**Modus tollens in logic**

In logic, there is an argument style called modus tollens:

If H0 then R

Not R

therefore

Not H0

This is a valid argument.

**Modus tollens misapplied to p-values**

Some people mis-apply this to p-values, saying:

If H0 then

probablynot R

Not R

therefore

Probably not H0

This is not valid.

Example of proper and improper modus tollens

Proper:

If a person is an American citizen, then that person is not a member of parliament

This person is a member of parliament

therefore

This person is not an American citizen

Improper

If a person is an American citizen, then that person is probably not a senator

This person is a senator

therefore

This person is not an American citizen