Posts filed under Denominator? (55)

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)

November 5, 2013

Can we bring out the real numbers now?

So, the decision has been made and the blood alcohol limit will be lowered.  Perhaps now we can start using realistic numbers for the impact.  The story in the Herald today shows the problem, although it’s actually much better than anything I’ve seen in the mainstream media previously:

The changes come after a two-year review of the impact of lowering the legal blood alcohol limit by 30mg suggested 3.4 lives would be saved a year and 64 injury-causing crashes avoided.

It would also save $200 million in social costs over 10 years.

“Alcohol impairment is a major cause of road accidents in New Zealand, with an average of 61 fatalities, 244 serious injuries, and 761 minor injuries every year caused by at-fault drivers who have been drinking,” said Transport Minister Gerry Brownlee.

“The social cost of these injuries and fatalities is $446 million – a huge sum in a country of our size.”

In the first paragraph the estimated benefit based on actual research is quoted. That’s a big step forward. The second paragraph is just wrong: the social costs aren’t in addition to the lives saved and injuries prevented; that’s where the social cost numbers come from. And it’s multiplied by ten years.

In the third and fourth paragraphs Mr Brownlee is quoted as justifying the change by quoting total costs of drink driving. The social cost number in the fourth paragraph is 22 times larger than the actual estimated benefit. You’d think that sort of discrepancy would draw some journalistic comment.

And later in the story we are told about a victim of a drunk driver. A driver whose blood alcohol concentration was 190mg/100ml, more than twice the existing legal limit, and who was duly convicted and sent to prison under the old laws. Not the sort of person whose behaviour is likely to be affected by this change.

October 31, 2013

Scary lack of context

A number that should be in all stories about accidents on special days of the year: 4500.  That’s roughly how many new claims ACC gets per day: divide the 1.7 million per year by 365.

The Herald passes on the ACC’s figures of 31 Halloween-related injuries and 840 attributed to Guy Fawkes. First you have to divide by five, since these are aggregate totals over five years. Then divide by the average number of claims per day to find that Guy Fawkes Day is responsible for about 4% of a typical day’s injuries, and Halloween racks up about 0.1% of a day.

It wouldn’t be surprising if Halloween actually prevented more injuries than it causes — participating children will be doing something safe under adult supervision, rather than teasing innocent pets, fighting with siblings, getting underfoot in the kitchen, or participating in team sports.

October 18, 2013

Cost-effectivness and meningococcal vaccine

There’s a story in the Herald arguing for mass vaccination in NZ against group C meningococcal disease.  There’s a good case for the vaccination — it’s a really nasty disease and there aren’t any other good treatment or prevention approaches — but I don’t see how the cost-effectiveness claims in the story can be right.

Dr Gravatt is quoted as saying there would be zero net medical cost for the vaccination program

Dr Gravatt estimated the net cost of vaccinating children at 12 months and again at 18 years would be zero for each “quality-adjusted” year of life saved at a vaccine price of $25 to $40 per dose. The listed prices were around $43 to $87, but discounts would be likely in a bulk contract.

He refers to a British vaccine study — which one isn’t specified.  However, there are cost-effectiveness analyses of the whole British group C meningococcal vaccination program (they vaccinate against group C but not group B, the opposite of NZ).  One, from 2002, estimates  a cost per life year saved of £6259. The second, from 2006, considers a wider range of possible vaccination programs: for the one that’s most similar to what Dr Gravatt proposed it estimates net medical costs of £9082 per quality-adjusted life year, and for the cheapest one, £3653 £2760 (update)per quality-adjusted life year. And that’s assuming the vaccine costs only £12 per dose, and in a country where group C meningococcal disease was slightly more common than it is here.

Another way to look at it: there are about 60000 births per year in NZ, so after the initial catch-up phase we’d be paying for 120000 doses per year. Even at $25 per dose, that comes to $3 million per year. According to the Herald’s story there are about 25 cases per year, so for the vaccination to be cost-neutral even at this lowest suggested price, the average disease case would have to cost the healthcare system $120000. That’s more than ten times what the UK cost-effectiveness study estimated (roughly £4000) including both the immediate cost of treating the disease and the cost of treating the long-term effects.

The vaccine looks to be a lot more cost-effective than, say, the prostate cancer drug that Campbell Live was pushing last week, and because herd immunity is important for this disease, there’s a relatively stronger case for vaccinating everyone, but that would be because the cost is worth it, not because the cost is zero.

Updates, including a lot more technical detail:  (more…)

October 13, 2013

Think of a number and multiply by 80000

Bernard Hickey in the Herald

Imagine the public outrage if it were discovered that more than 80,000 New Zealanders were receiving wages, salaries and investment incomes of more than $6 billion a year, but were also receiving a benefit from the Government.


Income figures this week from Statistics NZ show more than 80,000 New Zealanders over the age of 65 receive wages, salaries and investment returns of more than $6.5 billion a year while claiming NZ Super.

It certainly helps to summon the outrage if you uses totals rather than averages. I  think there could be a reasonable case for means-testing NZ Super, but these numbers are not a contribution to informed public debate.

I’m not even sure where he got the data: he says “income figures this week from Statistics NZ”, and the only plausible source on the Stats NZ release calendar seems to be the NZ Income Survey, released on October 4. But in the NZ Income Survey data, table 8 says there are only 53,900 people aged 65+ with income above $1150/wk, which works out to just under $60000/year (including their NZ Super, of course).  His figures could still be right — perhaps the very wealthy people at the top drag the total up —  but they can only be right in the same sense as Bill English‘s “people earning under $110000 collectively pay no net income tax”.

Imagine the public outrage if it were discovered that nearly 54000 retired New Zealanders were earning over $45000/yr  from investments and salaries and still collecting NZ Super as well. Go on, imagine it.

September 13, 2013

How dangerous are weddings?

According to the Herald, the ACC wants us to be careful about weddings — about getting injured at them, that is.

Weddings are supposed to be the happiest day of your life – try telling that to the hundreds of people who make ACC claims for injuries at ceremonies.

From tripping on the bride’s dress to swallowing the ring, nuptials can be surprisingly hazardous.

New figures show at least 600 people made claims to the ACC between 2010 and 2012.

So, how does the 600 claims over three years compare to what you’d expect from an average day?

The ACC accepted 1.7 million new claims last year, which gives about 0.4 claims per person per year, or about 0.001 per person per day.

There were about 20 000 marriages in New Zealand last year, so about 60 000 over 2010-2012, giving about 0.01 ACC claims per marriage.  The 600 reported claims would then be about what you’d expect if there were 10 person-days of exposure per marriage.

My experience is that wedding celebrations typically involve more than ten people, and, with setup and rehearsals, often more than one day.  It looks as though weddings, like Christmas, are actually safer than ordinary days.

July 15, 2013

Think of a number and multiply by eight

We haven’t had a good denominator post in a while, but I was struck by Stuff’s story on ‘social lending’.  By next April, an NZ company hopes to be able to start up peer-to-peer lending here, after changes in the law, and we’re told

“This will be a way for individuals to play alongside the big institutions,” Milsom said

Just how that can happen – and the scale that is possible – is shown from what has happened in the UK, where the largest peer-to-peer lender has lent more than £330 million since it launched in 2005.

That’s an average of just over £40 million per year over 2005-2012, or about 66p per capita per year in the UK.  On the same scale in New Zealand, that would come to perhaps $6 million per year in loans.  The UK lender in question appears to be Zopa, and they make their money by charging a 1% borrowing fee and 1% lending fee.  Under the same setup, $6 million per year in loans would mean $120 000 per year in income for an NZ equivalent, before paying any costs.

It’s certainty possible that peer-to-peer lending will take off, and it might not be long before it exceeds 1% of all unsecured consumer debt. But the idea makes more sense spun as ‘room for expansion’ not as ‘look at the scale in the UK’.