Stats Chat

Nature doesn’t care about round numbers in base 10, but people do.  From @rcweir, via Amy Hogan, this is Twitter data of the number of people followed and following (truncated at 1000 to be readable). The number of people you follow is under your control, and there are clear peaks at multiples of 100 (and perhaps at multiples of 10 below 100). The number following you isn’t under your control, and there aren’t any similar patterns.

For a medical example, here are self-reported weights from the US National Health Interview Survey

The same thing happens with measured variables that are subject to operator error: blood pressure, for example, shows fairly strong digit preference unless a lot of care is taken in the measurement.

As usual about this time of year, our Honours and M.Sc. students are giving talks on their research projects

• Modelling the natural inflows to New Zealand lakes
• Refactoring the xtable package
• Invertible reproducible documents
• Bootstrap goodness of fit tests
• Convex regression
• Using the Robust Covariance Matrix Estimator to improve the precision of principal component eigenvectors in the orthogonal multivariate test
• Orthogonalised multivariate survey-weighted linear models for medical data
• Factors affecting catch composition in NZ scampi fisheries
• Factors affecting tagging mortality in snapper
• Assessment of rapid eradication assessment
• Factors explaining the low income return for education among Asian New Zealanders
• A comparison of methods used to reconcile forecasts in hierarchical time series
• Numerical methods for drawing piecewise smooth curves
• An evaluation of the Christian Broadcasting Association’s Appeal and Donorcom campaigns
• Multi-choice and true/false assessments in introductory statistics: What can they tell us about student understanding?
• Bayesian computation for exoplanet data
• Modelling an Ophthalmology Clinic Booking List System: Assumptions and Implementation
• Reinforcement Processes on Graphs
• Influence analysis on phylogeny inference
• Statistical analysis of chemical soil composition in the Wairau Valley
• Describing the world’s nations
• Parameter estimation of the coalescent in continuous space

That doesn’t sound like a very interesting headline, but an important clinical trial whose results were released today has made definite steps towards re-convincing researchers on this point.

The trial, IMPROVE-IT, looked at adding a new drug, ezetimibe, to one of the standard statin drugs for cholesterol lowering, in people who had previously had a heart attack. Ezetimibe works by blocking cholesterol absorption in the gut, a completely different mechanism to the statins, which block cholesterol synthesis. The drug had previously shown unconvincing results in a preliminary study, made even less convincing by the behaviour of the manufacturer. There was increasing uncertainty that the cholesterol-lowering effect of the statins was really how they prevented heart disease, since no other drug appeared to be able to do the same thing.

Now, IMPROVE-IT has found a reduction in heart attacks and strokes. It’s very small — only 2 percentage points, even in this high-risk group of patients — but it looks real. Given the price of ezetimibe it probably won’t be widely used immediately, but it comes off patent in a few years and then use might spread a bit.  The results are also encouraging for dietary approaches to lowering cholesterol by reducing absorption: some cereals, and spreads with plant sterols.

Other stories: Forbes, New York Times 

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 November 21 2014.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of November 15 – 21 2014 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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When statisticians get quoted on the lottery it’s pretty boring, even if we can stop ourselves mentioning the Optional Stopping Theorem.

This week, though, John Oliver took on the US state lotteries: “..,more than Americans spent on movie tickets, music, porn, the NFL, Major League Baseball, and video games combined. “

(you might also look at David Fisher’s Herald stories on the lottery)

Via Michael Toth  I found this animated GIF from isomorphismes, showing the ‘yield curve‘ for Federal Reserve bonds

Michael modified the curve to make it prettier — alternatively, more similar to the style of The Economist.  In both cases, though, I felt the time context was missing.  Using animation rather than multiple plots lets you get a lot more on a page, but you can’t see what’s happening as clearly.

One possibility is to make a separate graphic that shows where you are in time; another is to keep some history by letting the graph leave shadows. In the graph below (based on both the linked examples), there are 12 months worth of shadow lines trailing the solid line, and a grey indicator bar showing where we are in history, with GDP growth and unemployment as context.

Even better (though not embeddable in WordPress) would be to make the time axis able to both autoplay and be controllable by the user, as in this example from the R animint package.

(update: the code)

New Zealand has a national school funding system that allocates money to schools based on socio-economic data about students.  This isn’t self-reported individual-level data, but is at the level of Census meshblocks (details here.) Schools are divided into ten deciles, and more funding given to lower-decile schools.  Despite the higher funding, lower-decile schools, on average, have poorer results on standardised assessments.  You can see good visualisations of this from Luis Apiolaza,

There are less-good ones at Stuff: dot plots aren’t ideal for this, and it really is better to look at cumulative categories (‘at standard or better’) rather than individual categories (‘at standard but not better’). Unfortunately, these graphs tell you almost nothing about the policy question of whether there are better ways to target the funding. There might be; there might not be.

One advantage of the current system is its automatic stabilisation. The Herald, earlier this week, had a good story about changing ethnic profiles of schools, with the sort of combination of data and individual stories it would be nice to see more often.  It turns out the low-decile schools are seeing fewer students of European ethnicity, and more Māori and Pasifika students. The phrase ‘white flight’ was used, but because of the funding system this isn’t the same sort of problem as the original ‘white flight’ from US inner cities.

In the US, a lot of public school funding comes from local government. When more-affluent families leave an area, the government funding for education goes down.  In New Zealand, when more-affluent families leave an area, the government funding for education goes up.  There’s still a concern about diversity, but not the same sort of vicious circle that was seen in the US.

From the Telegraph (via many people on Twitter)

Seeing this at the same time as hearing about Bob Geldof’s Band-Aid reboot really emphasises the point that Africa isn’t a single place. The first Band-Aid recording was intended to help people in Ethiopia; the new one is for the Ebola-stricken regions of West Africa. The distance from Freetown to Addis Ababa is about the same as Auckland to Dili in East Timor, or Los Angeles to Bogota (or Addis Ababa to Prague).

On the other hand, the graph does make an important point. Syphilis, starvation, and TB are all very inexpensively treatable. Malaria and HIV are largely preventable, also at low cost. An effective treatment for Ebola will help, especially for medical personnel who are otherwise at very high risk, but in the long run it isn’t going to be enough. If we can’t deliver penicillin effectively, we won’t be able to deliver Ebola drugs. To make a real difference, we need a vaccine that’s good enough to prevent outbreaks.

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 November 14 2014.
• Statistics can be bad, exemplary or fascinating.
• The statistic must be in the NZ media during the period of November 8 – 14 2014 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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This chart is from a beautiful infographic about cash crops.  I don’t believe the cannabis revenue number. That’s partly because I read Keith Humphreys and Mark Kleiman on the subject.

Keith Humphreys takes apart a claim of $120 billion for the total value of the US marijuana market, showing that it can’t be anything near that much.

Current pot smokers report that they use marijuana an average of 60 days a year. Using our current example, 40 ounces/60 days of use means that the average user would have to go through 2/3 of an ounce of marijuana on each day that they used marijuana. That’s .67 X 50 or 33.5 joints per day of use. And there’s a terrific bridge for sale in Brooklyn too.

Even then, the purported $120 billion was the price to the consumer.  That’s not what was used for the legal crops, and it makes a big difference.

Suppose we agree use consumer price rather than farmer revenue because the data are slightly more reliable. I don’t really believe a number above about $12 billion for the US.  The US has about 1/5 of the world GDP. If the US spent $12 billion/year on cannabis, the rest of the world would need to spend almost $300 billion, or more than six times as much as a fraction of their income.  A lot of the world would need to spend more on pot than on basic carbohydrates.

It’s not inconceivable that the number is right — maybe cannabis is really big in, say, Brazil or India and I just don’t know about it — but it’s surprising enough that I’d want a lot more detail to justify it.