Stats Chat

Three examples that have come across my Twitter feed recently:

A genetic “crystal ball” can predict whether certain people will respond effectively to the flu vaccine. Science News

This is actually really interesting research looking at why some people get high levels of antibodies and others don’t.  However, the ‘crystal ball’ is cloudy. If people are divided into ‘low’, ‘medium’ and ‘high’ responders, and you take one ‘low’ responder and one ‘high’ responder, the test has about a 75% chance of working out which is which.

Is Swiss cheese a superfood?, asks Food & Wine.

According to metro.co.uk, researchers at the University of Korea have found that Swiss cheese has a whole lot of health benefits. It contains a probiotic called—you ready for this?—propionibacterium freudenreichii, which reduces inflammation. Among other things, reducing inflammation can reduce the risk of getting a number of diseases and slow the aging process. Propionibacterium freudenreichii also boosts immune system functions.

The research was carried out in microscopic nematodes, and didn’t involve Swiss cheese. The nematodes eat bacteria, and these ones were given a diet of  Propionibacterium freudenreichii instead of their normal E. coli. While the live bacteria are present in Swiss cheese, the recipes linked from the story would make sure no live bacteria reached your gut.

From the Guardian

Dating from 1,000 years before Pythagoras’s theorem, the Babylonian clay tablet is a trigonometric table more accurate than any today, say researchers.

It’s pretty clear that this has to be bullshit. It’s harder to find what’s actually being claimed.  Popular Science has a more balanced view: the conjecture is that the Babylonians worked with triangles where the ratios of side lengths were simple fractions rather than where the angles were simple fractions of a circle.  Like we do in measuring slopes of roads or railways.  If that’s true, it’s an interesting idea and if they knew about trignometric relationships then it pushes back the discovery quite a bit.  It’s still not ‘more accurate than any today’; the rounding-off just happens in a different place.

The MMP voting system and its implications are relatively complicated. I’m going to try to give simple approximations and then corrections to them. If you want more definitive details, here’s the Electoral Commission and the Electoral Act.

Two votes: You have an electorate vote, which only affects who your local MP is, and doesn’t affect the composition of Parliament. You also have a party vote that affects the composition of Parliament, but not who your local MP is. The number of seats a party gets in Parliament is proportional to the number of party votes it gets.

This isn’t true, but it’s actually a pretty good working approximation for most of us.

There are two obvious flaws. First, if your local MP belongs to a party that doesn’t get enough votes to have any seats in Parliament, they still get to be an MP. Peter Dunne in Ōhariu was an example of this in the 2014 election. Second, when working out the number of seats a party is entitled to in Parliament, parties with less than 5% of the vote are excluded unless they won some electorate.  In the 2014 election, the Conservative Party got 3.97% of the vote, but no seats.

The Māori Party was an example of both exceptions: they did get enough votes in proportional terms for two seats, but not enough to make the 5% cutoff, but they didn’t have to because Te Ururoa Flavell won the Waiāriki electorate seat for them.

Proportionality: There are 120 seats, so a party needs 1/120th, or about 0.83%, of the vote for each one.

That’s not quite true because of the 5% threshold, both because some parties miss out and because the relevant percentages are of the votes remaining after parties have been excluded by the threshold.

It’s also not true because of rounding.  We elect whole MPs, not fractional ones, so we need a rounding rule. Roughly speaking, half -seats round up. More accurately, suppose there is some number N of votes available per seat (which will be worked out later). If you have at least 0.5×N votes you get one seat, 1.5×N gets you two seats, 13.5×N gets you fourteen seats.  So what’s N? It’s roughly 1/121th (0.83%) of the votes; it’s exactly whatever number you need to allocate exactly as many seats as you have available. (The Electoral Commission actually uses a procedure that’s identical in effect to this one and easier to compute, but (I think) harder to explain).

In 2014, the Māori Party got 1.32% of the vote, which is a bit more than 1.5×0.83%, and were entitled to two seats. ACT got less than 0.83% but more than 0.5×0.83% and were entitled to one seat.

Finally, if a party gets more seats from electorate candidates than it is due by proportionality those seats are extra, above the 120-seat ideal size of Parliament — except that seats won by a party or individual not contesting the party vote do come out of the 120-seat total.  So, in 2014, ACT got enough party votes to be due one of the 120 seats, but United Future didn’t. United Future did contest the party vote so Peter Dunne’s seat did not come out of the 120-seat total — he was an ‘overhang’ 121st MP. I’m guessing the reason overhangs by parties contesting the party vote are extra is that you don’t know how many there will be until you’ve done the calculation, so you’d have to go back to the start and recalculate if you counted them in the 120 (which might change the number of over-allocated seats and force another recalculation and so on).

Māori Roll: People of Māori descent can choose, every five years, to be on a Māori electoral roll rather than the general roll. If enough of them do, Māori electorates are created with the same number of people as the general electorates. There are currently seven Māori electorates, representing just over half of the people of Māori descent.  As with any electorate, you don’t have to be enrolled there to stand there; anyone eligible to be an MP can stand. 

The main way this is oversimplified is because of the people of Māori descent who aren’t on either roll, because they’re too young or just not enrolled yet. You can’t tell whether they would be on the general roll or the Māori roll, so there are procedures for StatsNZ to split the non-enrolled Māori-descent population up to calculate electorate populations.

Q: Does the Herald really know “The amount of sex you should be having according to your age group”

A: No.

Q: Can they really tell you “ if the regularity of your sex life is “normal”.”

A: No.

Q: Is that even a thing?

A: No.

Q: If it was, would a survey of people in the US be especially relevant to NZ?

A: It was from the US? The story didn’t say that.

Today’s episode of simple answers to complex questions is brought to you by the letters F and F and S. 

• On Thursday 7 September, 3pm, in Auckland, “The Future of Open Data in Aotearoa”, featuring Ed Corkery (CEO of Koordinates),  Harkanwal Singh (Data Editor, NZ Herald) and Liz MacPherson (Government Statistician)

• “The flip side of personal genomics: When a mutation doesn’t spell disease” from Nature News

• “Is it fair to say that most social programmes don’t work?” (yes, but some do)
• “Dramatic treatment effects are rare” from  the blog students4bestevidence

• Another story about machines learning stereotypes, this time in image recognition.

• Peter Griffin on an example of science news hype attributable to the research institution

• Peter Ellis has a nice pointy-clicky tool summarising the 2014 NZ Electoral Study (who voted for whom)

• A couple of eclipse graphs:
  From reddit user  superpaow
  
  and from Noah Illinsky
  

There’s a bunch of web pages/apps out there that supposedly help you to decide who to vote for.

On the Fence: This one asks you to move a slider to ‘balance’ competing principles, then works out which party you agree with.

There are some obvious problems. First, the scale isn’t clearly calibrated.  If you’re at 50:50 on government vs private-sector roles in providing affordable housing, does that mean you think 50% of it should be state houses, or that it should all be state-owned but built by private sector construction companies, or something vague and woolly?

Second, as lots of people have pointed out, there’s some false dichotomies there, like the privacy:security tradeoff.

Perhaps more important, when there is a genuine tradeoff, it’s a genuine tradeoff. You typically can’t decide it by abstract principle without reference to the facts.

Vote Compass:  This one takes advantage of the empirical observation that people’s voting preferences compress fairly well into two dimensions.  The questions are much more clearly calibrated: eg, the affordable-housing one is “The government should build affordable housing for Kiwis to buy” with a ‘Strongly agree” to “Strongly disagree” scale.

Most usefully, there’s a tool for you to explore how your position differs from that of the parties on each of the questions, and to reweight the results depending on which issues you care about.  Annoyingly, there’s a category “Moral Issues” that includes marijuana legalisation but not the questions about refugees or climate-change or affordable housing

Policy: The Spinoff has a tool that seems philosophically different from the others. It has much more emphasis on comparing actual party policies and less on trying to find out what your ideal party would be. As a result, it’s less useful if you want to be told what you think, but might be more useful if you want to look at specific policies. Whether you do, I suppose, depends on how much you believe the policies — especially from the minor parties, where you’d need to know how the policies rank in their actual negotiating position for coalition or confidence & supply.

Team Ratings for Round 25

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 176 matches played, 107 of which were correctly predicted, a success rate of 60.8%.
Here are the predictions for last week’s games.

Predictions for Round 25

Here are the predictions for Round 25. 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.

Team Ratings for Round 2

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 7 matches played, 5 of which were correctly predicted, a success rate of 71.4%.
Here are the predictions for last week’s games.

Predictions for Round 2

Here are the predictions for Round 2. 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.

Team Ratings for Round 7

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 18 matches played, 11 of which were correctly predicted, a success rate of 61.1%.
Here are the predictions for last week’s games.

Predictions for Round 7

Here are the predictions for Round 7. 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.

There’s a story in New Scientist, and in the NY Daily News, based on this research paper, saying that choosing alternative treatment instead of conventional treatment for cancer is bad for you.

The research is well done: they looked at the most common cancers in the US and found a small set of people who turned down all conventional treatment in favour of ‘alternative’ medicine.  They matched these people on cancer type, age, clinical group stage, what other disease they had, insurance type, race, and year of diagnosis, to a set who did get conventional treatment.   Even after all that matching, there was a big difference in survival.

There are two caveats to the story. First, this is people who turned down all conventional treatment, even surgery. That’s rare. In the database they used, 99.98% of patients received some conventional treatment. It’s much more common for people to receive some or all of the recommended conventional treatment, plus other things — not ‘alternative’ but ‘complementary’ or ‘integrative’ medicine.

Second, the numbers are being misinterpreted.  For example, New Scientist says

Among those with breast cancer, people taking alternative remedies were 5.68 times more likely to die within five years.

The actual figures were 42% and 13%, so about 3.1 times more likely. Here’s the graph

Similarly, the New Scientist story says

They found that people who took alternative medicine were two and half times more likely to die within five years of diagnosis.

The actual figures were 45% and 26%; 1.75 times more likely.

What’s happening is a confusion of rate ratios and actual risks of death; these aren’t the same.  The rate (or hazard) is measured in % per year; the risk is measured in %.  The risk is capped at 100%; the rate doesn’t have an upper limit.   Because of the cap at 100%, risk ratios are mathematically less convenient to model than rate ratios. As a tradeoff, it’s harder to explain your results using rate ratios. The Yale publicity punted on the issue, not mentioning the numbers and leaving reporters to get it wrong.  When this happens, it’s the scientists’ fault, not the reporters’.

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 August 25 2017.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of August 19 – 25 2017 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…)