Stats Chat

More students cheat in exams, and most are in Auckland, says the Herald.

This story combines two frequent StatsChat themes: denominators, and being careful about what was actually measured.

Auckland, as we have noted before, has a higher population than other regions.  As you will recall, it’s about a third of the NZ population, so it looks like making up about 50% of those caught cheating is excessive. That’s the sort of work that the paper might do for you — as well as checking if 1/3 is still about right as the proportion of students sitting NCEA exams (it seems to be).

On similar lines, if you look just at the totals without denominators, you’ll miss some notable values.  Northland had 25 students caught cheating, which is more than the much-larger Waikato and Canterbury regions. You’d expect about 10 at the national average rate and about 15 at the Auckland rate.

Much more important is the question of what proportion of those cheating were caught — to say things like

Again Central Plateau and the Cook Islands had no cheaters, and Wairarapa and Southland students were also honest

or to draw conclusions about trends over time assumes that you’re not missing many.

The story says

NZQA received 1,314,207 entries in NCEA and New Zealand Scholarship examinations from 145,464 students last year.

The 290 attempts at cheating that were caught come to just under 0.2% of students and just over 0.02% of exams.  Maybe I’m just cynical, but I’d be surprised if the real rate was as low as one exam in a thousand, let alone five times lower.

I posted predictions for Round 15 before the international games. I have just updated the predictions because I had not taken into account that the Chiefs versus Crusaders game is to be on a neutral ground.

See the updated post atSuper 18 Predictions for Round 15

Team Ratings for Round 17

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 118 matches played, 71 of which were correctly predicted, a success rate of 60.2%.
Here are the predictions for last week’s games.

Predictions for Round 17

Here are the predictions for Round 17. 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.

From the BBC coverage of the Brexit referendum. With great power comes great responsibility.

• Facebook, on how they do ethics review for research

• In Brexit, the YouGov estimate that I mentioned last week was pretty accurate, but the result genuinely was too close to call.  The real-time forecasts from Chris Hanretty at the University of East Anglia seemed to work well.

• If you combine turnout estimates with voting estimates by age group, the proportion of 18-24 year olds voting Remain (75% of the 36% turnout) was less than the proportion of 65+ year olds (39% of the 83% turnout).  Turnout matters.

• You’re much more likely to survive a cardiac arrest on TV than in real life.

• Estimates of Uber driver earnings per hour in US. Also, see the posts on NZ Uber by Ben Wilson at Public Address.

• What theoretical physicists (statisticians, etc,) look like when working (Dr Katie Mack, astrophysics/cosmology). No lab coats; no brighly coloured Erlenmeyer flasks.

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 July 1 2016.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of June 25 – July 1 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.

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It’s a useful habit, when you see a causal claim based on observational data, to turn the direction around: the story says A causes B, but could B cause A instead? People get annoyed when you do this, because they think it’s silly. Sometimes, though, that is what is happening.

As a pedestrian and public transport user, I’m in favour of walkable neighbourhoods, so I like seeing research that says they are good for health. Today, Stuff has a story that casts a bit of doubt on those analyses.

The researchers used Utah driver’s-licence data, which again included height and weight, to divide all the neighbourhoods in Salt Lake County into four groups by average body mass index. They used Utah birth certificates, which report mother’s height and weight, and looked at 40,000 women who had at least two children while living in Salt Lake County during the 20-year study period.  Then they looked at women who moved from one neighbourhood to another between the two births. Women with higher BMI were more likely to  move to a higher-BMI neighbourhood.

If this is true in other cities and for people other than mothers with new babies, it’s going to exaggerate the health benefits of walkable neighbourhoods: there will be a feedback loop where these neighbourhoods provide more exercise opportunity, leading to lower BMI, leading to other people with lower BMI moving there.   It’s like with schools: suppose a school starts getting consistently good results because of good teaching. Wealthy families who value education will send their kids there, and the school will get even better results, but only partly because of good teaching.

Q: Did you see food allergies are caused by diet?

A: That makes sense, I suppose.

Q: Does it make sense that low-fibre diets are why people get peanut allergy more now?

A: Ah. No.

Q: Why not?

A: Because fibre in the typical diet hasn’t changed much in recent years and peanut allergies have become much more common.

Q: It could still be true that adding more fibre would stop people getting peanut allergies, though?

A: Could be.

Q: And that’s what the research found?

A: Up to a point.

Q:  Mice?

A: Mice.

Q: But peanut allergy and dietary fibre?

A: Yes, pretty much. And a plausible biological reason for how it might work.

Q: So it’s worth trying in humans?

A: Probably, though getting little kids to eat that much fibre would be hard.

Q: But the story just says “a simple bowl of bran and some dried apricots in the morning”

A: Sadly, yes.

Q: So how much fibre did they give the rats?

A: They compared a zero-fibre diet to 35% fibre

Q: Is 35% a lot?

A: Well, it’s more than All-Bran, and that was their whole diet.

Q: A more reasonable dose might still work, though?

A: Sure. But you wouldn’t want to assume it did before the trials happened.

• The Data Journalism Awards from the Global Editors Network (scroll down past the ceremony stuff to get the links to the award-winners). And a commentary from Simon Rogers

• Colorado legalised cannabis recently. They have data on teenage cannabis use over time. It hasn’t gone up, probably because teens who wanted pot could already get it.
  I still haven’t seen anything on the two more important potential health impacts: do car crashes go up or down, does alcohol consumption go up or down.

• A nice detailed explanation of how YouGov is doing its predictions for the Brexit referendum.  At the moment they are robustly unsure, estimating 48%-53% vote for “Leave”.  They do discuss how badly the last election polling went, and conclude  “if we have a problem, it will probably not be the same problem as last time.” (via Andrew Gelman)

From the Guardian

The NHS is increasingly publishing statistics about the surgery it undertakes, following on from a movement kickstarted by the Bristol Inquiry in the late 1990s into deaths of children after heart surgery. Ever more health data is being collected, and more transparent and open sharing of hospital summary data and outcomes has the power to transform the quality of NHS services further, even beyond the great improvements that have already been made.

The problem is that most people don’t have the expertise to analyse the hospital outcome data, and that there are some easy mistakes to make (just as with school outcome data).

A group of statisticians and psychologists developed a website that tries to help, for the data on childhood heart surgery.  Comparisons between hospitals in survival rate are very tempting (and newsworthy) here, but misleading: there are many reasons children might need heart surgery, and the risk is not the same for all of them.

There are two, equally important, components to the new site. Underneath, invisible to the user, is a statistical model that predicts the surgery result for an average hospital, and the uncertainty around the prediction. On top is the display and explanation, helping the user to understand what the data are saying: is the survival rate at this hospital higher (or lower) than would be expected based on how difficult their operations are?