Lecture

Comparison Statistics: Hypothesis Testing and ANOVA

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In course

MICRO-110: Probability & statistics for engineers

This course covers the basics of probability and statistical techniques for engineers, including major probability concepts, data analysis, and statistical inference.

Description

This lecture covers the design and analysis of experiments, focusing on comparison statistics. It starts with checking if an experimental factor affects a measured response, then delves into hypothesis testing methodologies like t-tests and ANOVA. The ANOVA methodology is explained, followed by an example of blood coagulation based on diet. The lecture also discusses ANOVA table generation, interpretation of F-ratio values, correlation analysis, and linear regression. Key topics include the Pearson correlation, coefficient of determination, and handling outliers in regression analysis.

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Instructor

Vivek Subramanian

Teaching & PhD PhD Students Giovanni Ruffolo, Giada Romano, Sanjay Manoharan, Kyle Haas, Claude Dahan, Biruktait Ayele Lemecho, Yagmur Ceren Alatas, Tugçe Delipinar Past EPFL PhD Students Amin Hodaei, Mustafa Mohieldin Fadlelmula Fadlelseed Past EPFL PhD Students as codirector Mohammad Jafarpour Courses Organic and printed electronics MICRO-505 This course addresses the implementation of organic and printed electronics technologies using large area manufacturing techniques. It will provide

Official source

Ontological neighbourhood

Statistics

Data analysis: Regression analysis

Related concepts (32)

Linear regression

In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called simple linear regression; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable.

Correlation

In statistics, correlation or dependence is any statistical relationship, whether causal or not, between two random variables or bivariate data. Although in the broadest sense, "correlation" may indicate any type of association, in statistics it usually refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the height of parents and their offspring, and the correlation between the price of a good and the quantity the consumers are willing to purchase, as it is depicted in the so-called demand curve.

Nonlinear regression

In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fitted by a method of successive approximations. In nonlinear regression, a statistical model of the form, relates a vector of independent variables, , and its associated observed dependent variables, . The function is nonlinear in the components of the vector of parameters , but otherwise arbitrary.

Bayesian linear regression

Bayesian linear regression is a type of conditional modeling in which the mean of one variable is described by a linear combination of other variables, with the goal of obtaining the posterior probability of the regression coefficients (as well as other parameters describing the distribution of the regressand) and ultimately allowing the out-of-sample prediction of the regressand (often labelled ) conditional on observed values of the regressors (usually ).

Pearson correlation coefficient

In statistics, the Pearson correlation coefficient (PCC) is a correlation coefficient that measures linear correlation between two sets of data. It is the ratio between the covariance of two variables and the product of their standard deviations; thus, it is essentially a normalized measurement of the covariance, such that the result always has a value between −1 and 1. As with covariance itself, the measure can only reflect a linear correlation of variables, and ignores many other types of relationships or correlations.

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