Univariate Tests

Modeling of real-world problems almost always involves multiple variables, which is why this book focuses on regression analysis. Yet even in large regression models, the eventual comparisons made still often boil down to simple univariate tests. This chapter serves as reference material for those tests.

Which tests should I know?

There is little benefit in memorizing a large number of tests. If you know how to put to words what you want to compare, you can just look up how to do it. However, some univariate tests keep reappearing, even later when you start learning about more complex models. It is therefore important to understand the following basic tools and their typical use-cases:

• \(t\)-test
  • Compare means
  • Compare regression coefficients to zero
• \(\chi^2\)-test (the Greek letter \(\chi\), pronounced ‘kai’)
  • Compare observed and expected frequencies
  • Perform a goodness-of-fit test
• \(F\)-test
  • Compare variances
  • Perform an omnibus test