This course delves into statistical modeling, focusing on ANOVA, ANCOVA, and experimental design principles. It provides a mathematical foundation for designing experiments for data science applications. Emphasizing important design-related concepts such as randomization, blocking, and factorial design, this course also addresses ethical issues in experimentation.
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This course comprises four modules. Module 1 introduces ANOVA and experimental design, Module 2 covers hypothesis testing in the ANOVA context, Module 3 delves into two-way ANOVA and interactions, while Module 4 explores experimental design concepts and designs.
This module provides an introduction to ANOVA, covering experimental design and the one-way ANOVA and ANCOVA models as linear regression models. It also delves into ANOVA variance decomposition, sums of squares, and the F-test, along with ANCOVA with interactions and its implementation in R.
Module 2 explores hypothesis testing in the ANOVA context, including planned comparisons, post hoc comparisons, type II error, and power. It also discusses assessing type S (Sign) and type M (Magnitude) errors, providing practical solutions and considerations.
This module delves into the two-way ANOVA model, its interpretation as a regression model, interaction terms, formal tests, and hypothesis testing. It also looks ahead to the application of two-way ANOVA and experimental design.
Module 4 covers the conceptual framework of experimental design, including completely randomized designs, randomized complete block designs, factorial designs, and ethical issues. It provides a comprehensive understanding of the principles and applications of experimental design in data science.
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