and .

Variance

In probability theory and statistics, variance is the squared deviation from the mean of a random variable. The variance is also often defined as the square of the standard deviation. Variance is a measure of dispersion, meaning it is a measure of how far a set of numbers is spread out from their average value. It is the second central moment of a distribution, and the covariance of the random variable with itself, and it is often represented by , , , , or .

Expected value

In probability theory, the expected value (also called expectation, expectancy, expectation operator, mathematical expectation, mean, average, or first moment) is a generalization of the weighted average. Informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. The expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. In the case of a continuum of possible outcomes, the expectation is defined by integration.

Related lectures (55)

Understanding Statistics & Experimental Design

Covers basic probability theory, ANOVA, experimental design, and statistical reporting errors.

Statistics essentials: ANOVA

Covers the essentials of ANOVA, explaining its concept, calculations, assumptions, and interpretation of results.

Analysis of Variance (ANOVA)

Covers Analysis of Variance (ANOVA) for assessing categorical variable effects on quantitative outcomes.

Statistics Essentials: Two-way ANOVA

Covers the essentials of Two-way ANOVA, focusing on calculating decision variables and checking assumptions.

Advanced Probabilities: Random Variables & Expected Values