Saturday, December 29, 2007

Sensitive Trends Update: IA, NH, SC and US

Here is an update comparing the standard "blue line" estimate of poll trends with the more sensitive "red line", and a simple 5 poll moving average for comparison.

I talked at length about these estimators and issues related to them in an earlier post here, so won't comment further. See the earlier post for details.

These data include polls released through December 29, with ARG's 12/26-28, Research2000's 12/26-27, Strategic Visions 12/26-27 and LATimes/Bloomberg's 12/20-23,26 polling as the latest from Iowa.

The Ghost of Caucus Past

As we pour over the latest data, it is worth taking a look back at a previous year in Iowa.

The Democratic contest in 2004 was strikingly dynamic, with a sudden surge for Kerry and Edwards as Gephardt and Dean slumped. (And note the gap in polling. Those are the holidays we are in right now when polling wasn't done.) By the last polls, Kerry had established a clear lead, but Dean, Edwards and Gephardt were within four points of each other. The polling got the trends pretty close to right. Edwards was clearly on his way up through the last 12 days of the race, as was Kerry. Dean may or may not have reversed his fall in the last week, and the polls said Gephardt was coming down. So far, so good.

But the Democratic caucus process does a lot to change the outcomes, with supporters of non-viable candidates joining forces with their second choices. That process is likely to boost the well off candidate, while robbing the struggling campaigns. And of course there is always the issue of which candidate's supporters actually turn out on caucus night.

The entrance poll is the best measure we have of whose supporters actually show up on caucus night, even with all the appropriate cautions about the entrance poll itself. Comparing the entrance poll to that last estimated trend value for candidate support from pre-caucus polling, we can see how the two rising campaigns did even better than the polling predicted. Kerry's last poll trend estimate was 25.9%, good for first place. But his entrance poll support was 34.8%. For Edwards, his final trend estimate was 21.4%, but the entrance poll found 26.2% supporting him.

For Gephardt the story was the opposite. His supporters stayed home on caucus night. The pre-caucus trend had Gephardt falling but at 17.8%. But the entrance poll found only 10.3% to be Gephardt supporters.

Dean was the only top candidate whose preelection and entrance poll numbers match closely. His trend estimate was 20.3% and the entrance poll put his support at 20.5%.

Caucus night had the effect of stretching out the differences between the candidates, advantaging the top two while damaging the fourth place candidate. (Dennis Kucinich was the exception in the back of the pack, with a trend estimate of 1.7 but an entrance support of 4%.)

Then they vote. And form coalitions with non-viable supporters. And weight the delegates in a complex formula and finally there is an allocation of delegates to the state convention. That allocation is the best we can do to consider a "final" outcome of this process.

The results there further favored Kerry and Edwards. Kerry moved up to 38% of delegates, from 34.8% in the entrance poll and 25.9% in the pre-caucus poll trend. Edwards got 32% of delegates, up from his 26.2% in the entrance poll and 21.4% in the poll trend.

Dean ended up with 18% of delegates, down a bit from the 20.5% in the entrance and 20.3% in the poll trend. And Gephardt's delegates just about matched his entrance poll, 11% of delegates and 10.3% in the entrance poll. A disappointment from his 17.8% final trend estimate.

So let's take one important lesson away from this Caucus Past. The pre-election poll trend got the order of finish right, if only by a point separating Edwards and Dean. But the process of caucus night that makes it tough to come out means that enthusiastic supporters are more likely to turn out than those who are discouraged by recent slippage. That is probably true for both parties. On the Democratic side, the complex voting and coalition formation further exaggerates the lead of the top candidates and diminishes the showing of marginal ones. And that process is seen even in comparison with the entrance polls, let alone the pre-election polling.

In Iowa the "outcome" is quite a few steps removed from the simple balance of preferences among the population. The mechanisms themselves intervene to affect the final delegate counts. So don't expect to see the pre-election polls hit the final delegate percentages very closely. If the polls get the order right, that will be good enough.

For a fair test of how good the polling is this year, wait for New Hampshire where pollsters poll, voters vote, and they just count up the results.

Primary State Voters Making Up Their Minds

Voters in the early primary states are making up their minds, or at least picking a candidate when pollsters call. For all that has been written about how unsettled the races in both parties have been, we are now seeing a clear decline in the rate of "don't know" answers to the vote question. Interestingly, that trend is clear in the earliest primary/caucus states, but only faintly visible if at all for the nation as a whole. This is further evidence that early state voters really do pay more attention and move to a choice sooner than the nation as a whole. Looming election days concentrate the mind apparently.

In both parties, the undecided rate has turned down the most in Iowa, to about 5% or a shade less. This is down from about 14% early in the year for Democrats and over 15% for Republicans. Even as recently as November 1, over 14% of Republicans were unable to give a candidate choice. Democrats were at about 11% undecided at that time. In both parties the undecided rate has fallen rapidly in November and December.

New Hampshire also shows some fast movement to a decision. NH Dems have been steadily decreasing their don't know rate all year from 17% in January, but it still stands around 10% across the most recent polls. NH Republicans were a bit slower to choose until the first of December. Since then we've seen a rapid decline to about 8% now.

And in South Carolina where there are fewer polls and the undecided rate has been all over the place, we are seeing evidence of more decision making since early November. That pattern has held for both parties, with Dems now at about 9% and Reps at around 10%.

Nationally there is no trend at all in Democratic undecided rates, which have held at 10% all year. For Republicans there has been a little movement nationally, down from about 15% to about 11% since late October.

Pollsters allow voters a variety of ways to say they haven't decided, so there are various ways we can measure the crystallization of preferences. One is to just use the percent who say they are "undecided", which is simple enough. But some voters, especially early on, pick options like "someone else" or "won't vote" and pollsters vary in how the report the no-preference alternatives. So I've calculated the percent who fail to choose any of the candidates the poll asks about. This is the blue "no preference" line. As it happens, these alternative measures track together pretty well, and recently any gap between them has largely vanished.

You can also see large differences across pollsters in how large an undecided rate they produce. A few national polls have zero percent undecided, while the highs at the same time are over 25% for Republicans and over 20% for Democrats. This is one of the sources of house effects in surveys.

There is one methodological issue that we can't address with these data. Near the end of the race some pollsters push voters harder to get a response to the vote question. That would, of course, artificially lower the "don't know" rate, and to some extent may be what we are seeing in these data. Such practices are not normally disclosed so there is no way to statistically adjust for them here.

Friday, December 28, 2007

Graphing Debate Time by Candidate

A brief break from polls to comment on graphics and politics. Today's New York Times has an op-ed by NBC's political director Chuck Todd and a graphic designed by Nicholas Felton. The text and graphic are here. The text describes the data (quite completely-- an unusual but welcome touch!) noting that candidates are stratified by time in rough line with their poll standing and that debates played a part in both the rise of Mike Huckabee and the slippage of Hillary Clinton.

The graphic is a variation on a pie chart, showing the total number of minutes each candidate spoke in the 21 debates held in 2007. It is an odd fact that statisticians and analysts of statistical graphics universally hate pie charts, while graphic designers for mass media love them. The latter seem to equate statistical graphics with pie charts, while the former have ranted for years about their defects.

The appealing metaphor of a pie chart is its division of a whole into parts. Whatever the slices represent, they have to add up to a "whole" pie. The trouble here is that the text and data are about amounts of time, and only implicitly about the share of a total that each candidate receives. Further, the pie mixes the two parties into one whole pie, but there really should be two pies, each divided within party and assuming we care about shares of the pies, since Republicans can't eat any of the Democratic debate pie, nor vice versa.

When what we want to compare are magnitudes, rather than shares of a whole, the data are more clearly presented as distances rather than areas. It is easy to compare which distances are longer than others, and relatively difficult to see differences between the areas of pie slices, especially when the slices are not adjacent to each other.

So let's look at the same data in a different format and see what we can see.

The chart above reproduces the information given in the original pie chart. It plots the number of minutes each candidate spoke during all debates, and distinguishes party by the use of color (here red and blue, in the pie chart by shading.)

The main points made in the op-ed are also evident here. There is clearly a great deal of stratification across the candidates, with front runners getting more time than the "back of the pack" candidates. But there are a few comparisons I think stand out more in this chart. The advantage of Obama and Clinton over Edwards and Richardson is clear here. Richardson got only about 2/3 of the time of Obama, with Edwards a bit better but still well short of Clinton. The next cluster of Democrats-- Dodd, Biden and Kucinich-- got only about half the time of Obama, with Gravel far behind even that.

On the Republican side, Giuliani and Romney were closely matched with McCain a little bit behind. As with the Democrats, there is then a large gap until we reach Huckabee at about 3/4 of Giuliani's time. A smaller but still clear gap separates Huckabee from the cluster of Paul, Hunter, Fred Thompson and Tancredo. Another gap separates Brownback and then one more puts the short-lived candidacies of Tommy Thompson and Gilmore and the single appearance by Keyes together.

To my eye, these differences are easier to perceive and compare when the number of minutes is simply the location of the dot in the chart above than when it is the area of a pie slice.

There is actually more data presented in the text of the op-ed than is present in the graphic. Todd's text notes differences in number of debates by party (11 for Dems, 10 for Reps), which means Dems should have about 10% more total time available than Reps (if, that is, the debates were equal length, something we don't know from the text but see below). He also gives the data on how many debates each candidate participated in, an obviously important point since we are comparing Keyes' minutes in a single debate with Obama's time in 11 debates. For some purposes we might care only for total time, but for others we might want to adjust for number of debates. I do that in the chart below, which shows the average number of minutes per debate for debates in which the candidate participated.

One immediately clear point in this chart is that Obama and Clinton retain their advantage over Giuliani and Romney even when we adjust for the extra Dem debate. Giuliani and Romney got the same time per debate that Edwards and Richardson received, but that leaves them well back of Obama and Clinton.

The most important shift in the chart is the movement of Fred Thompson to the midst of the top 4 Republicans. Thompson only participated in 5 of the 10 debates, so his total time in the first chart (and the original pie chart) dramatically misrepresents the attention he received after entering the race. Thompson received substantially more time per debate than did Huckabee, though in 10 debates Huckabee had 73 total minutes to the 49 Thompson got in 5 debates, as shown in the first chart.

In his one debate, Alan Keyes got more time than any other second tier Republican averaged over more debates.

But why do Giuliani and Romney continue to get less time per debate than do Obama and Clinton? Todd's text points out that there are 12 Republican candidates but only 8 Democrats who have to divide the time. That seems reasonable, but the data are a bit more complicated. While there are 12 Republicans in the charts, three of them participated in four or fewer debates while all but 1 of the 8 Democrats participated in at least 10 debates. When we count total candidate debate appearances, the Republicans had 88 and the Democrats 81, less than a 10% difference due to number of candidates and appearances, not the 12 to 8 ratio of candidates.

What is quite different is the total number of minutes the candidates of each party spoke. Democrats totaled 794 minutes over 11 debates, a total time per debate of 72.2 minutes of candidates actually speaking. For Republicans, the total in 10 debates was 666 minutes, or 66.6 minutes per debate. So the Democratic advantage in the original pie chart and my first chart above has built into it a longer total for Democrats regardless of the number of debates.

Further, if we divide by number of candidate appearances, we get how many minutes each candidate would have gotten if the total speaking time had been divided exactly equally for each debate appearance. The result for Democrats is 794/81=9.8 minutes per candidate per debate, while Republicans had 666/88=7.6 minutes per candidate per debate. For whatever reasons of debate format and schedule, Democrats enjoyed more time to talk even adjusting for number of candidates and number of debates. (Had Reps had the same 81 appearances as Dems, they would still have only had 8.2 minutes each.)

So the disadvantage in minutes per debate even for Republican frontrunners compared to Democratic leaders is not just an artifact of number of debates or of candidates. It is a real difference and it might be of political interest to know what accounts for it. Did Republican debates run shorter on average? Did questions to Republicans run longer on average, leaving less time for answers? The data don't answer these questions. But over even an equal number of 10 debates and equal number of candidates, Democrats would have enjoyed almost an hour longer to speak (721 minutes vs 666.)

Let's adjust the speaking time to show which candidates got more than their fair share relative to the time available per candidate per debate. In this case, 100% means the candidate got exactly the "fair share", or 7.6 minutes per debate for Republicans and 9.8 minutes per debate for Democrats. On this scale, leading candidates got up to 140% of their party's fair share, while the lowest share was 63%.

This new scale now removes the differences in total time between parties, and lets us compare relative advantage or disadvantage between parties and candidates. The data are plotted below.

Now that we are no longer confounding differences in total time between parties, new perspectives emerge from the data. The top two candidates in both parties were equally advantaged-- all four got about 140% of the time that an equal time rule would have given them. The previous comparisons masked this due to the shorter Republican times. But relative to a fair division of time, the top two were treated almost identically in both parties.
But the 3rd and 4th places were treated rather differently. In the Republican debates, McCain and Fred Thompson received about 120% of a fair share, while on the Democratic side Edwards and Richardson got only slightly more than a fair share would entitle them to, Richardson at 101% and Edwards at 109%. Based on this share of time comparison, then, the debates treated the Republican race as more of a 4 person contest, while the Democratic debates divided a top 2 from an "average" third and fourth.

The extra shares for leaders must come, of course, from the rest of the pack. Huckabee who now threatens to win Iowa has received only a 96% share of a fair time allocation. The bottom 5 among Republicans all got less than 80% shares. Among Democrats the gap between Richardson and the rest is from 101% to 80.7% and below.

So total time favored the Democrats, but did so even after adjusting for number of debates and debate participants. The separation into top 2 vs 3rd and 4th was especially clear for Democrats. The Republican race gave relatively more time to 3rd and 4th place candidates.

The text of the op-ed only contains four sentences that give interpretations of the data:
The front-running Democrats, thanks mostly to a smaller field (but also to one additional debate), got a lot more time to speak than the front-running Republicans.

Not surprisingly, the times for each candidate seem to follow the polls, with the leading contenders getting more minutes. As Mr. Huckabee’s poll numbers rose, his speaking time increased.

The debates had effects on both voters and candidates. Mr. Huckabee’s performances helped him emerge from the pack, and a few tough moments for Mrs. Clinton set the stage for her eventual fall in the polls.

The first point is right that Dems got more time, as the charts all show. But that advantage wasn't entirely due to fewer candidates and one more debate. The advantage was more real than that: Democrats got more time to speak per debate and per candidate. Changing the graph allows us to see this in a way the pie chart did not.

Also revealed by the charts here are systematic differences between candidates that illuminate the nature of the stratification within and between parties. Front runners are advantaged, but the Democratic race was treated as having 2 clear leaders while the Republican race had 4 apparent contenders, based on speaking time. That too is masked by the pie chart.

Finally, two of Todd's three points above are not addressed by the graphic or the data given. While it is clear that the order of speaking times roughly follows support in the polls, this is not entirely the case. For example Biden has more poll support than Dodd, yet Dodd got slightly more speaking time. (For that matter, and more powerfully, Clinton held a large lead in the national polls during almost all of the debates, yet trails Obama in total time.) Moreover, the dynamic element Todd mentions is not illustrated by the graphic at all. If Huckabee's speaking time rose with his polls we can't see it here. And did Thompson's time drop with his polls? Alas, the op-ed doesn't list these data (which would be quite lengthy.) But a graphic could have illustrated this dynamic aspect of the data in no more space than the pie chart.

Nor does the pie chart provide any evidence of the role of debates in the rise of Huckabee or the decline of Clinton. Did the polls move up or down noticeably following any of the debates? Did candidate time in one debate precede a rise in polls, or did a rise in polls precede more speaking time? We could see these things in a graph, but it would take well more than a thousand words to describe them. The better the graph the more words it is worth.

Wednesday, December 26, 2007

Pollster Variation in Iowa

(LARGE graphs-- you probably should click once or twice to see them at full resolution in order to see the details.)

A new American Research Group (ARG) poll of Iowa has caused quite a debate in the comments at Today Mark Blumenthal takes a close look at polling the "Dark Side of the Moon" in Iowa during the holiday season and the unknowns involved, including the unknowns of the ARG poll. So while the pollsters are busy trying to get one more Iowa poll in this week, let's look at the track records of the pollsters in Iowa.

The chart above shows the polling of the Democratic nomination race in Iowa since January. In 2007, twenty four different polling organizations conducted Democratic caucus polls. Of these, only 7 have conducted three polls or more. That means that for most pollsters, we have no way to separate random error from systematic "house" effects. To do that, we need multiple polls, and to do it reliably we need a number of polls from each organization. But we can at least look at the seven organizations with three or more polls, and see how they compare to the trend estimates. The trend, of course, reflects the best estimate across all pollsters, but until we see the actual vote (itself a very slippery concept in Iowa) we can't say if the trend was better than individual polls or not. Still, this reveals when pollsters seem to follow the trend and when they systematically seem to miss it.

The clear result of the comparison above is that ARG generally showed a much better performance for Clinton than the trend in the first half of the year. From January through June, ARG usually had Clinton some 6-10 points above the trend estimate, with one exception in which ARG agreed almost exactly with the Clinton trend. During this period, ARG was the most discrepant of all pollsters from the Clinton trend.

In the second half of the year, ARG's polling has generally been much closer to the trend estimates, usually less than 4 points away from the Clinton trend. During this time ARG has mixed in with other polling pretty consistently.

That is, until the most recent December 20-23 poll, which again shows a large Clinton deviation of about +6 points from the trend. (I'm using the standard blue trend line. The upturn in the red "sensitive" estimate is interesting, but it is also sensitive to the ARG poll, an example of why you might not entirely trust the red estimator.) This is the first large ARG deviation recently, and quite a change from ARG's previous poll of Dec 16-19 which was close to trend.

In an inversion of the Clinton effect, ARG consistently underestimated Obama's support, compared to the trend, in the first half of the year, but their polling fell much closer to the trend during the second half. At least until the latest poll which has Obama some 10 points below the standard trend. (Again, note the downturn of the sensitive estimator, which would be turning down even without ARG, but which is turning down somewhat more because of ARG.)

ARG's polling for Edwards has been more variable. Early 2007 polling fluctuated quite a bit, sometimes below and sometimes above trend. More recent ARG results for Edwards has generally been a few points below trend, with the latest result about as much below trend as has been "normal" for ARG recently.

ARG's results this year have been more heterogeneous than some oversimplifications claim. There was a substantial overestimate of Clinton early in the year, along with an underestimate of Obama's support. That was important during this period because there were relatively few other polls available for Iowa in this period. But in the second half of the year, the ARG results for Clinton and Obama have been much closer to trend estimates, though still with a small average advantage for Clinton and small disadvantage for Obama.

In light of this, the ARG poll for December 20-23 does look out of line with their own previous polling, certainly their polling of the last 4-5 months.

Let's look at their Republican results for Iowa.

On the Republican side, ARG's results have been especially favorable to John McCain, and to a lesser but still substantial degree to Giuliani. Unlike the Democratic results, these effects have not diminished much in the second half of the year. McCain has often been as much as 10 points above trend, with only one poll below trend and one more right on the trend. No other pollster has been so consistently far from the trend for McCain.

For Giulinai, the results are less far from trend, but still quite consistently above trend. Only 2 of the last 10 ARG polls have Giuliani below trend.

Romney has fared close to trend in the ARG surveys, though on average a bit below trend. The discrepancies for Romney are much less dramatic than for McCain or Giuliani.

The last two ARG polls show shifts of -3 and +4 points for McCain and Romney respectively, and a single point difference for Giuliani. (And a -5 and +6 for Huckabee and Paul.) For the Dems the shifts were +5, -6 and +2 for Clinton, Obama and Edwards respecively.

As Mark Blumenthal notes, the reasons for these discrepancies are largely matters of speculation. But the consistency of the ARG house effects are pretty clear in these data. The ARG results currently stand on the same side as their long term house effects: above trend for Clinton, Giuliani and McCain, and below trend for Obama, Edwards and Romney. Compared to other pollsters, these house effects for ARG appear to be the largest of any polling firm in Iowa.

Friday, December 21, 2007

Comparing Primary Trend Estimates

Lots of exciting movement in the polling in both parties has pushed me to review the bidding on trend estimators. As regular readers know, the "blue" line estimator that is our standard is deliberately tuned to be a bit conservative. It requires a good bit of evidence that a change in direction is "real" before the trend will move sharply. With lots of polling, this estimator has an excellent track record of finding turning points of opinion while not chasing wild geese.

But in a hot primary, with relatively few polls each week (this week has been an exception!) it is reasonable to ask if there is short term change taking place that "old blue" just isn't quick enough to catch. So let's take a look at two alternatives.

Before we go there, let's remember that the variation across polls is quite large compared to some of the changes in support we are talking about. The variation around the trend estimates here is about +/-5 points while the trend differences are often a point or two. That means we are using quite noisy polls to estimate trends that vary much less than do the individual polls. (Mark Blumenthal has spent much of the fall discussing the variation in poll methodology and the implications this has for how uncertain we should be about individual results.)

So let's think of the single most sensitive alternative estimator we could pick: the latest poll. That would certainly move rapidly, and so be "responsive". But it would also reflect individual "house" effects due to polling organization and practices. It would also be highly unstable as an estimate of support, because individual polls vary over that approximate +/- 5 point or more range we see in the plots. In effect, this most sensitive possible estimator would just connect the dots and produce a plot that looks a lot like an earthquake on a seismograph. Lot of noise, but hard to see the systematic trend.

So we'd like to smooth out this random variation (and non-random variation due to house effects). One option is to take a rolling average. The more polls in the average the smoother the result, and you can take your pick of 5, 10 or more polls to smooth over. Of course, the more your include in the average, the more out of date the average is because it includes some polls taken a while back. I've chosen a 5 poll average here, because it should be quite sensitive yet still gain some of the advantages of averaging. Using more polls would smooth more, but defeat the purpose of having an especially sensitive estimate of trend.

The second comparison uses the same "local regression" methodology that is our standard approach here, but sets the degree of smoothing to about half that of the standard blue estimator. This "red line" estimator is more sensitive than the standard, but not as prone to jumping around as the moving average. "Red" should detect short term change more quickly than "blue", but it will also chase phantom changes due to flukes of a few polls that happen to be too high or too low. (The 5 poll average will be even more susceptible to this.)

So what do we see when we compare these estimators in IA, NH, SC and the US?

For the most part, all are in substantial agreement about big trends over the full year. The red line and black moving average show more variation than does blue, and may have picked up some "real" short term change that blue considered noise. But over all the 44 state x candidate x party comparisons, the agreement among estimators is pretty close most of the time.

For the Dems in Iowa, all three estimators are in quite close agreement right now. The differences are in the range of a point of each other. A sharp eye can see some differences of trajectory. For example, Clinton in Iowa is trending down in the blue estimator, while red sees a very recent upward trend while the black moving average fluctuates erratically. But zoom in and the differences are about a half a point or so. My experience is that you just can't reliably estimate such small differences, but feel free to make your own call here.

On the Republican side in Iowa you see similar agreement with small differences near the end. Small differences for Romney and Huckabee are seen in comparing red and blue estimators-- Red and the moving average see a bit of upturn for Romney and downturn for Huckabee in the most recent polls that the blue estimator isn't convinced of. As with the Dems, none of these differences is very large.

In New Hampshire, the picture is essentially the same for the Dems. Blue sees Clinton moving down, Obama up and Edwards gaining more slowly. Red and the MA think Clinton has turned back up in the last few days, while Obama has stalled or turned down. But all these differences are again matters of at most a percentage point difference in estimated current support.

For Republicans in New Hampshire, there are somewhat bigger differences for Romney and McCain, though the trends agree for the other candidates. Red and MA think Romney took a turn down recently by as much as a couple of points, while blue sees a continuing upward trend. The blue and red estimators are still within 2 points of each other, but a real difference in upward or downward momentum would, of course, be important.

For McCain, the latest couple of polls show a substantial spike in support, and red and MA chase that spike, leading to the largest difference we've seen so far among the estimators. All three see McCain gaining, but red puts him about 4 points higher than does the standard blue trend, while MA is a point lower than red.

In South Carolina where there has been less polling and more noise, we see the biggest differences of all. It is worth appreciating what a huge range of results we've seen in recent SC polling for Clinton and Obama. I am not willing to believe that the true level of support has really varied between 20 and 45 points! But this makes the estimation especially tricky (and is why I prefer the stability that the blue estimator provides in the face of extremely noisy polling.

Blue sees Clinton as flat for some while, in the process splitting the difference between some quite high polls and other quite low ones. Either her support has suddently collapsed (but with simultaneous high and low polls) or the best bet is what the blue line estimates. Red and the MA in contrast see a downturn recently from about 43 to about 35, a major drop.

For Obama, all three see an upward trend, but with red and MA moving up much more sharply than blue. Blue puts Obama at 31, while red would go for 35 or 36.

For SC Republicans the big difference is with Huckabee, where red and MA see a very large recent gain, while blue agrees on the sharp trend but doesn't put the support as high yet. Blue puts Huckabee at about 20, while red and MA would go as high as 28.

There are small differences of recent trend for Romney and Giuliani, but these are quite small-- more on the order of the Iowa differences.

Finally, on the national scene, we gain the advantages of more dense polling. The Democratic trends are quite close to one another. And on the Republican side, even the rapid rise of Huckabee is picked up quite well and with close agreement among all three estimators.

The bottom line is that most of the differences we see among the estimators are small-- on the order of a point or two in the estimates. The apparent differences in the most recent trends strike me as generally being too small to reliably distinguish. What constitutes a "real" change in trend is hard to define, but I think most of the current differences are too small to put a lot of faith in.

In the case of the large differences in South Carolina, I'm inclined to pay more attention to the very large spread across individual polls, and demand clearer evidence of change, but the red and moving averages are perhaps telling us that real change is taking place. More polls would help, but in their absence I think a more prudent reading is that it is hard to know exactly what is happening. (And again I'd refer readers to Mark's posts on the differences across pollsters in practices and methods.)

But the bottom line is this is a fun game. I'll be updating with all three trend lines so you can pick your favorite and place your bets accordingly. Starting January 3 we'll begin to see how the polls and the trends line up with actual votes.

Wednesday, December 12, 2007

Bush Approval: Still around 33%

President Bush's approval rating remains about where it has been for several months: 33% plus or minus a fraction. The current trend estimate is 33.2%, including December polling from LATimes/Bloomberg, AP/Ipsos, CBS/NYT, ABC/WP and USAToday/Gallup, the last from 12/6-9/07, finding 37% approve and 58% disapprove.

This now represents one of the longest periods of stable approval for Bush. His presidency has been characterized by a long decline from the post 9/11 highs, interrupted by generally short rallies and spikes due to the start of the Iraq war and the capture of Saddam Hussein. The most important exception has been the long rise in approval starting in March 2004 and continuing through the election in November of that year. The second term has been marked more by long term decline, but with rallies up in late 2005 and the late spring and summer of 2006. Rarely has support simply held stable, neither rising nor falling.

The only period of nearly comparable length was the winter and early spring of 2007, when approval held at a steady 34% for nearly 4 months.

The current plateau at around 33% has now lasted slightly longer, starting a rise in late July and stabilizing around 33% by September. Since that time, trend estimates have varied within less than a percentage point of 33%.

The current polling shows considerable variation, from a low of 28% in CBS/NYT to a high of 37% in the latest Gallup poll (both taken within a week of each other.) The CBS/NYT just barely crosses over into outlier territory in the residuals plot below. Even with these two extremes removed, the remaining polls also balance around 33%.

The final plot below shows that the sensitive "red" estimator is in agreement with the more conservative "blue" standard trend estimate. Neither see much change in recent polls.

If you want dynamic exciting polling, better turn to the primary races.

Monday, November 26, 2007

Zogby Internet Poll Trial Heats are Odd

A new Zogby Interactive poll, conducted using volunteers over the internet, has produced some odd results for trial heats involving Senator Clinton against all four top Republican opponents. What makes this especially odd is that the results are not equally unusual for Obama.

This poll was reported by Reuters' John Whitesides, who also reports on the Reuters sponsored polling Zogby does by conventional telephone methods. The similarities in the reports make it hard to tell, but apparently these results are not part of the Reuters-Zogby polling partnership, but are independent work by Zogby Interactive. Likewise Zogby's website posts the results without mention of who sponsored the work, so presumably Reuters did not.

The Zogby poll was conducted 11/21-26/07 with 9150 respondents who had agreed to take part in Zogby's online polling. This is not a normal random sample of the population. More on the technical issues below.

The hugely surprising result is that the Zogby poll finds Sen. Hillary Clinton losing to all four top Republicans in head-to-head trial heats. What makes that surprising is that Clinton LEADS all four of those Republicans in the trend estimates based on all other polling by between 3.8 and 11.6 points. Zogby also has Clinton losing to Arkansas Governor Mike Huckabee by 5 points. There are too few Clinton-Huckabee trial heat polls from other organizations for me to compute a trend estimate for that comparison.

The chart above shows all the trial heat data from national polling and the estimated trend lines for each pairing. The data points for the new Zogby data are indicated in the charts as "Zogby Inet" in blue for Clinton and red for each Republican.

What is immediately clear is that the Zogby Clinton numbers are well below the estimated trend for Clinton in each of the four comparisons. Clinton is consistently 8-10 points below her trend estimate based on other polling.

In contrast, the Republican results are quite close to the trend estimate in most cases: Giuliani is at 43 in Zogby, with a trend of 44. Romney is 43 in Zogby, 38.3 in trend; Thompson is 44 in Zogby, 41.3 trend, and McCain is 42 Zogby, 42.7 trend. Those Republican numbers are about the kind of normal noise we see around the trend estimate, so don't seem out of line.

Why then is Clinton so far down in comparison to other polls? The Reuters story doesn't note that these results are far from other polling, and instead uses the theme that Clinton is declining to frame these Zogby results:

The results come as other national polls show the race for the Democratic nomination tightening five weeks before the first contest in Iowa, which kicks off the state-by-state nomination battles in each party.

Some Democrats have expressed concerns about the former first lady's electability in a race against Republicans. The survey showed Clinton not performing as well as Obama and Edwards among independents and younger voters, pollster John Zogby said.

While this is certainly a theme of recent reporting, boosted by a pre-Thanksgiving ABC/WP poll showing Obama leading Clinton in Iowa, it is striking that no other poll has found recent results as far from the trend estimates as are Zogby's results and that the Reuters story fails to note that fact.

One answer to why Clinton does so badly MIGHT be that the poll has too few Democrats and thus biases its results. But if that were so, we'd expect Obama to also underperform his trend estimates. That doesn't happen, as the chart below makes clear.

The Zogby results for Obama are all quite close to his trend estimate from all polls:
Zogby has Obama at 46% vs Giuliani, while the trend puts him at 44.3. Against Romney Zogby has Obama at 46%, while trend says 46.6. Against Thompson Zogby has Obama at 47, while trend is 47.0, and against McCain Zogby has Obama at 45 while trend puts him at 43.4.

This is clearly not consistent with a general anti-Democratic bias in the Zogby Internet poll. It is also clear from the graph that the Obama pairings find Republicans doing quite close to the trend estimates as they did against Clinton.

(Trial heats against Edwards are not very common recently, so the Zogby results for him lack much polling for comparison.)

And so we are left with a puzzle: What is it about these respondents that so strongly affects Clinton support but no one else?

We can probably rule out one easy explanation: That Clinton has suddenly collapsed and Zogby is just the first to find it. The reason is internal to the Zogby result. If Clinton really has suddenly become 10 points less attractive, we'd expect all four Republicans paired against her to do BETTER than their trend estimates when facing her. But what happens is Clinton goes down and they don't do any better. That is hard to reconcile with a real change in Clinton's support. (A tortured version would say Clinton must have collapsed among Dems who now say they are undecided while refusing to move towards any of the Republicans. But that isn't usually what happens in real data when one candidate declines sharply. Usually the other moves up at least a bit, drawing not only from unhappy partisans but especially from independents who now are disenchanted with the former front-runner. So while you could make the math work with this story, it doesn't seem very well supported by the data.)

The Zogby Internet polling has a questionable track record in statewide races for Senate and Governor in 2006, where they often far over-estimated the competitiveness of races compared to conventional phone polls taken at the same time. One way to make sense of those problems turns out not to help much here. It is reasonable that the people who volunteer to take political polls over the internet are considerably more interested in politics (and likely more strongly partisan) than is a random sample of likely voters. That should be expected to lead to fewer people with "don't know" responses as better informed and more partisan respondents are likely to both know more about the candidates and to have made up their minds sooner than a proper random sample. That helps explain why Zogby's 2006 internet polls looked as they did.

But this does no good in Clinton's case. What we see is that MORE internet respondents are undecided about their vote between Clinton and four Republicans than the trend estimates based on less involved and partisan phone samples show. The Zogby undecided rates for the Clinton pairings are 20, 17, 17 and 16% (plus 17% undecided in the Huckabee comparison.) The comparable undecided rates based on the trend estimates are 8.2, 12.8, 9.0 and 10.6. That is an average undecided rate of 17.5 in Zogby vs 10.15 in the trends. Likewise the undecided rate is slightly lower for Obama pairings than it is for Clinton: 17, 13, 14, 13, and 14 for Huckabee. How could it be that a sample that is almost certainly more involved, knowledgeable and partisan can be LESS decided about Cinton, the single best known figure in the race? Again, a tortured story might be constructed, but I think a simpler explanation is that this result is not consistent within the Zogby data itself, or in comparison with outside polling.

Where does this leave us? Puzzled. If these results came from voting machines, I'd suspect that something in the ballot design or the recording mechanism caused a modest but consistent undercount of the Clinton support. The effect seems confined only to that one candidate, and not to any others, Democrats or Republicans. And there was no boost in support for the Republicans paired against Clinton. In this case, I'm similarly inclined to wonder if there is the possibility that the Zogby online survey had a glitch that caused a systematic "undervote" for Clinton. Certainly if my research assistant brought me these results, I'd want to check the software for mistakes before I published it.

Let's assume the Zogby organization has checked for any such possible mistakes or glitches and has ruled that out. (One would assume they were as surprised by the data as anyone and since their reputation is on the line, would have checked very carefully before releasing the data.) Is there any reasonable model of how candidate preferences are evolving that might explain this result, and the stability of Republicans paired against Clinton AND the stability of Obama support and that of his Republican pairings?

Without access to the raw data it is impossible to test any speculation here. But here is one possibility: Internet polls, presumably including Zogby's, use weighting to adjust for non-representativeness in their volunteer respondents. (There is a huge debate about whether this, and more sophisticated approaches, can produce generalizable population estimates with good statistical properties, but we'll leave that for another day.) Clinton has more support among women and somewhat older people. Both those groups are likely to be underrepresented in any pool of internet respondents. As a result the responses of those with these characteristics who ARE present in the sample are likely to be weighted up quite a bit to reach population proportions in the weighted sample. If the relatively few older women who are in the sample are ALSO atypical in other ways that both make them volunteer for internet surveys AND be less disposed to support Clinton than are non-internet volunteering older women, then weighting these respondents up won't properly capture Clinton's support and will lead to a systematic underestimate of her support.

That could do it, but it sounds pretty tortured to me.

I'd check the software one more time.

And based on the large outliers the Clinton results produce, I'd hold off on the Reuters headline until I saw some confirmation from other polls.

Thursday, November 15, 2007

Recent polls in IA and NH plus US

I don't have time to write about these, so let's let six pictures do the talking. The blue line is the standard trend estimate, and the red the more sensitive trend.

I've added the names of the last two polls (last three if there is a tie on the date of last interview.) This helps put the latest results in some perspective, both poll vs poll and poll vs trend.

These are relatively high resolution plots so you may need to click once or twice for full resolution.

Tuesday, November 13, 2007

State v. Nation as Mitt leads (IA&NH) , Fred falters

The Republican race has had something for everyone this year. Front runners have faltered (McCain, remember, was the widely declared "front runner" until early spring, though he trailed Giuliani in the vast majority of national polls.) The puzzle of Giuliani's national lead continues to confound explanation in a party of social conservatives. Despite the most visible pre-primary season in history, the leader in IA and NH, Romney, remains less known nationally. The reluctant actor waited in the wings and perhaps missed his scene, certainly entering after his peak. And just to round things out there is an Arkansas governor from Hope who is beginning to be taken seriously and a Texas congressman whose internet strength is disproportionate to his polls.

(A technical note: the blue line in the figures is our standard trend estimator. The red line is more sensitive to recent change, but also less reliable because it can respond to "noise" in the data rather than real changes in trend. It is great for speculation to consider the red line, but safer for prediction to rely on the blue line, which has a better track record over the long run.)

The single most important feature for the Republican race is the discrepancy between state polls in IA and NH and the national polls. Nationally, Giuliani continues to hold a significant lead of nearly 2:1 over his nearest rivals. But in the initial states, Romney has established his own 2:1 lead in IA and a smaller 8 point lead in NH, while Giuliani struggles in IA and has remained basically flat in NH. This sets up Romney to run a classic momentum campaign based on two early successes to carry him to national prominence and through the second round of pre-February 5th primaries and caucuses.

The Iowa data in the top chart shows Romney's early success there, reaching 20% by April 1, when his national support was a modest 8%. Romney has now built his support to nearly 29% in Iowa, a significant lead over his rivals there, though not enough to dominate the race. Meanwhile he is at less than half that (12%) nationally.

Romney demonstrated his organizational strength by winning the Iowa straw poll back in August. But that story also demonstrated a potential problem for him. The straw poll win would have been news to many Republican primary voters outside of Iowa, where Romney still needs to build his visibility and support. But the press corps (and pollsters) strongly discounted his win as "expected", and focused instead on the narrow second place finish of Mike Huckabee, well behind first place. This seems to be the danger for Romney in January. He has carefully built a strong Iowa presence and support and if the election were held today would probably win (you do believe these polls, right?). That would be big news to lots of voters, and should dominate the headlines. But Romney's lead in IA has become conventional wisdom among reporters and a win is likely to be treated as the straw poll win-- news, but not surprising. The surprising second place finisher would be Huckabee, based on current polls, and that would likely be the bigger story from Iowa.

The rise of Mike Huckabee in Iowa is correctly seen as a big polling story. With limited money Huckabee has climbed into second place in the Iowa polls, and currently enjoys the sharpest upward trajectory of any Republican candidate there. While still well behind Romney, a Huckabee defeat of both Giuliani and Thompson would be legitimate "big news", and could propel the former Arkansas governor to the kind of national momentum he must have to compete after Iowa. His current trajectory is getting him noticed more, and his second place standing probably deserves even more attention than it is currently getting. Coupled with Thompson's failures, Huckabee's ascent could be come a major asset.

The other bit of news from Iowa is the failure of the Thompson campaign to launch. For all the high expectations built up in the pre-campaign campaign of Thompson, Iowa voters have failed to respond. The trend has even taken a bit of a turn down in recent weeks. At only about 12% support, Thompson trails Huckabee and Giuliani.

And the picture only gets worse for Thompson in New Hampshire where his trajectory looks like a failed rocket launch, now at less than 5% support.

It is debatable whether Giuliani, as national leader in the polls (see below) can survive losses in Iowa and New Hampshire. It seems even more unlikely that Thompson, who is falling nationally as well, can survive two poor early finishes.

This morning's news is that Thompson will receive the endorsement of the National Right to Life Committee, a potentially important boost to his campaign. The organizational strength of Right to Life organizations could be a significant advantage, and might help Thompson secure the status of "choice of social conservatives". However a consensus candidate of social conservatives has yet to emerge, as demonstrated by the scattered endorsements we saw last week. If Thompson is to secure that standing it will come despite his standing in the polls, rather than because of it. Certainly the fear of other Republicans that Thompson would be the late arrival who swept all before him as not materialized.

And then there is John McCain, who has been all but written off by analysts, including me. Yesterday's news that McCain may actually borrow money to finance his campaign through the early caucuses is further evidence that the analysis is not wrong, at least in an organizational sense. McCain's campaign not only lost most of its staff, it has failed to raise money and is back to the days of the bus. Voters, however, haven't entirely gotten that message. McCain's long decline in the polls halted in the third quarter and has made a small gain nationally. A similar rebound may also have occurred in New Hampshire (but only in the more sensitive red estimator.) Still, at 15% there, McCain would be a distant third place, hardly a strong foundation to relaunch a campaign despite previous success in NH. And in Iowa, never his strong suit, McCain is at a dismal 7%, despite his line that he "drinks a cup of ethanol before breakfast every day".

The contrast between Giuliani as national poll leader, while Romney dominates in the first two states, and a possible late emergence of a relative unknown in Huckabee, sets the stage for a candidate to "emerge" from Iowa and New Hampshire. The Giuliani campaign still banks on a "firewall" in Florida and a great February 5th to maintain his campaign, and some chance that a convincing 2nd place in New Hampshire will keep him strongly in the game. For Thompson, South Carolina looks to be his best bet, though he is currently only tied with Giuliani for first place there, and is declining there as well. (A SC win for Giuliani would be huge, of course.) And Romney has had two good a two mediocre polls in SC recently, leaving it unclear if he is moving up there or not. McCain still needs a miracle. But Huckabee has moved in Iowa strongly and a little bit in New Hampshire. Elsewhere he will live or die based on those two states.

As a spectator sport, the Republican race this year has something for everyone, and is vastly entertaining. I can't wait to see what happens next.

Monday, November 12, 2007

Did Clinton take a hit after the debate?

Since the October 30 Democratic debate, political conversation has focused on how much Sen. Clinton may have been damaged by her first "rough" debate performance. After uniformly positive evaluations of her handling of previous debates, especially in August and September, Clinton stumbled with answers that her rivals portrayed as waffling and inconsistent.

This weekend two new New Hampshire polls appeared that lend credence to the notion that Clinton's standing has taken a dip, though whether due to the debate or not remains "debatable."

The Boston Globe and University of New Hampshire found Clinton falling to 35% 11/2-7/07 from 41% in the CNN/WMUR/UNH poll of 9/17-24/07. Obama had a small rise, to 21% in the latest from 19% in the earlier poll.

Meanwhile, the Marist College poll taken 11/2-6/07 put Clinton at 38%, compared to 43% in Marist's previous reading 10/4-9/07. Obama gained five points over those two polls, to 26% from 21%.

Finally, a Rasmussen "robopoll" taken on 11/5/07 has Clinton at 34%, down from 40% in their 9/16/07 poll. Rasmussen also has Obama rising to 24% from 17%.

So on the basis of these three polls, and "apples-to-apples" comparisons of polls done by the same polling organization, there is pretty good reason to think Clinton has dropped a few points in New Hampshire, and that Obama has gained a few. The Clinton average change in the three polls is -5.7 points, and Obama's gain is 4.7 points.

If we turn to the trend estimates, based on all the polling rather than just the last three, we see a different but still interesting picture. The vertical black line in the charts marks the date of the debate.

With just three new polls, the standard trend estimator will respond to the new polls, but won't "bend". The blue trend is deliberately conservative, and wants more evidence that the trend has actually turned down before it will change direction. However, the level of the estimated trend does respond to new data. For example, on Friday with Rasmussen included but not the Globe/UNH or Marist results, Clinton's trend estimate was 40.2%. With the new polls it is down to 39.3%. Likewise Obama was at 21.0% on Friday and is now at 21.7%.

But the standard estimator may be too conservative. So we have a second estimator that picks up changes more quickly, though it can fall victim to noisy data and "see" a change when there isn't really one. So with some risk, it is fun to compare the more sensitive "red" estimator with the standard "blue" one.

Red reveals two interesting details not visible in the blue trends. Clinton appears to have flattened out, at least, starting in late September. Obama had a noticeable dip in August-September, and since that time has been trending up for over a month.

If we put a VERY sensitive estimate on the Clinton polls, we would even see a parabola shaped trend, one that rose sharply in September and early October, then fell equally sharply in November. This amounts to just connecting the polls, and ignoring all the noise and house effects present, something I am loath to do.

But even being a bit cautious there is evidence that Clinton's good rise (about 5 points) in the third quarter has stopped and perhaps dipped a tiny bit in the fourth quarter so far. If more polls come in where the last three have, then even the blue standard estimator will flatten and turn down. Meanwhile the sensitive red estimator may be prone to chase the latest polls a bit too much. But it's suggested path for the dynamics of the race is neither as foolish as chasing each poll, nor as slow to notice change in trends as the standard estimator. "Red" may have something here.

The story for Obama is also more hopeful in the red estimator. The few low polls in late August through late September suggested a slump down to the mid-to-upper-teens. The sensitive estimator catches this dip, but sees a steady rise since, to nearly 24% now.

From the point of view of even the sensitive estimator, the changes affecting both Clinton and Obama pre-date the October 30 debate, though the estimate is influenced by the three post debate polls. The story "red" tells is that Clinton had a very good third quarter-- good news about her campaign, it's strength, and her good debate performances-- helped raise her New Hampshire standing by five points. Perhaps the same news, or reviews of his failure to make progress, helped sink Obama's support about 4 points during the same third quarter. But since October 1, these patters have changed, with Clinton seeing no further gains and Obama returning to the mid-20s.

Before reaching too strong a conclusion, let's check some other data, and see if we can find any evidence for similar changes in trend in other data.

In Iowa, where they watch the candidates at least as closely as in New Hampshire, there is no evidence of a flattening of the Clinton trend. If anything, the red trend estimate is slightly higher than is the standard blue estimate (30.5% vs 29.9%). Clinton has climbed steadily since the start of the third quarter and both red and blue estimates put that trend at almost the same rate.

Obama has also seen gains since the start of the third quarter in Iowa, though the red estimate thinks the gains started from a bit lower level. At present the two trends agee quite closely, 24.8% for blue and 24.5% for red.

(The Edwards and Richardson campaigns have both suffered losses since the start of the third quarter in Iowa, though slight or no losses in New Hampshire over the same period.)

If we look at the national picture, we see a substantial Clinton rise in the third quarter (with a plateau midway, followed by a surge) and a mild decline for Obama, reversed only at the start of the fourth quarter. The sensitive estimator matches the standard trend pretty well, certainly leading to the same conclusions.

As my partner at, Mark Blumenthal, pointed out in an important post last week, New Hampshire and Iowa are not typical of the nation as a whole and are being exposed to vastly greater advertising and campaign appeals. Citizens there are also paying more attention to the race, given both advertising and their prized "first in the nation" status. So if we are going to detect changes in the fortunes of candidates, these two states are the best places to look. And when we do, we see some evidence of change but only in New Hampshire.

As always, more data can lead to a reconsideration, but at this point I think the evidence favors a view that Clinton's problems in New Hampshire may be more specific to that state rather than reflecting a more widespread change in her campaign's fortunes. New polling for Iowa could change that. At the moment we only have one post-debate poll from Iowa so the trends there are almost entirely driven by earlier data. But the 5 post-debate national polls are included in the national estimate with no effect, so that is some evidence that any impact is still to develop.

Sen. Clinton may have given her opponents an opening in the last debate. It remains up to them to exploit that opening to their advantage, and up to the Clinton campaign to deflect such critiques. At the moment the New Hampshire polls suggest some changes in that state. But not yet elsewhere.

Thursday, November 08, 2007

Bush Approval: Trend 32.6%

New polls: Marist/WNBC (10/29-11/1/07) Approve 34%, disapprove 58%; Gallup (11/2-4/07) approve 31%, disapprove 64%; NBC/WSJ (11/1-5/07)approve 31%, disapprove 63%.

With these new polls, the trend estimate moves to 32.6%. The rise in approval since June has now clearly leveled off and is perhaps starting slightly down. Both the conservative blue trend estimate and the more sensitive red line agree on both the level of the trend and its recent changes.

After a flurry out both high and low outliers in recent weeks, the current crop of polls are generally falling within the 95% confidence interval around the trend. The last 6 polls are all quite close to the trend estimate.

Tuesday, November 06, 2007

U. S. Monthly Deaths in Iraq

I wrote yesterday about changes in opinion of the Iraq war. In the process I said that the death toll is rarely presented in systematic form by news coverage. Totals, or totals for the month are frequently mentioned, but seldom in the context of the entire war. Likewise, yesterday's news story was that 2007 has now become the costliest year, with more U.S. deaths than in any previous year of the war. So let's take a little of our own medicine and put the monthly totals in context.

The last two months have indeed seen substantially fewer US losses than any previous months in 2007. April, May and June produced exceptionally high casualty counts with only 5 previous months reaching the same level of over 100 deaths. In contrast, October casualties fell to under 40 deaths, a low matched in only 7 previous months.

But looking at the last 12 months, it is really only September and October that have been well below recent casualty rates. There is some visual impression of a sharp decline since May, but that is deceptive since May was the third highest death toll of the entire war.

The bottom line: deaths have declined recently and especially in the last two months. But that decline is from very high levels compared to the rates in the entire war. Even the "lower" September rate is actually in the middle of rates for the war as a whole.

There is a lot of month-to-month variation in the death rate. That makes it a bit hard to see the systematic trend in the midst of the variability. The plot below shows the trend in deaths, abstracting out the noise of month to month variation.

We see three clear phases. After the invasion, deaths fell to about 45 per month and stayed there until early 2004. Then the rate increased over a period of about 4-6 months to a new and more intense rate of about 67 deaths per month. This became the status quo death rate for the second half of 2004, all of 2005 and the first half or so of 2006. Late 2006 saw an increase which peaked in the first half of 2007, with an apparent fall since. The current trend estimate stands at the low 60s, not much different from the 2004-2006 level. Unless the very low casualty rate of October becomes the new norm, we are back to about where we have been since mid-2004. It seems more likely that October will prove to have been unusually low and November and subsequent rates will return to around 60 deaths per month. (This is a statistical, not a military judgment. At the moment, October looks out of line with the rest of the data, so a good statistical guess is that subsequent months will be closer to the trend. Of course if conditions or tactics have changed in ways that actually reduce the risk, then casualties can remain near October's low level.)

Yesterday my point was that opinion on the war has turned somewhat more positive, but that while changes in the "objective" facts of the war might contribute some to that shift, the stronger driver of opinion was political debate from Washington. Looked at over the entire course of the war, there have been large month-to-month changes in the casualty rate. Opinion on the war shows no evidence of such high variability, as it should if opinion of the war simply and directly mirrored contemporaneous casualty rates. Rather we've seen a pretty consistent long run decline in positive views of the war, but in 2007 a flattening of the trend followed by a recent rise in positive views of the war. Those changes came despite the substantial rise in casualties in 2007. There is little evidence of a direct link of opinion to current casualty rates.