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Discussion on ANOVA, t test and F test

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Below are a list of questions that I find particularly interesting to get some basic fundamentals down. There does not need to be much detail into any of these questions, just enough information to suffice the question (i.e. maybe a couple of sentences or key points).

What is an ANOVA? Why is it called ANOVA (Explain the basic ideas behind an ANOVA)?

What test statistics do we derive in ANOVAs (include something about X^2 and relation to F-statstics)?

How do those test statistics fit into the standard linear model theory?

What is the connection between F and t-tests?

What are the differences between a nested and a crossed design?

What are fixed effects? What are random effects? What are mixed effects models?

What is interaction?

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Solution Summary

The solution gives detailed discussion on the nature of ANOVA and relationship between t test and F test.

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What is an ANOVA? Why is it called ANOVA (Explain the basic ideas behind an ANOVA)?
Answer: ANOVA is the abbreciation of analysis of variance. ANOVA is a statistical model that we use it to test the difference of means for multiple groups (we require at least 3 groups). The reason why we call it ANOVA is because it compares group means by analyzing comparisons of variance estimates.

What test statistics do we derive in ANOVAs (include something about X^2 and relation to F-statstics)?
Answer: We use either chi square or F test ...

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