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Discussion on some statistical terms: F-ratio, error variance

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What is an F-ratio? Define all the technical terms in your answer.
What is error variance and how is it calculated?
Why would anyone ever want more than two (2) levels of an independent variable?
If you were doing a study to see if a treatment causes a significant effect, what would it mean if within groups variance was higher than between groups variance? If between groups variance was higher than within groups variance? Explain your answer
What is the purpose of a post-hoc test with analysis of variance?
What is probabilistic equivalence? Why is it important?

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Solution Summary

The solution discusses some statistical terms: F-ratio, error variance, independent variable, between groups variance, within groups variance, post-hoc test and probabilistic equivalence.

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What is an F-ratio? Define all the technical terms in your answer.
Answer: F ratio is the division of two variances from two independent samples. Usually, the formula is F=s12/s22 where s12 and s22 are two sample variances from two samples. And F-ratio is used to test the independence of two samples.

What is error variance and how is it calculated?
Answer: error variance is a measurement to show how far the actual data is far from the fitted data. Usually, the formula is error variance=total variance-systematic variance.

Why would anyone ever want more than two (2) levels of an independent ...

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