Are primary challenges a bad sign for an incumbent president?

[FerrisBueller86]

I've noticed that there seems to be a correlation between the presence of a significant primary challenge to an incumbent president and the ousting of the incumbent president in November.  It's easy to see why - a significant primary challenge means that a significant portion of the party base doesn't like the incumbent.  This makes it harder to rally the base voters, takes resources away from going after the swing voters, and helps rally the opposition.  On the other hand, the lack of a primary challenge to an incumbent president means that the party base likes the incumbent, makes it easier to rally the base voters, allows the incumbent to go after the swing voters, and doesn't lend ammunition to the opposition.

The results:
1964: no primary challenge to LBJ, LBJ wins in the biggest Democratic landslide since FDR and even wins Utah, Wyoming, Idaho, and ALL of the Great Plains states
1968: primary challenges to LBJ, LBJ drops out of re-election race due to extreme unpopularity
1972: no primary challenge, Nixon wins every state except Massachusetts
1976: Reagan challenges Ford, Ford loses to Carter
1980: Ted Kennedy challenges Carter, Reagan unseats him in a landslide
1984: no primary challenge, Reagan wins every state except Minnesota
1992: Buchanan challenges Bush, Clinton unseats Bush
1996: no primary challenge, Clinton wins
2004: no primary challenge, Bush wins

Has there been a presidential election in which the incumbent president faced a strong primary challenge but won?  Or a presidential election in which the incumbent president faced no primary challenge but lost? 

[minionofmidas]

Truman didn't face a Primary challenge as far as I know*, since the primaries were nowhere near as important then as they are now, and indeed appeared to be on their way out, but he was certainly unpopular with large parts of the party base, as viz. Thurmond's and Wallace's candidacies. He was reelected anyways.
I'm not sure if Hoover, the last defeated president before 1976, faced any opposition within the party in 1932.

*except in Alabama. Alabama held primaries for electors, and the Democratic electors primary was won by a slate pledged to Strom Thurmond. As a result, Truman was not on the ballot in Alabama.

[muon2]

To use older elections, consider the situation where the incumbent party has a fight for the presidential nomination. One definition of a fight is where one or more rival candidates have a significant number of delegate votes (for instance more than a third) in the first round at the convention.

Since the current two parties in 1860, there have been 37 elections. Only three times did the presence or lack of a fight for the incumbent's party nomination not forecast the winner of the popular vote. Those elections were losses by Nixon (1960) and Hoover (1932), and a win by Garfield (1880).

[Beet]

Nxion was challenged in 1972

[minionofmidas]

Nxion was challenged in 1972

By whom? How successful was that challenge?

[Beet]

Nxion was challenged in 1972

By whom? How successful was that challenge?

John Ashbrook (R-OH). He campaigned actively in New Hampshire, Florida and California, but received less than 10% of the vote.

[minionofmidas]

That's basically not a challenge.

[PBrunsel]

Nxion was challenged in 1972

By whom? How successful was that challenge?

John Ashbrook (R-OH). He campaigned actively in New Hampshire, Florida and California, but received less than 10% of the vote.

Also by Representative Paul McCloskey, a "Peace republican."

[No more McShame]

Doesn't the popularity of the incumbent in the first place factor into a primary challenge?  I guess it's the age-old chicken or the egg question.

[muon2]

Nxion was challenged in 1972

By whom? How successful was that challenge?

John Ashbrook (R-OH). He campaigned actively in New Hampshire, Florida and California, but received less than 10% of the vote.

Also by Representative Paul McCloskey, a "Peace republican."

Nixon received all but one vote at the nominating convention. That qualifies as no challenge.

The nominating convention test is also used in A. Lichtman's 13 Keys to the Presidency. He notes that it is the most powerful predictor in his model.