Math matters

Hey Chris… what the hell is up with that headline?  Um, “so far, so good” for whom?

So far, so good on anti-gay rights measure signature check

The secretary of state’s office said Monday evening that it has completed its second day of checking signatures on Referendum 71 – the attempt to repeal Washington’s “everything but marriage” same-sex domestic partner law.

So far the error rate is low, 12.31 percent.

R-71 proponents turned in 137,689 signatures – 14 percent more than the minimum needed to be placed on the November ballot. Whether Referendum 71 will ultimately qualify is still unclear.

As of Monday state election workers had checked 11,502 signatures, and 10,087 have been OK’d with 1,415 rejected, mostly because the person does not show up on the voter rolls.

Okay, let me explain this for my friends in the media one last time. Juxtaposing a 12.31 percent invalidation rate versus that widely quoted 14 percent cushion tells the reader absolutely nothing. In fact, it misinforms by implying that signatures are being invalidated a full 1.69 percent below the maximum rate, when in fact the actual maximum invalidation rate beyond which the measure fails to qualify for the ballot, the signature cushion divided by the number of signatures submitted, is 12.43% (17,112/137,689).

Math matters.

In fact, math matters so much that it can give us valuable insight into the true prospects for R-71… prospects which, given the latest batch of numbers, don’t look so good so far for R-71′s sponsors.

Without adjusting for the exponential increase in duplicate signatures as the sample size increases, the invalidation rate on the first batch of 5,646 signatures was 11.34 percent, while the invalidation rate on the second batch of 5,856 signatures rose to 13.35 percent… not exactly what R-71 backers were hoping for. I’ve yet to see a breakout of duplicates in the second batch, so I can’t refine our 3 to 3.25 percent projection of the duplication rate for the entire universe of signatures, but when adjusting the combined 12.31 percent rate from the 11,502 signatures checked thus by the number of duplicates projected from the first sample, we’re now looking at a total invalidation rate in excess of 15 percent. Which would be pretty typical for a petition drive using a mix of volunteer and paid signature gatherers.

To put that in perspective, should these trends hold up, R-71 would fall short of the 120,577 minimum by over 3,500 valid signatures, or nearly 3 percent.

Failing by 3 percent is a lot different than passing by 1.69 percent, dontcha think? Like I said, math matters.

Speaking of which, it doesn’t take much more data to declare R-71′s failure a near statistical certainty, whatever the final margin, and Darryl will run some simulations as the next few batches come in. But honestly, this measure is toast.

UPDATE:
The SOS has broken out the dupes from yesterday’s batch: 16… which is roughly along the lines of what would be expected, as the percentage of dupes increases with the total sample size. (There were 7 dupes in the first, slightly smaller batch.) Darryl’s simulations are more accurate, but my rough calculations now project a roughly 2.4% duplication rate. Combined, this comes to about an adjusted 14.5% invalidation rate across the two batches, well above the maximum 12.43% rate needed to qualify.

Comments

  1. 1

    Roger Rabbit spews:

    I not only refused to sign this bigot petition, I also told the signature gatherer to “go to hell,” in those precise words.

  2. 2

    jeff spews:

    The increase in the number of duplicates signatures should be quadratic, not exponential.

  3. 4

    spews:

    The odds are pretty great against the invalidity rate differing that much between these large batches (11.34% in one batch of 5,645 signatures and 13.35% in another batch of 5,856). Probably the impact of the growing rate of duplicates is happening, and some of the valid signatures in the first batch had duplicates in the second batch. Or, these are not random samples.

  4. 5

    spews:

    Rob @4,

    These are not random samples, and while part of the difference can be explained by the growing number of duplicates, it’s likely less than a quarter of a percent at this point.

  5. 6

    spews:

    Yes, I just saw on the SofS website that these are not random samples. So, we can’t make projections from them. I guess we just have to wait and see…

  6. 8

    rhp6033 spews:

    Just a note – if a lot of those signatures are being collected in local churches, the duplicate error rate might actually be lower than average. That’s because the signature gatherers are probably volunteers who know the people signing the petition, and would discourage duplicate signings.

    Paid signature gatherers hanging around outside the local grocery store, however, are another matter.

  7. 9

    Lurleen spews:

    SOS has posted the dupes from yesterday:

    David Ammons says:
    August 4, 2009 at 9:27 AM

    Due to popular demand — the breakouts! yesterday’s number of signatures checked was 5,856, with 5,096 accepted and 760 rejected. there were 16 dupes, 40 no match of petition signature with what’s on file, 682 not found on voter registration database, 22 listed on the database as registered voters but missing a signature on the database and we’re checking back with the counties.

    the cumulatives as of close of biz yesterday: 11,502 checked, 10,087 accepted, 1,415 rejected, including 23 dupes, 81 no match, 1,274 not registered voters, 37 missing signature and we’re checking.

    Some of the final category, missing signature on the state database, can be shifted over the the accepted pile once we hear back from the counties involved.

  8. 10

    spews:

    Lurleen @9,

    I’ve updated the post to reflect the new data. It looks like a duplicate adjusted 14.5% invalid rate for the moment.

  9. 11

    uptown spews:

    Is it just me, or does the new PI seem to be sliding to the right? Seen several posts with misleading headlines about Healthcare reform.

  10. 12

    jeff spews:

    Goldy @3,

    If the SOS has checked 10% of the signatures then they have likely found about 1% (.01=(.1)^2) of the errors. More generally the fraction of the duplicates that they have found is about the square of the fraction of signatures they have checked. If they have checked p percent of the signatures the they have found about 100(p/100)^2 percent of the duplicates. Quadradically means that the percentage is in the base and the exponent is 2. If it were exponentially in the percentage of signatures checked then the formula would look like 2^p.

    A lot of people use exponentially when they mean faster than linearly so I normally wouldn’t comment your choice of words. But in a post called Math Matters it is best to use the proper mathematical term.

    Thanks again for trying to get the press and the public to use mathematics properly.

  11. 15

    spews:

    Jeff @ 12, thanks for the formula. Of course, it assumes a random sample. If the signatures are being checked in some sort of geographic order, the early duplicate counts would be skewed upward (I think).

  12. 16

    manoftruth spews:

    you all make me laugh. i thought you didnt want any kind of check, id or otherwise when you came to voting. you people are so stupid, you dont even see your own hypocracy.