According to the just-released State House News poll, each of the three Democratic candidates for Governor is heavily favored over [OK! OK! -ed.] would handily beat Kerry Healey if the election were held today.
Gabrieli vs. Healey: 47% – 26%
Patrick vs. Healey: 43% – 30%
Reilly vs. Healey: 38% – 30%
In a poll whose margin of error is 4.8%, those numbers are close to indistinguishable. The truth is that each Democrat is more than capable of beating Kerry Healey. So vote for the guy who represents your values. You know, the one who you really want to win. And then do everything you can to help him beat Kerry Healey in November. They’re all eminently electable.
Oh, and in case you were wondering, these numbers are great news for Deval Patrick!
David, I thought it was you who earlier pointed out that a September (or October) lead for the Democrat is irrelevant.
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O’Brien had 12 point lead 4 weeks before 2002 election, lost by 10.
Right now, based on what we know, there’s no discernable diffeerence. It’s best to vote your gut, not make any strange rationalizations. The truth is we don’t know how any of them would do better than any others. Well, we know that Tom Reilly is prone to campaign gaffes, so that certainly doesn’t help him… but even in Reilly’s case, he’s still odds on to be able to beat Kerry Healey if nominated.
One point is that there’s no difference, vote your gut. No beef with that. I just disagree that there’s no difference in electability, but your view is totally fair.
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What I disagree with is that any Dem is currently HEAVILY FAVORED against Healey.
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I thought David’s earlier point was precisely that drawing the “Heavily Favored” from a September poll is WRONG.
In a poll whose margin of error is 4.8%, those numbers are close to indistinguishable.
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And Austraila was like, “WTF mates?”
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With a moe of 4.8%, the poll shows that all three have a statistically significant lead on Healey. But, those numbers are far from indistingushable. It can be said with (95%?) confidence that the gap Gabs beats Healey will exceed the gap that DP beats Healey, and that the gap DP beats Healey will exceed the gap that TR beats Healey.
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The concusion for all three sets of numbers is the same: Democratic victory. However, those three sets of numbers are not close to indistinguishable — they are quie distinguishable, statistically speaking.
The margin of error is not 4.8%. The margin of error is PLUS OR MINUS 4.8% for any given candidate’s support.
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A reported Gabrieli vs. Healey: 47% – 26% and Patrick vs. Healey: 43% – 30%
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means it could be anywhere from
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Gabrieli 52% to Healey 21%
to
Gabrieli 42% to Healey 31%
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and
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Patrick 48% to Healey 25%
to
Patrick 38% to Healey 35%
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See that within the given margin of error, Patrick could actually have a greater lead over Healey (48-25) than Gabrieli does (42-31) (for the unknown confidence level, I agree with you, usually 95%. Also, please allow me to round to 5% instead of 4.8%, fractions in this context are annoying)
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A +/- margin of error for each candidate’s level of support does NOT translate into that same MOE for the lead! From the American Statistical Association’s explainer on Margin of Error:
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The difference between two uncertain proportions (e.g., the lead of one candidate over another in a political poll in which both are estimated) has more uncertainty associated with it than either proportion alone. Accordingly, the margin of error associated with the lead of one candidate over another should be larger than the margin of error associated with a single proportion, which is what media reports typically mention (thus the need to keep your eye on whats being estimated!).
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Until media organizations get their reporting practices in line with actual variation in results across political polls, a rule of thumb is to multiply the currently reported margin of error by 1.7 to obtain a more accurate estimate of the margin of error for the lead of one candidate over another. Thus, a reported 3 percent margin of error becomes about 5 percent and a reported 4 percent margin of error becomes about 7 percent when the size of the lead is being considered.
How much electronic ink was spilled around here insisting that a Patrick lead just a fraction outside the MOE, or sometimes even within the MOE, was a bona fide, real, unassailable lead? Remember???
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And now a 21-point lead is nearly indistinguishable from a 13-point lead when the MOE is 4.8%???
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Don’t make me write more question marks, because I will if I’m backed into a corner.
Take out the buggery and that’s me in a nutshell.
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Help! I’m in a nutshell! How did I get into this bloody great big nutshell? What kind of shell has a nut like this?
If the poll has a 4.8% MOE, that number applies to the support percentage of an individual candidate, NOT when you’re trying to compare the lead in one pair of matchups against another. That has a much larger margin of error.
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Here’s why.
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In any given poll, there is most certainty for any one candidate’s support percentage.
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The uncertainty is higher when you are talking about the LEAD one candidate has over another candidate. That’s because you are combining two uncertain numbers (the support of each candidate) to create an even less certain number.
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In my post above, I note that the American Statistical Association says to multiply a poll’s margin of error by 1.7 to get a reasonable MOE for the lead one candidate has over another candidate.
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But in this case, you’re NOT comparing the support for one individual candidate (the most certain) over another. You’re comparing the LEAD of each PAIR of candidates — two less certain numbers.
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I don’t know what the multiplier is to get the correct margin of error when comparing two different leads to get the difference. But for the sake of argument, I’m going to assume that one is also 1.7.
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Here’s what would happen.
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Margin of error for each of the candidate’s support level: 4.8%.
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Margin of error for the lead each potential Democratic nominee has over Healey: 4.8 x 1.7. That’s 8.16% margin of error for either of those leads.
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But now, you want to compare each of those leads to create a third level — who’s got the lead in leads. If you assume another 1.7 multipler, that’s 8.16 x 1.7 — 13.872% MOE. Way more than the difference between a 13 and 21 point lead.
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It’s been a long time since my political statistics course, maybe someone who knows how to calculate margin of error for comparing leads can jump in here. But it’s totally plausible to me that the difference between Patrick and Gabrieli LEADS over Healey would be well within the margin of error in this poll. And I’m sure (95% confidence level) that taking the 4.8% MOE in this poll and applying it straight to comparing the Gabrieli-Healey and Patrick-Healey matchups is statistically invalid.
I’m sorry, but I’m not going to read this long, math-filled comment. A quick glance suggests you’re trying to argue a 21-point lead is not better than a 13-point lead.
then I suggest you stop misusing them to argue your point. You do not fully understand the concept of margin of error. You can’t simply take the number as it applies to one aspect of the poll, and pretend it applies to the part of the poll you want it to. You look at “4.8%” and think that applies to every number and every possible set of comparisons in the poll. It doesn’t! My point would be exactly the same even if the difference between the Gabrieli and Patrick matchups was outside the CORRECT margin of error. I’m a numbers geek. Seriously. So it bothers me when people toss around statistics without fully understanding how they work.
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Frankly, I don’t think polling on hypothetical general-election matchups before the primary are worth much in any case. Unlike many here, I’m not going to get worked up over size differences in early September. Healey hasn’t had a chance to unlease her attacks on the nominee (and I’m concerned Gabrieli will be vulnerable to a charge of total lack of government experience of any kind); while the nominee hasn’t had a chance to frame his campaign for the general. There haven’t been head-to-head debates. Non-primary voters probably still haven’t started paying attention.
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It’s a snapshot in time, and the time isn’t nearly as important as next month will be. Without question, I’d rather my guy be farthest ahead – if nothing else, it looks good, since most of the media as well as the voters do not understand how to interpret the numbers. But I’m content enough that everyone’s ahead of MOE.
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My issue here is helping people understand what they’re talking about. Since this is a site for political junkies, I thought people might actually want to delve more into the numbers to understand them. Sorry you’re not interested. It would be fair to argue that a result at the outside edges of an uncertain MOE still carries some meaning. But to be OK with a 4.8% margin of error and outraged at a 13% margin of error properly calculated is kind of silly.
but your analysis is incorrect.
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First off, simply because the margin of error is 5% (or whatever) with 95% confidence doesn’t mean that it is equally likely that, given the poll numbers above, that Gabrieli is anywhere from 42% to 52%, and Patrick is anywhere from 38% to 48%. These are all numbers that are POSSIBLE given the MOE, but Gabs having the reported 47% is far more likely than having 42% or 52%. Your post makes it seem like all numbers within the range are equally likely, which is false.
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This is the same fallacy that you see all the time in the media. A race in which one candidate is winning 51% to 49% with a 4% MOE at 95% confidence is NOT a “statistical dead heat” as commonly reported. It is a close race, for sure, and the 49% candidate very well could be winning. Nevertheless, the most likely scenario, even with the MOE at 4%, is that the 51% candidate is indeed winning by 2%. Thus it is not a “statistical dead heat” — it is a likely real lead for that candidate.
did I say that the all the possible numbers are equally probable. Can you please read what I wrote before you criticize? I understand that all numbers aren’t equally likely, just as you pointed out. Did you get to this part? “It would be fair to argue that a result at the outside edges of an uncertain MOE still carries some meaning.” What you said. We don’t disagree here.
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What bothers me is pretending a 4.8% margin of error for an individual candidate’s support means the same number applies when comparing the lead for two different candidate matchups. IT’S NOT. That’s a larger margin of error.
and, yes, I stand by the fact that you were mistaken.
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You quite explicitly stated in your first post that the difference between Gabs’ and Patrick’s leads was not significant. This is similar to when the media claims that a 51% to 49% poll finding is “not significant” because it’s within the margin of error. This is a fallacy and I explain why above.
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I agree with your use of the x1.7 multiplier for determining the MOE of the leads as well as your observation that the general election is 2 months away (making these polls less reliable for future use), but to say that Gabs’ bigger lead over Healey than Patrick’s is “insignificant” is incorrect.
My first post on the subject is here. WHERE do I “quite explicitly” say the difference is “not signficant.” You keep using those quotation marks about “significance” and “insignificance,” but I didn’t use either “significant” or “insignificant” in ANY of my posts on this. Do a search on the entire page of threads for “signif” if you don’t believe me. Please don’t put words into my mouth (or fingers) that I didn’t use. If you’re going to claim I’m wrong, please respond to what I actually wrote instead of what you or someone else think I wrote.
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I said the difference is within margin of error. YOU are jumping to the conclusion that saying it’s within margin of error somehow means I’m saying it’s “insignificant.”
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I said this: “See that within the given margin of error, Patrick could actually have a greater lead over Healey (48-25) than Gabrieli does (42-31).”
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I did NOT say this means that it’s JUST AS LIKELY Patrick’s lead is bigger, as another post implied. I’M SAYING IT MEANS IT’S WITHIN MARGIN OF ERROR. Yeesh. People are jumping to conclusions here just because I’m a Patrick supporter.
The guy you responded to stated: “The concusion for all three sets of numbers is the same: Democratic victory. However, those three sets of numbers are not close to indistinguishable — they are quie distinguishable, statistically speaking.”
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You title your response “I don’t think so” and go on to present numbers claiming that Patrick could indeed have the greatest lead. Not sure why else you meant by that.
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In any case, I’m glad that you now agree that Gabs’ greater polling lead vs. Healey is significant, because it is.
Are you sure you’re “seriously” a “numbers geek”? You prefaced your calculations by admitting, “I don’t know what the multiplier is to get the correct margin of error when comparing two different leads.” Then you ended your comment by saying, “It’s been a long time since my political statistics course, maybe someone who knows how to calculate margin of error for comparing leads can jump in here.” Thanks for “helping us understand” what we’re talking about.
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My original reference to MOE was not to do statistical analysis, but to contrast how Deval supporters used it here to how they used it when Deval had a small lead. Back then, they were 95% certain the lead was real. Now, a big gap in vs.-Healey #s is somehow eclipsed by the MOE and “the electability issue is fading.”
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They should enjoy this week’s polls but refrain from trying to stomp out, Ministry of Information style, all other data.
doesn’t mean I claim to know everything. I don’t. But I’m sure I know SOMETHING.
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In any case, if Deval’s “small lead” was within the margin of error and people here were claiming it was meaningful, and those same people are now saying that this lead is not meaningful, then I understand your frustration. But I was never one of those original posters you are talking about. I’m relatively new to this site, but I think the point of the posts here is to say that if everyone would beat Healey by a greater than MOE, then the electability issue is fading since the “electability” objective is to win. Usually electability refers to one candidate being able to win while another one wouldn’t. (In 2004, I recall that Kerry supporters argued he was the most likely to beat Bush, not that any Democrat could beat Bush but Kerry could beat him by the largest amount.) If any candidate would win a theoretical matchup, why worry about “electability” when there are so many other things to take into account? I understand you might disagree when the big reported lead belongs to the candidate you favor, but to other voters, “clearly could win” is enough and they don’t need “maximum possible polled lead.” The fact that I believe the differences in those leads are probably within margin of error makes it even less important to me.
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But this is all assuming one thinks that a poll taken before the primary has great bearing on what would happen in November. It’s heartening to see all the Democrats doing so well, but I always doubt polls taken too far in advance of anything — not necessarily because they’re not accurately reflecting the moment, but because opinions change. Two months is a long time when the final matchup isn’t even set. Based on how much the polls have changed over the past two months in the Democratic primary, I really don’t see how we can expect any numbers — even 100% certain ones for this snapshot in time — to hold constant over the next two.