Posts from October 2016 (37)

From the Herald (via Mark Hanna)

Warnings about feeding bones to pets are overblown – and outweighed by the beneficial effect on pets’ teeth, according to pet food experts Jimbo’s.

and

To back up their belief in the benefits of bones, Jimbo’s organised a three-month trial in 2015, studying the gums and teeth of eight dogs of various sizes.

Now, I’m not a vet. I don’t know what the existing evidence is on the benefits or harms of bones and raw food in pets’ diets. The story indicates that it’s controversial. So does Wikipedia, but I can’t tell whether this is ‘controversial’ as in the Phantom Time Hypothesis or ‘controversial’ as in risks of WiFi or ‘controversial’ as in the optimal balance of fats in the human diet. Since I don’t have a pet, this doesn’t worry me. On the other hand, I do care what the newspapers regard as reliable evidence, and Jimbo’s ‘Bone A Day’ Dental Trial is a good case to look at.

There are two questions at issue in the story: is feeding bones to dogs safe, and does it prevent gum disease and tooth damage? The small size of the trial limits what it can say about both questions, but especially about safety.  Imagine that a diet including bones resulted in serious injuries for one dog in twenty, once a year on average. That’s vastly more dangerous than anyone is actually claiming, but 90% of studies this small would still miss the risk entirely.  A study of eight dogs for three months will provide almost no information about safety.

For the second question, the small study size was aggravated by gum disease not being common enough.  Of the eight dogs they recruited, two scored ‘Grade 2’ on the dental grading, meaning “some gum inflammation, no gum recession“, and none scored worse than that.   Of the two dogs with ‘some gum inflammation’, one improved.  For the other six dogs, the study was effectively reduced to looking at tartar — and while that’s presumably related to gum and tooth disease, and can lead to it, it’s not the same thing.  You might well be willing to take some risk to prevent serious gum disease; you’d be less willing to take any risk to prevent tartar.  Of the four dogs with ‘Grade 1: mild tartar’, two improved.  A total of three dogs improving out of eight isn’t much to go on (unless you know that improvement is naturally very unusual, which they didn’t claim).

One important study-quality issue isn’t clear: the study description says the dental grading was based on photographs, which is good. What they don’t say is when the photograph evaluation was done.  If all the ‘before’ photos were graded before the study and all the ‘after’ photos were graded afterwards, there’s a lot of room for bias to creep in to the evaluation. For that reason, medical studies are often careful to mix up ‘before’ and ‘after’ or ‘treated’ and ‘control’ images and measure them all at once.  It’s possible that Jimbo’s did this, and that person doing the grading didn’t know which was ‘before’ and which was ‘after’ for a given dog. If before-after wasn’t masked this way, we can’t be very confident even that three dogs improved and none got worse.

And finally, we have to worry about publication bias. Maybe I’m just cynical, but it’s hard to believe this study would have made the Herald if the results had been unfavourable.

All in all, after reading this story you should still believe whatever you believed previously about dogfood. And you should be a bit disappointed in the Herald.

Each week, we would like to invite readers of Stats Chat to submit nominations for our Stat of the Week competition and be in with the chance to win an iTunes voucher.

Here’s how it works:

• Anyone may add a comment on this post to nominate their Stat of the Week candidate before midday Friday November 4 2016.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of October 29 – November 4 2016 inclusive.
• Quote the statistic, when and where it was published and tell us why it should be our Stat of the Week.

Next Monday at midday we’ll announce the winner of this week’s Stat of the Week competition, and start a new one.

(more…)

If you’d like to comment on or debate any of this week’s Stat of the Week nominations, please do so below!

Graeme Edgeler nominated this, from PBS Frontline, to @statschat as a bad graph

It’s actually almost a good graph, but I think it’s trying to do too many things at once. There are two basic numerical facts: the number of people trying to cross the Mediterranean to escape the Syrian crisis has gone down substantially; the number of deaths has stayed about the same.

If you want to show the increase in risk, it’s much more effective to use a fixed, round denominator —  the main reason to use this sort of graph is that people pick up risk information better as frequencies than as fractions.

Here’s the comparison using the same denominator, 269, for the two years. It’s visually obvious that there has been a three-fold increase in death rate.

It’s harder to convey all the comparisons clearly in one graph. A mosaic plot would work for higher proportions, which we can all hope doesn’t become a relevant fact.

• A long post on the use and misuse of the ‘Twitter firehose’, from Bloomberg View

• A long story at Stuff about discharge without conviction, though a bit undermined by the fact that, as the story says, “[the] number of discharges without conviction has plummeted, from 3189 in 2011, to 2103 in 2015,“

• While the idea of  predicting the US election using mako sharks (carchariamancy?) is no sillier than psychic meerkats or lucky lotto retailers, I don’t think the story really works unless the people pushing it at least pretend to believe it.

• On the other hand, some people did seriously argue that shark attacks affected the results of presidential elections. And were wrong

• There’s been a lot of interest in the voting intentions of evangelical Christians in the US for this election: they’re a moderately large and active group.  They’re also hard to identify in polling. Ed Setzer writes about a new definition. Fred Clark explains why the definition is hard — partly because of  issues the new definition wants to address, but also because of issues it’s trying to bypass.

Nate Silver’s predictions at 538 give Donald Trump a much higher chance of winning the election than anyone else’s: at the time of writing, 20% vs 8% from the Upshot, 5% from Daily Kos, or 1% from Sam Wang at the Princeton Election Consortium.

That’s mostly not because Nate Silver thinks Trump is doing much better: 538 estimates 326 Electoral College votes for Clinton; Daily Kos has 334; the Princeton folks have 335.  The popular vote margin is estimated as 5.7% by 538 and about 8.4% by Princeton (their ‘meta-margin’ is 4.2%).

Everyone also pretty much agrees that the uncertainty in the votes is symmetric: if the polls are wrong, the estimated support for Clinton could as easily be too high as too low.  But that’s the uncertainty in the margin, not in the chance of winning.  Probabilities can’t go above 100% or below 0%, and when they get close to these limits, a symmetric uncertainty in the vote margin has to turn into an asymmetric uncertainty in the probability prediction, and a larger uncertainty has to pull the probability further away from the boundaries.

Nate Silver’s model thinks that opinion polls can be off by 6 or 7 percent in either direction even this close to the elections; the others don’t. It’s question that history can’t definitively answer, because there isn’t enough  history to work with. If Silver is wrong, we won’t know even after the election; even if he’s right, the most likely outcome is for the results to look pretty much like everyone predicts.

Before a medical diagnostic test is introduced, it is supposed to be evaluated carefully for accuracy. In particular, if the test is going to be used on the whole population, it’s important to know the false positive rate: of the people who test positive, what proportion really have a problem?  Part of  this process is to make sure that the test works as a biological or chemical assay: is it accurately measuring, say, carbon monoxide or glucose in the blood.  But that’s only part of the process.  You also need to worry about what threshold to use — how high is ‘high’ — and whether people could have high carbon monoxide levels without being smokers, or high glucose levels without being diabetic.

I haven’t heard any suggestion that the tests for methamphetamine contamination in houses fail the first step. There’s meth present when they find it. But Housing NZ were treating the high assay value as evidence that (a) the house was dangerous to live in, and (b) that the tenant was responsible. The false positive rates for (a) and (b) were not established, and appear to be shockingly high given the consequences.

The Ministry of Health has now released new guidelines on meth contamination, with concentration thresholds based on evidence (though towards the low end of what their evidence would support).  They claim to have repeatedly warned Housing NZ. Russell Brown has an excellent summary of the situation at Public Address.

While this is all a step forward, it’s not addressing the question of (b) above: if there’s methamphetamine present at above the new action threshold, it appears that this is still going to be taken as evidence of the tenant’s culpability. That would only make sense if, contrary to the advertising from the meth-testing companies, low-level meth contamination were very rare in rented NZ houses.

From the election on the other side of the Pacific.

Wikileaks also shows how John Podesta rigged the polls by oversampling democrats, a voter suppression technique.

Now, as Josh Marshall at Talking Points Memo goes on to point out, the email in question is not to or from John Podesta, is eight years old, and refers to the Democrats internal polls not to public polls. So it’s kind of uninteresting. Except to me.  I’m a professional sampling nerd. I do research on oversampling; I publish papers on it; I write software about it: ways to do it and ways to correct for it. And just like a sailing nerd who has heard Bermuda rigging described as a threat to democracy, I’m going to explain more than you ever needed to know about oversampling.

The most basic form of oversampling in medical research has been widely used for over sixty years. If you want to study whether, say, smoking causes lung cancer, it’s very inefficient to take a representative sample of the population because most people, fortunately, don’t have lung cancer. You need to sample maybe 1000 people to get two people with lung cancer. If you have access to hospital records you could find maybe 200 people with lung cancer and 800 healthy control people.   Your case-control sample would have about the same cost as a representative sample of 1000 people, but nearly 100 times more information.  And there are more complex versions of the same idea.

Your case-control sample isn’t representative, but you can still learn things from it.  At a simple level, if the lung cancer cases are more likely to smoke than the controls in the sample, that will also be true in the population. The relationship won’t be the same as in the population, but it will be in the same direction.  For more detailed analysis we can undo the oversampling. Suppose we want to estimate the proportion of smokers in the population. The proportion of smokers in the sample is going to be too high, because we’ve oversampled lung-cancer patients, who are more likely to smoke. To be precise, we’ve got one hundred times too many lung cancer patients in the sample. We can fix that by giving each of them one hundred times less weight in estimating the population total. If 180 of the 200 lung cancer patients smoked, and 100 of the 800 controls did, you’d have a weighted numerator of 180×(1/100)+100×1, and a weighted denominator of 200×(1/100)+800×1, for an unbiased estimate of  12.7%, compared to the unweighted, biased (180+200)/1000 = 38%.

In polling, your question might be what issues are important to swing voters. You’d try to oversample swing voters to ask them, and not waste time and money annoying people whose minds were made up.  Obviously that would make your sample un-representative of the whole population. That’s the point; you want to talk to swing voters, not to a representative sample.  Or you might want to compare the thinking of (generally pro-trump) evangelical Christians and (often anti-Trump) Mormons. Again, if you oversampled conservative religious groups you’d end up with an unrepresentative sample; again, that would be the point. Oversampling isn’t the best strategy when your primary purpose is finding out what a representative sample thinks; it often is the best strategy when you want to know more about some smaller group of people.

However, if you also wanted an estimate of the overall popular vote you could easily undo the oversampling and downweight the swing voters in your sample to get an unbiased estimate as we did with the smoking rates.  You have to do that anyway;  even if you try to get a representative sample it probably won’t work because some groups of people are less likely to answer their phones and agree to talk to you.  The weighting you use to fix up accidental over- and under- sampling is exactly the same as the weighting you use when it’s deliberate.

Team Ratings for the Mitre 10 Cup Finals

The basic method is described on my Department home page.

Here are the team ratings prior to this week’s games, along with the ratings at the start of the season.

Performance So Far

So far there have been 74 matches played, 52 of which were correctly predicted, a success rate of 70.3%.
Here are the predictions for last week’s games.

Predictions for the Mitre 10 Cup Finals

Here are the predictions for the Mitre 10 Cup Finals. The prediction is my estimated expected points difference with a positive margin being a win to the home team, and a negative margin a win to the away team.

My StatsChat posts, and especially the ‘Briefly’ links, tend to be pretty negative about big data and algorithmic decision-making. I’m a statistician, and I work with large-scale personal genomic data, so you’d expect me to be more positive. This post is about why.

The phrase “devil’s advocate” has come to mean a guy on the internet arguing insincerely, or pretending to argue insincerely, just for the sake of being a dick. That’s not what it once meant. In the early eighteenth century, Pope Clement XI created the position of “Promoter of the Faith” to provide a skeptical examination of cases for sainthood. By the time a case for sainthood got to the Vatican, there would be a lot of support behind it, and one wouldn’t have to be too cynical to suspect there had been a bit of polishing of the evidence. The idea was to have someone whose actual job it was to ask the awkward questions — “devil’s advocate” was the nickname.  Most non-Catholics and many Catholics would argue that the position obviously didn’t achieve what it aimed to do, but the idea was important.

In the research world, statisticians are often regarded this way. We’re seen as killjoys: people who look at your study and find ways to undermine your conclusions. And we do. In principle you could imagine statisticians looking at a study and explaining why the results were much stronger than the investigators thought, but since people are really good at finding favourable interpretations without help, that doesn’t happen so much.

Machine learning includes some spectacular achievements, and has huge potential for improving our lives. It also has a lot of built-in support both because it scales well to making a few people very rich, and because it fits in with the human desire to know things about the world and about other people.

It’s important to consider the risks and harms of algorithmic decision making as well as the very real benefits. And it’s important that this isn’t left to people who can be dismissed as not understanding the technical issues.  That’s why Cathy O’Neil’s book Weapons of Math Destruction is important, and on a much smaller scale it’s why you’ll keep seeing stories about privacy or algorithmic prejudice here on StatsChat. As Section 162 (4) (a) (v) of the Education Act indicates, it’s my actual job.