The latest Rasmussen Reports national telephone survey shows former New York City Mayor Rudy Giuliani holding a statistically insignificant one-point lead over former North Carolina Senator John Edwards. The poll shows Giuliani earning the vote for 45% of the nation’s voters while Edwards attracts 44%.

While the lead is statistically insignificant, it is the first time Giuliani has held even a nominal advantage over Edwards in nine polls dating back to March. A month ago, Edwards had a nine-point lead over Giuliani. Two months ago, the Democrat enjoyed an eight-point lead.

The question yet to be answered is whether this poll reflects a new reality in the match-up or is merely statistical noise.

Individual polls with a four-point margin of sampling errors, sometimes overstate the volatility in a race. One way to address that issue is to consider results on a three-poll rolling average basis. Averaging the last three poll results shows Edwards maintain a 48% to 42% lead over Giuliani. That’s exactly the same average result for the match-up following polling in both August and September.

In fact, when matched against Giuliani on a three-poll rolling average basis, Edwards has attracted a remarkably stable 46% to 48% of the vote for eight straight polls dating back to May. During that same time frame, Giuliani’s numbers have remained in the 42% to 45% range.

The only way to determine if the latest poll represents a break from those trends or is simply an aberration is to wait for the next Rasmussen Reports survey of the race.

The current poll also shows Edwards leads former Senator Fred Thompson 48% to 39%. That is completely in line with the current three poll-rolling average results. In fact, using the three-poll average, Edwards has been at the 48% to 50% range against Thompson for five straight monthly results. During that time, Thompson’s numbers have been stable in the 38% to 40% range.

Edwards has consistently been a distant third in the race for the Democratic Presidential Nomination. However, he has often outperformed both Senator Hillary Clinton and Senator Barack Obama in general election match-ups against Republican hopefuls. The relative electability of the top Democratic candidates may be shifting a bit. It is interesting to note that Edwards and Clinton attract very similar levels of support when matched against Republican candidates.

Barack Obama, a distant second in the Democratic nomination race, leads Giuliani by five points and Thompson by six in recent match-ups.

Giuliani and Thompson lead nationally in polls for the Republican nomination, but there is no real frontrunner in the race. John Edwards is now viewed favorably by 50% of likely voters, unfavorably by 43%. That's a moderate improvement over his numbers earlier in October and about where he was in September.

Giuliani is viewed favorably by 51%, unfavorably by 47%. That’s the first time he has moved back above the 50% positive mark in six weeks.

Those with no opinion of Thompson now number only 13%, down from 22 points two weeks ago. He is now viewed favorably by 43%, unfavorably by 44%. Two weeks ago his favorables were 39% and 39%.

See survey questions and top-line results. Crosstabs available for Premium Members only.