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I Really Can't find some exact definition to the Simultaneous tests. So I am not sure if Simultaneous tests and Multiple Comparison are same concepts or not.

I also need a source (Book or Article) to the definitions.

Any Help will be appreciated.

kjetil b halvorsen
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SirSaleh
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2 Answers2

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My understanding:

Simultaneous tests: The null hypothesis has multiple restrictions. One test statistics is derived and one p-value is given. For example: In linear model. null hypothesis can be $\beta_1=0$ and $\beta_2 = 0$. Then F value, finally one p-value.

Multiple Comparison: Multiple null hypotheses with multiple p-values. For example: From null hypothesis $\beta_1 = 0$, one p-value is generated; from null hypothesis $\beta_2 = 0$, another p-value is produced.

user158565
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I believe the correct terminology is "multiple comparison". It means you do multiple statistical inferences together. You don't need a book for the definition (read Wikipedia).

SmallChess
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