Posts filed under Estimation (29)

January 24, 2015

Measuring what you care about

Via Felix Salmon, here’s a chart from Credit Suisse that’s been making the headlines recently, in the Oxfam report on global wealth.  The chart shows where in the world people live for each of the ‘wealth’ deciles, and I’ve circled the most interesting piece.


About 10% of the least wealthy people in the world live in North America. This isn’t (just) Mexico, Guatemala, Nicaragua, etc, it’s also the US, because some people in the US have really big debts.

If you are genuinely poor, you can’t have hundreds of thousands of dollars of negative wealth because no-one would give you that sort of money. Compared to a US law-school graduate with student loans, you’re wealthy.  This is obviously a dumb way to define wealth. Also, as I’ve argued on the ‘net tax’ issue, cumulative percentages just don’t work usefully as summaries when some of the numbers are negative.

This doesn’t mean wealth inequality doesn’t exist (boy, does it) or doesn’t matter, but it does mean summaries like the Credit Suisse one don’t capture it. If you wanted to capture the sort of wealth inequality worth worrying about, you’d need to think about what it really meant and why it was a problem separately from income inequality (which is much easier to define).

There seem to be two concerns with wealth inequality that people on a reasonably broad political spectrum might care about, if we stipulate that redistributive international taxation is not on the agenda:

  • transfer of wealth from parents to children leads to social stratification
  • high concentrations of wealth give some people too much power (and more so in societies more corrupt than NZ).

Both of these are non-linear ($200 isn’t twice as much as $100 in any meaningful sense) and they both depend on where you are ($20,000 will get you much further in Nigeria than in Rhode Island). There probably isn’t going to be a good way to look at global wealth inequality. Within countries, it’s probably feasible but it will still take some care and I expect it will be necessary to discount debts quite a lot.  If you owe the bank $10, you’re not wealthy, but if you owe the bank $10 million, you probably are.

October 7, 2014

Enumerating hard-to-reach populations

I’ve written before about how it’s hard to get accurate estimates of the size of small subpopulations, even with large, well-designed surveys.

Via the Herald

Mr Key said that was an emerging issue for New Zealand. “If I was to spell out to New Zealanders the exact number of people looking to leave and be foreign fighters, it would be larger, I think, than New Zealanders would expect that number to be.”

If the government really knows the ‘exact number’, there must have been a lot more domestic surveillance than we’ve been told about.

New Zealanders probably don’t have any very well formed expectations for that number, since we have basically no information to go on. My guess would be along the lines of “Not very many, but people are strange,  so probably some.” I’d be surprised if it were less than 10 or more than 1000.


March 18, 2014

Three fifths of five eighths of not very much at all

The latest BNZ-REINZ Residential Market Survey is out, and the Herald has even embedded the full document in their online story, which is a very promising change.

According to the report 6.4% of homes sales in March are  to off-shore buyers, 25% of whom were Chinese. 25% of 6.4% is 1.6%.

If you look at real estate statistics (eg, here) for last month you find 6125 residential sales through agents across NZ. 25% of 6.4% of 6125 is 98. That’s not a very big number.  For context, in the most recent month available, about 1500 new dwellings were consented.

You also find, looking at the real estate statistics, that last month was February, not March.  The  BNZ-REINZ Residential Market Survey is not an actual measurement, the estimates are averages of round numbers based on the opinion of real-estate agents across the country.  Even if we assume the agents know which buyers are offshore investors as opposed to recent or near-future immigrants (they estimate 41% of the foreign buyers will move here), it’s pretty rough data. To make it worse, the question on this topic just changed, so trends are even harder to establish.

That’s probably why the report said in the front-page summary “one would struggle, statistically-speaking, to conclude there is a lift or decline in foreign buying of NZ houses.”

The Herald  boldly took up that struggle.

February 4, 2014

Approximately quantified self

What happens if you wear two activity-monitoring devices at the same time, on the same wrist:




November 27, 2013

Interpretive tips for understanding science

From David Spiegelhalter, William Sutherland, and Mark Burgman, twenty (mostly statistical) tips for interpreting scientific findings

To this end, we suggest 20 concepts that should be part of the education of civil servants, politicians, policy advisers and journalists — and anyone else who may have to interact with science or scientists. Politicians with a healthy scepticism of scientific advocates might simply prefer to arm themselves with this critical set of knowledge.

A few of the tips, without their detailed explication:

  • Differences and chance cause variation
  • No measurement is exact
  • Bigger is usually better for sample size
  • Controls are important
  • Beware the base-rate fallacy
  • Feelings influence risk perception
October 10, 2013

Innovation and indexes

The 2013 Global Innovation Index is out, with writeups in Scientific American and the NZ internets, but not this year in the NZ press. Stuff, instead, tells us “Low worker engagement holds NZ back”, quoting Gallup’s ’employee engagement’ figure of 23% for NZ, without much attempt to compare to other countries.

The two international rankings are very different: of the 16 countries above us in the Global Innovation Index, 13 have significantly lower employee engagement ratings, one (Denmark) is about the same, and one (USA) is higher (one, Hong Kong, is missing because Gallup lumps it in with the rest of the PRC).  It’s also important to consider what is behind these ratings. If you search on  “Gallup employee engagement”, you get results mostly focused on Gallup’s consulting services — getting you to worry about employee engagement is one of the ways they make money.  The Global Innovation Index, on the other hand, came from a business school and was initially sponsored by the Confederation of Indian Industry  and has now expanded with wider sponsorship and academic involvement: it’s not biased in any way that’s obviously relevant to New Zealand.

With any complicated scoring system, different countries will do well on different components of the score.  If you believe, with the authors of Why Nations Fail,  that quality of institutions is the most important factor, you might focus on the “Institutions” component of the innovation index, where New Zealand is in third place. If you’re AMP econonomist Bevan Graham you might think the ‘business sophistication’ component is more important and note that NZ falls to 28th.

If you want NZ innovation to improve, the reverse approach might be more helpful: look at where NZ ranks poorly, and see if these are things we want to change (innovation isn’t everything) and how we might change them.



October 9, 2013

Prediction is hard

How good are sales predictions for newly approved drugs?

Not very (via Derek Lowe at  In the Pipeline)


There’s a wide spread around the true value. There’s less than a 50:50 chance of being within 40%, and a substantial chance of being insanely overoptimistic. Derek Lowe continues

Now, those numbers are all derived from forecasts in the year before the drugs launched. But surely things get better once the products got out into the market? Well, there was a trend for lower errors, certainly, but the forecasts were still (for example) off by 40% five years after the launch. The authors also say that forecasts for later drugs in a particular class were no more accurate than the ones for the first-in-class compounds. All of this really, really makes a person want to ask if all that time and effort that goes into this process is doing anyone any good at all.


August 16, 2013

Collateral damage

There’s a long tradition in law and ethics of thinking about how much harm to the innocent should be permitted in judicial procedures, and at what cost. The decision involves both uncertainty, since any judicial process will make mistakes, and consideration of what the tradeoffs would be in the absence of uncertainty. An old example of the latter is the story of Abraham bargaining with God over how many righteous people there would have to be in the notorious city of Sodom to save it from destruction, from a starting point of 50 down to a final offer of 10.

With the proposed new child protection laws, though, the arguments have mostly been about the uncertainty.  The bills have not been released yet, but Paula Bennett says they will provide for protection orders keeping people away from children, to be imposed by judges not only on those convicted of child abuse but also ‘on the balance of probabilities’ for some people suspected of being a serious risk.

We’ve had two stat-of-the-week nominations for a blog post about this topic (arguably not ‘in the NZ media’, but we’ll leave that for the competition moderator). The question at issue is how many innocent people would end up under child protection orders if 80 orders were imposed each year.

The ‘balance of probabilities’ standard theoretically says that an order can be imposed (?must be imposed) if the probability of being a serious risk is more than 50%.  The probability could be much higher than 50% — for example, if you were asked to decide on the balance of probabilities which of your friends are male, you will usually also be certain beyond reasonable doubt for most of them.  On the other hand, there wouldn’t be any point to the legislation unless it is applied mostly to people for whom the evidence isn’t good enough even to attempt prosecution under current law, so the typical probabilities shouldn’t be that high.

Even if we knew the distribution of probabilities, we still don’t have enough information to know how many innocent people will be subject to orders. The probability threshold here is the personal partly-subjective uncertainty of the judge, so even if we had an exact probability we’d only know how many innocent people the judge thought would be affected, and there’s no guarantee that judges have well-calibrated subjective probabilities on this topic.

In fact, the judicial system usually rules out statistical prior information about how likely different broad groups of people are to be guilty, so the judge may well be using a probability distribution that is deliberately mis-calibrated.  In particular, the judicial system is (for very good but non-statistical reasons) very resistant to using as evidence the fact that someone has been charged, even though people who have been charged are statistically much more likely to be guilty than random members of the population.

At one extreme, if the police were always right when they suspected people, everyone who turned up in court with any significant evidence against them would be guilty.  Even if the evidence was only up to the balance of probabilities standard, it would then turn out that no innocent people would be subject to the orders. That’s the impression that Ms Bennett seems to be trying to give — that it’s just the rules of evidence, not any real doubt about guilt.  At the other extreme, if the police were just hauling in random people off the street, nearly everyone who looked guilty on the balance of probabilities might actually just be a victim of coincidence and circumstance.

So, there really isn’t an a priori mathematical answer to the question of how many innocent people will be affected, and there isn’t going to be a good way to estimate it afterwards either. It will be somewhere between 0% and 100% of the orders that are imposed, and reasonable people with different beliefs about the police and the courts can have different expectations.

July 31, 2013

It depends on how you look at it

Collapsing lots of variables into a single ‘goodness’ score always involves choices about how to weight different information; there isn’t a well-defined and objective answer to questions like “what’s the best rugby team in the world?” or “what’s the best university in the world?”.  And if you put together a ranking of rugby teams and ended up with Samoa at the top and the All Blacks well down the list, you might want to reconsider your scoring system.

On the other hand, it’s not a good look if you make a big deal of holding failing schools accountable and then reorder your scoring system to move a school from “C” to “A”. Especially when it’s a charter school founded by a major donor to the governing political party.

Emails obtained by The Associated Press show Bennett and his staff scrambled last fall to ensure influential donor Christel DeHaan’s school received an “A,” despite poor test scores in algebra that initially earned it a “C.”

“They need to understand that anything less than an A for Christel House compromises all of our accountability work,” Bennett wrote in a Sept. 12 email to then-chief of staff Heather Neal, who is now Gov. Mike Pence’s chief lobbyist.


July 13, 2013

Visualising the Bechdel test

The Bechdel Test classifies movies according to whether they have two female characters, who at some point talk to each other, about something other than a man.

It’s not that all movies should pass the test — for example, a movie with a tight first-person viewpoint is unlikely to pass the test if the viewpoint character is male, and no-one’s saying such movies should not exist.  The point of the test is that surprisingly few movies pass it.

At Ten Chocolate Sundaes there’s an interesting statistical analysis of movies over time and by genre, looking at the proportion that pass the test.  The proportion seems to have gone down over time, though it’s been pretty stable in recent years.