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

Lecture

ANOVA: Partitioning Total SS

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 by the instructor covers the analysis of variance (ANOVA) method, focusing on the partitioning of the total sum of squares (SS) into treatment and error components. The lecture explains the calculation of SST (sum of squares treatment) and SSE (sum of squares error) and their respective degrees of freedom. It also delves into the mean square treatment (MST) and mean square error (MSE) calculations, emphasizing the significance of these values in ANOVA. Additionally, the lecture discusses the Fisher statistic and the F-distribution, providing insights into hypothesis testing and the interpretation of ANOVA results.

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

Ontological neighbourhood

Statistics

Statistical inference: Mathematical statistics

Data analysis: Regression analysis

Related concepts (32)

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 .

Residual sum of squares

In statistics, the residual sum of squares (RSS), also known as the sum of squared residuals (SSR) or the sum of squared estimate of errors (SSE), is the sum of the squares of residuals (deviations predicted from actual empirical values of data). It is a measure of the discrepancy between the data and an estimation model, such as a linear regression. A small RSS indicates a tight fit of the model to the data. It is used as an optimality criterion in parameter selection and model selection.

Pareto distribution

The Pareto distribution, named after the Italian civil engineer, economist, and sociologist Vilfredo Pareto, is a power-law probability distribution that is used in description of social, quality control, scientific, geophysical, actuarial, and many other types of observable phenomena; the principle originally applied to describing the distribution of wealth in a society, fitting the trend that a large portion of wealth is held by a small fraction of the population.

Stable distribution

In probability theory, a distribution is said to be stable if a linear combination of two independent random variables with this distribution has the same distribution, up to location and scale parameters. A random variable is said to be stable if its distribution is stable. The stable distribution family is also sometimes referred to as the Lévy alpha-stable distribution, after Paul Lévy, the first mathematician to have studied it. Of the four parameters defining the family, most attention has been focused on the stability parameter, (see panel).

Binomial distribution

In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes in a sequence of n independent experiments, each asking a yes–no question, and each with its own Boolean-valued outcome: success (with probability p) or failure (with probability ). A single success/failure experiment is also called a Bernoulli trial or Bernoulli experiment, and a sequence of outcomes is called a Bernoulli process; for a single trial, i.

Related lectures (43)

Linear Regression: Simple

Introduces simple linear regression, properties of residuals, variance decomposition, and the coefficient of determination in the context of Okun's law.

Linear Regression: Maximum Likelihood Approach

Covers linear regression topics including confidence intervals, variance, and maximum likelihood approach.

Understanding Statistics & Experimental Design

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

Linear Regression: Estimation and Testing

Explores linear regression estimation, hypothesis testing, and practical applications in statistics.

Linear Regression: Estimation and Inference