H1: A collect of countries will only form a federation when they
face an external threat.

There are two parts to this sentence: the formation of a
federation and the presence of an external threat.  Which one
implies the other?  The federation implies the threat!  The
formation of a federation is a sufficient condition for the
existence of an external threat because if a federation forms
then a threat must exist.  An external threat is a necessary
condition for the formation of a federation. ie a federation can
not form without an external threat.
 This hypothesis is falsified by observing a federation form
without an external threat.  It is not falsified by an external
threat that does not result in federation because an external
threat is a necessary but not a sufficient condition for the
formation of federation.
 

Decide whether the following are necessary or sufficient (or
both) conditions.  Describe the circumstances that would falsify
the statement.  Where appropriate give a historical example.

1)  A nation must have a navy to form a large empire.

2)  Democratic nations don't fight each other.

3)  Power transition theorists maintain that wars only occur when
there is power parity.

4)  US Presidents are more hawkish in their first term than their
second term.

5)  High investment results in economic growth.

6)  I do not want what I have not got.  (S. O'Connor)

7)  Unpopular governments are more likely to become involved in
wars than popular ones.

8)  In a bipolar system competing alliances resemble one another.

9)  A power vacuum leads to war.

10)  A nation only intervenes in an ongoing war if it is allied
with one of the belligerents.