In the wake of a highly successful Republican National Convention, GOP partisans must feel a bit like Luke Skywalker shooting down his first TIE fighter, letting out a triumphant “I got him!”

So let me play Han Solo: Great, kid; don’t get cocky.

Both Time and Newsweek showed the President coming out of the convention with an 11-point lead. But both of the newsweeklies used samples too rich with Republican voters. Presumably, Republicans were more likely to be home watching the convention when pollsters called them last week, while Democrats were more likely to be out. Scott Rassmussen has pointed out that if the results of those polls are weighted based on the mix of Republicans, Democrats, and independents who voted in 2000, Newsweek would show a six-point lead, Time a three-point lead.

That’s not to say the President hasn’t made gains. Rassmussen’s daily tracking poll yesterday showed only a nominal lead for the President — one-point — but not even Rassmussen himself believes it. The tracking poll, says Rassmussen, “includes a Saturday sample that is way out of synch with all the days before it and with the Sunday data that followed. In fact, Saturday’s one-day sample showed a big day for Kerry while all the days surrounding it showed a decent lead for the President.” Rassmussen believes that Saturday’s polling, which will be part of the tracking data through today, was a “rogue sample.” Excluding that sample, Rassmussen showed, as of yesterday, a 4-point lead for Bush.

It’s worth dwelling a bit here on how statistical error works, since our esteemed press corps has a bad habit of hyperventilating over meaningless swings in the polls. Let’s take the new CNN/USA Today/Gallup poll, which showed Bush leading 52-48 among likely voters, as an example. Gallup’s sample of likely voters — those who remain after their answers to a series of questions meant to filter out non-voters are processed — has a margin of error of plus or minus 4 points, with 95% confidence. What that means is that in at least 19 out of 20 similar polls, the proportion of support for each candidate will vary within that range. Though reporters typically get this wrong (until recently I didn’t understand it myself), the margin of error number does not refer to statistical variation in the lead that one candidate has over the other. According to the American Statistical Associations, a good rule of thumb is to multiply the reported margin of error by 1.7 to estimate the margin of error on the lead. This means that the seven-point lead for Bush is statistically significant, but only just barely.

(This is partially why state polls, which often have relatively large margins of error, are of limited value. They indicate which states are in the toss-up category, but the value of calculating the state of the Electoral College horserace by collecting a bunch of very close polls from battleground states is dubious as best. If a candidate can open up a big lead in the national polls, the chances are very good that this translates into an electoral college victory; if the race remains close nationally, then the race in a few key states is almost certainly too close to call.)

All of that said, a barely-significant lead is still a significant lead in a race which has remained stubbornly tied for months, and it can be inferred from the fact that several different polls are moving in the same direction that the President is indeed doing quite well. His numbers certainly look better than Kerry’s did after his convention. Democrats are not altogether wrong to be as panicky as they now seem. But Republicans would be wise to remember that a lot can happen between now and election day.