Posts filed under Denominator? (61)

January 6, 2015

Foreign drivers, again

The Herald has a poll saying 61% of New Zealanders want to make large subsets of foreign drivers sit written and practical tests before they can drive here (33.9%: people from right-hand drive countries; 27.4% everyone but Australians). It’s hard to tell how much of this is just the push effect of being asked the questions and how much is real opinion.

The rationale is that foreign drivers are dangerous:

Overseas drivers were found at fault in 75 per cent of 538 injury crashes in which they were involved. But although failure to adjust to local conditions was blamed for seven fatal crashes, that was the suspected cause of just 26 per cent of the injury crashes.

This could do with some comparisons.  75% of 538 is 403, which is about 4.5% of all injury crashes that year.  We get about 2.7 million visitors per year, with a mean stay of 20 days (PDF), so on average the population is about 3.3% short-term visitors.

Or, we can look at the ‘factors involved’ for all the injury crashes. I get 15367  drivers of motorised vehicles involved in injury crashes, and 9192 of them have a contributing factor that is driver fault (causes 1xx to 4xx in the Crash Analysis System). This doesn’t include things like brake failures.  So, drivers on average are at fault in about 60% of the injury crashes they are involved in.

Based on this, it looks as though foreign drivers are somewhat more dangerous, but that restricting them is very unlikely to prevent more than, say, 1-2% of crashes. If you consider all the ways we might reduce injury crashes by 1-2%, and think about the side-effects of each one, I don’t think this is going to be near the top of the list.

January 2, 2015

Using the right denominator

We go on and on about denominators on StatsChat: the right way to report things that happen to people is usually a rate per capita rather than a total, otherwise you end up saying that Auckland has the highest number of whatever it is in New Zealand.  You do have to use the right denominator, though.

The Vatican City has the world’s highest crime rate.

That’s because the permanent population is less than 500, but the daily tourist population is about 100 times larger. The right denominator would be the tourist population.

In most countries this isn’t really an issue. For example,  in New Zealand,which has a lot of tourism, short-term visitors are only about 5% of the population. Even in the Cook Islands, residents outnumber tourists.


June 18, 2014

Counts and proportions

Phil Price writes (at Andrew Gelman’s blog) on the impact of bike-share programs:

So the number of head injuries declined by 14 percent, and the Washington Post reporter — Lenny Bernstein, for those of you keeping score at home — says they went up 7.8%.  That’s a pretty big mistake! How did it happen?  Well, the number of head injuries went down, but the number of injuries that were not head injuries went down even more, so the proportion of injuries that were head injuries went up.


To be precise, the research paper found 638 hospitalised head injuries in 24 months before the bike share program, and 273 in the 12 months afterwards. In a set of control cities that didn’t start a bike-share program there were 712 head injuries in the 24 months before the matching date and 342 in the 12 months afterwards. That is, a 14.4% decrease in the cities that added bike-share programs and a 4% decrease in those that didn’t.



June 10, 2014

Eat your greens

Stuff has a story about ‘Powerhouse Fruits and Vegetables”.  They get points for linking to the source, and for pointing out that although

“The rankings provide clarity on the nutrient quality of the different foods

the rankings are quite different from other rankings that are supposed to do the same thing.

They don’t point out that it’s silly to list scores to four digit accuracy when nutrient content varies enough to make the first digit somewhat unreliable.They also don’t point out that these are nutrient scores not per serving, but per 100 Calories of the food. Google thinks watercress has about 11 Calories/100g, so that’s 900g of watercress. The data are for raw watercress — the research paper doesn’t say how much the score goes down if you stir-fry it, Chinese-style.

If you much through a couple of pounds of watercress, it’s not surprising you’d pick up a few nutrients along the way. The applicability of this fact to NZ daily life must be a bit limited, though.

June 8, 2014

Foreign drivers

From the ChCh Press

Foreign drivers cause more fatal and injury crashes in the South Island than the national average – and the West Coast is the worst spot.

They don’t actually mean “more,” they mean “a higher proportion of”.

New Zealand Transport Agency (NZTA) safety directions chief adviser Lisa Rossiter said its crash statistics for the past 10 years showed foreign drivers were involved in about 6 per cent of all fatal or injury crashes in New Zealand, and were at fault in about 2 per cent.

On average, short-term visitors make up roughly 2.5% of people in New Zealand (2.78 million visitors in the year to April 2014, median visit of 9 days, so I’m guessing mean visit about two weeks). About another 2% of people in New Zealand are international students, who are at least sometimes counted as foreign drivers.

So, the risk seems to be a bit higher for foreign drivers, but probably not twice as high. Some of the excess can probably be explained by age: international students, backpackers, and drunk Australians in Queenstown are younger than the population average.

It’s different in parts of the South Island

The tourist hot spots of Otago and the West Coast fared worst.

A foreign driver was identified as a factor in 13 per cent of fatal crashes on the coast, and 5 per cent of fatal crashes in Otago from 2004 to 2013.

A lot of this must be because tourists are over-represented in tourist hot spots: that’s what ‘tourist hot-spot’ means. The proportion of short-term visitors is about 2.5% nationwide, but it’s probably rather lower that than in Gisborne and rather higher on the West Coast.

It’s also worth noting that “identified as a factor” is fairly weak. If you go to the Ministry of Transport reports and add up the percentage of times different factors were involved in a crash, you get a lot more than 100% (for the 2010 report I get 225% for fatal crashes and 185% for injury crashes)

For crashes involving a tourist driver and more than one car, the foreign driver was fully or partly responsible two out of three times.

This at least gets rid of the denominator problem, but the “partly” responsible is still a problem. We aren’t told what proportion of the time the local driver was fully or partly responsible — based on the information given, that could also be two out of three times.

It’s quite likely that foreign drivers are at higher risk, especially those from countries that drive on the right, but the problem is not a big fraction of the NZ road toll. It’s worth considering things that can sensibly be done to reduce it — which doesn’t include withdrawing from the U.N. Convention on Road Traffic — but if you’re trying to stop road deaths it may be more effective to concentrate on interventions that don’t just affect foreign drivers.  Clearer signage, guard rails and median barriers, separated bike lanes, improved public transport… there are many things that might knock a percentage point off road deaths more easily than targetting foreign drivers.

May 23, 2014

Is Roy Morgan weird?

There seems to be a view that the Roy Morgan political opinion poll is more variable than the others, even to the extent that newspapers are willing to say so, eg, Stuff on May 7

The National Party has taken a big hit in the latest Roy Morgan poll, shedding 6 points to 42.5 per cent in the volatile survey.

I was asked about this on Twitter this morning, so I went to get Peter Green’s data and aggregation model to see what it showed. In fact, there’s not much difference between the major polling companies in the variability of their estimates. Here, for example, are poll-to-poll changes in the support for National in successive polls for four companies



And here are their departures from the aggregated smooth trend



There really is not much to see here. So why do people feel that Roy Morgan comes out with strange results more often? Probably because Roy Morgan comes out with results more often.

For example, the proportion of poll-to-poll changes over 3 percentage points is 0.22 for One News/Colmar Brunton, 0.18 for Roy Morgan, and 0.23 for 3 News/Reid Research, all about the same, but the number of changes over 3 percentage points in this time frame is 5 for One News/Colmar Brunton, 14 for Roy Morgan, and 5 for 3 News/Reid Research.

There are more strange results from Roy Morgan than for the others, but it’s mostly for the same reason that there are more burglaries in Auckland than in the other New Zealand cities.

March 30, 2014

Inflation adjustment before breakfast

I saw this story in the Herald and didn’t read it in detail, just thought it was an interesting calculation to do

The Financial Times reported last week that the average global price of eight breakfast staples had risen almost 25 per cent this year.

The increases mainly affected coffee, orange juice, wheat, sugar, milk, butter, cocoa and pork.

We decided to create a Kiwi version of the Financial Times story and Statistics NZ food price figures reveal New Zealand families are not exempt from the trend.

David Farrar did read the story, and so was rather less impressed, as he also mentioned on Twitter.  The problem is that the calculation was done wrong.

If you served tomatoes, mushrooms, bacon, toast, eggs, tinned spaghetti and cereal, with coffee, tea and orange juice this weekend, it would have cost you 6.9 per cent more than the same meal in 2008, and almost 3 per cent more than in 2012. Breakfast food prices have risen more quickly than other prices.

Over the past five years, the compound average annual rate of inflation was 2.1 per cent.

If the average annual rate was 2.1%, which sounds about right, the total increase over five years would be 2.1% five times, which turns out to be 11%. Since 6.9% is less than 11%, breakfast food prices have risen less quickly than other prices. Quite a bit less. The story has it completely backward.

If you’re reading especially carefully, you might also notice that it’s more than five years from “this weekend” back to 2008 — for example, a comparison of end of March 2008 to this weekend would be a six year period.

This is the sort of thing that a subeditor should spot. It’s also the sort of thing the RBNZ inflation calculator is useful for — you put in a number and two years and it does the calculations.  If you use the calculator, you find that “this weekend” is apparently December 2013, and the 2008 comparison is December 2008, rather than March 2008 to March 2013. You’d also see that the sub-index for food had increased less than the total CPI, which would presumably make you more suspicious about the story.

There’s also some discussion of individual item prices. This doesn’t have the awful 5:1 error ratio of the main argument, but it still demonstrates where a bit of thinking could have helped

Mild Arabica coffee was trading on the commodity markets for US$1.76 ($2.03) a pound (453g) in February, up from US$1.35 in January. Mild Arabica coffee was trading on the commodity markets for US$1.76 ($2.03) a pound (453g) in February, up from US$1.35 in January.

If you go to the Countdown website you find that their Signature range coffee beans cost NZ$6 for 200g, or roughly US$12 per pound. Obviously most of the cost is not the wholesale commodity price. That’s presumably even more true for instant coffee (the authentic version of the beverage in a ‘traditional cooked breakfast’)

The components of the CPI that have increased fastest aren’t all that surprising if you read the Herald regularly. For example, the cost of home ownership was up 27% over that five-year period, insurance was up 26%, education, and cigarettes and tobacco were up 67%.

If some things go up faster than average, others must go up slower or even decrease. Household appliances and furniture are down a bit. Telecommunications equipment, computing equipment,  and telecommunications services have gotten much cheaper. You can hardly give away a 2008 phone or computer (though if you’re trying to, Te Whare Marama refuge will put it, and more recent kit, to good use)

March 27, 2014

Individual risk and population risk

The Herald and Stuff both have a story about the most dangerous intersections in the country, based on the Ministry of Transport press release. The Herald continues its encouraging new policy of providing the actual data, so we can look in more detail.

The first thing to note is that no intersection in the country appears to have had more than two fatal crashes in ten years, which is better than I would have expected. That’s why crashes involving even minor injuries need to be included in the ranking.

The second issue is the word ‘dangerous’. These 100 intersections are the ones that most need something done to them; they are where the most crashes happen. That’s not the same as the usual use of ‘most dangerous’ — these aren’t the intersections that pose the greatest risk to someone driving through them. The list is from a population or public health viewpoint: these intersections are more dangerous in the same way that dogs are more dangerous than sharks, or flu is more dangerous than meningitis.


January 9, 2014

Infographic of the week

Via @keith_ng, this masterpiece showing that more searches for help lead to more language. Or something.


It’s not, sadly, unusual to see numbers being used just for ordering, but in this case the numbers don’t even agree with the vertical ordering.  And several of them aren’t, actually, languages. And the headline is just bogus.

This version, by Kevin Marks (@kevinmarks), at least is accurate and readable.


but it’s hard to tell how much of Java’s dominance is due to it being popular versus being confusing.

Adam Bard has data on the most popular languages on the huge open-source software repository GitHub. This isn’t quite the right denominator, since Stack Overflow users aren’t quite the same population as GitHub users, but it’s something.  Assigning iOS, Android, and Rails, to Objective-C, Java, and Ruby respectively, and scaling by GitHub popularity, we find that C# has the most StackOverflow queries per GitHub commit; Objective-C and Java have about two-thirds as many.  In the end, though, this data isn’t going to tell you much about either high-demand programming skills or the relative friendliness of different programming languages.



November 16, 2013

Fun with percentages

This week there was a quarterly report estimating smartphone market share for different operating systems, which turned out to be  packed with trapdoors for the unwary reporter.  The NZ media largely avoided  the problems (mostly by sensibly ignoring the report) but many international tech sites leaped in with both feet.

The basic information is in this table:



There are some important nerdy details in interpreting the numbers, such as the difference between “shipments” and “sales,” but we can ignore those for now. The main problem came in picking which numbers to report. The popular ones were the 81.0% market share for Android, the 1.5% fall in market share for Apple’s iOS, and the 156% increase in shipments for the Windows Phone.

The big rise in Windows phones is due (as the report points out) to the fact that there were basically no Windows phones being sold last year, and that’s now increased to some Windows phones being sold — not only is Windows still well behind iOS and Android, but its increase in actual phones shipped was smaller than the increase for either iOS or Android.  That’s all clear just from the numbers in the report.

Android has obviously been really successful, but 80% market share doesn’t mean quite as much as it sounds: this is just one quarter of phone shipments, and nowhere near 80% of the smartphones already out there are Android — the installed base is still much larger for iOS. If you’re writing the next Candy Crush or Angry Birds, what you care about most is the number of potential customers on each operating system. On the other hand, if you’re interested in current cash flow, so that one quarter’s shipments are relevant, you care about revenue or profit, which are lower per phone for Android (which is why I now have an Android phone).

And, finally, if you’re a tech writer, as Kit Eaton points out, you should know enough about the industry to realise that Apple made a much-anticipated announcement of two new iPhone models at the end of September.  Given a choice, many people (and not just psychotic Apple fanboys) would want to wait until the new phones appeared, either to buy one or to get discounted obsolete model. You’d expect iOS sales to be lower  in the preceding quarter. This isn’t just hypothetical: the chart from the April IDC press release (we’re not digging very deep here) shows the contraction and expansion in Apple market share around the release of the previous model, the iPhone 5, last September.



On the  other hand, at least the fact that last year also had a new iPhone release means that ignoring the context sort of cancels itself out.

(via @juhasaarinen)