Model Building: Analysis of Means

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Description

This lecture covers a model building example using analysis of means, focusing on the effects of applied load and previous cuts on the removal rate of osteotomy drills. It explains how to find the effects of factors, interactions, and build a predictive model. The lecture also discusses experimental results, dealing with noise-induced errors, replication, and pooling of interactions. It demonstrates the use of replicates and ANOVA to eliminate factors, calculating interaction terms, and building the overall equation for adhesion strength. The content includes examples, formulas, and practical applications in experimental design.

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https://mediaspace.epfl.ch/media/0_vcvzi0g9

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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.

A glossary of terms used in experimental research. Statistics Experimental design Estimation theory Alias: When the estimate of an effect also includes the influence of one or more other effects (usually high order interactions) the effects are said to be aliased (see confounding). For example, if the estimate of effect D in a four factor experiment actually estimates (D + ABC), then the main effect D is aliased with the 3-way interaction ABC. Note: This causes no difficulty when the higher order interaction is either non-existent or insignificant.

In the design of experiments, optimal designs (or optimum designs) are a class of experimental designs that are optimal with respect to some statistical criterion. The creation of this field of statistics has been credited to Danish statistician Kirstine Smith. In the design of experiments for estimating statistical models, optimal designs allow parameters to be estimated without bias and with minimum variance. A non-optimal design requires a greater number of experimental runs to estimate the parameters with the same precision as an optimal design.

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