The era of conservative dominance?

A lot of people call 1968-2006 the "era of conservative dominance" in American politics. But was it? Just looking at presidential elections, the pattern looks like this:

Republican (2 terms) - Nixon/Ford
Democrat (1 term) - Carter
Republican (2 terms) - Reagan
Republican (1 term) - Bush I
Democrat (2 terms) - Clinton
Republican (2 terms) - Bush II

Now, the
Republicans win that matchup 7 terms to 3. But if you extend the list back to include 1944-1968 - a period of supposed liberal dominance - and forward to 2008, here's what you get:

Democrat (1 term) - Roosevelt/Truman
Democrat (1 term) - Truman
Republican (2 terms) - Eisenhower
Democrat (1 term) - Kennedy/Johnson
Democrat (1 term) - Johnson
Republican (2 terms) - Nixon/Ford
Democrat (1 term) - Carter
Republican (2 terms) - Reagan
Republican (1 term) - Bush I
Democrat (2 terms) - Clinton
Republican (2 terms) - Bush II
Democrat - Obama

In other words, with the exception of the Reagan/Bush I transition in 1988, the presidency has never been in the hands of one party for more than 8 years in a row since World War 2. Each part has had exactly 1 president who lost re-election in that time period (Carter and Bush I), and both of those came in the later "conservative" period. Throw in the fact that Democrats controlled Congress for most of the entire postwar period, and 1968-2006 really doesn't look like anything special for conservatives.

It's like if I flipped a coin and got:

1. heads, 2. heads, 3. tails, 4. tails, 5. heads, 6. heads, 7. tails, 8. tails, 9. heads, 10. tails, 11. tails, 12. tails, 13. heads, 14. heads, 15. tails, 16. tails, 17. heads

and I picked flips 7-16 as the "era of tails dominance". It just doesn't make sense. (Forget about the fact that a real series of coin flips would probably have more strings of all-heads or all-tails than this series does.)

Now there are some arguments to be made that 1968-2006 really was an era where America turned more toward political conservatism. The three Republican landslides of the 1980s were pretty overwhelming. And it could be argued that Clinton and Carter were more conservative than the typical Democrat (and Eisenhower and Nixon more liberal than the typical Republican). But on the basis of electoral success alone, 1968-2006 did not see substantial Republican dominance. They just acted like they ruled the universe.