Posts filed under Correlation vs Causation (60)

January 16, 2015

Women are from Facebook?

A headline on Stuff: “Facebook and Twitter can actually decrease stress — if you’re a woman”

The story is based on analysis of a survey by Pew Research (summary, full report). The researchers said they were surprised by the finding, so you’d want the evidence in favour of it to be stronger than usual. Also, the claim is basically for a difference between men and women, so you’d want to see summaries of the evidence for a difference between men and women.

Here’s what we get, from the appendix to the full report. The left-hand column is for women, the right-hand column for men. The numbers compare mean stress score in people with different amounts of social media use.


The first thing you notice is all the little dashes.  That means the estimated difference was less than twice the estimated standard error, so they decided to pretend it was zero.

All the social media measurements have little dashes for men: there wasn’t strong evidence the correlation was non-zero. That’s not we want, though. If we want to conclude that women are different from men we want to know whether the difference between the estimates for men and women is large compared its uncertainty.  As far as we can tell from these results, the correlations could easily be in the same direction in men and women, and could even be just as  strong in men as in women.

This isn’t just a philosophical issue: if you look for differences between two groups by looking separately for a correlation each group rather than actually looking for differences, you’re more likely to find differences when none really exist. Unfortunately, it’s a common error — Ben Goldacre writes about it here.

There’s something much less subtle wrong with the headline, though. Look at the section of the table for Facebook. Do you see the negative numbers there, indicating lower stress for women who use Facebook more? Me either.


[Update: in the comments there is a reply from the Pew Research authors, which I got in email.]

September 25, 2014

Asthma and job security

The Herald’s story is basically fine

People concerned that they may lose their jobs are more likely to develop asthma than those in secure employment, a new study suggests.

Those who had “high job insecurity” had a 60 per cent increased risk of developing asthma when compared to those who reported no or low fears about their employment, they found.

though it would be nice to have the absolute risks (1.3% vs 2.1% over two years) , and the story is really short on identifying information about the researchers, only giving the countries they work in (the paper is here).

The main reason to mention it is to link to the NHS “Behind the Headlines” site, which writes about stories like this one in the British Media (the Independent, in this case).

Also, the journal should be complimented for having the press release linked from the same web page as the abstract and research paper. It would be even better, as Ben Goldacre has suggested, to have authors listed for the press release, but this is at least a step in the direction of accountability.

September 10, 2014

Cannabis graduation exaggeration


Teenagers who use cannabis daily are seven times more likely to attempt suicide and 60 percent less likely to complete high school than those who don’t, latest research shows.

Me (via Science Media Center)

“The associations in the paper are summarised by estimated odds ratios comparing non-users to those who used cannabis daily. This can easily be misleading to non-specialists in two ways. Firstly, nearly all the statistical evidence comes from the roughly 1000 participants who used cannabis less than daily, not the roughly 50 daily users — the estimates for daily users are an extrapolation.

“Secondly, odds ratios are hard to interpret.  For example, the odds ratio of 0.37 for high-school graduation could easily be misinterpreted as a 0.37 times lower rate of graduation in very heavy cannabis users. In fact, if the overall graduation rate matched the New Zealand rate of 75%, the rate in very heavy cannabis users would be 53%, and the rate in those who used cannabis more than monthly but less than weekly would be 65%.

That is, the estimated rate of completing high school is not 60% lower, it’s about 20% lower.  This is before you worry  about the extrapolation from moderate to heavy users and the causality question. The 60% figure is unambiguously wrong. It isn’t even what the paper claims.  It’s an easy mistake to make, though the researchers should have done more to prevent it, and that’s why it was part of my comments last week.

You can read all the Science Media Centre commentary here.


[Update: The erroneous ‘60% less likely to complete high school’ statement is in the journal press release. That’s unprofessional at best.]

(I could also be picky and point out 3News have the journal wrong: The Lancet Psychiatry, which started this year, is not the same as The Lancet, founded in 1823)

August 20, 2014

Good neighbours make good fences

Two examples of neighbourly correlations, at least one of which is not causation

1. A (good) Herald story today, about research in Michigan that found people who got on well with their neighbours were less likely to have heart attacks

2. An old Ministry of Justice report showing people who told their neighbours whenever they went away were much less likely to get burgled.

The burglary story is the one we know is mostly not causal.  People who tell their neighbours whenever they go on holiday were about half as likely to have experienced a burglary, but only about one burglary in seven happened while the residents were on holiday. There must be something else about types of neighbourhoods or relationships with neighbours that explains most of the correlation.

I’m pretty confident the heart-disease story works the same way.  The researchers had some possible explanations

The mechanism behind the association was not known, but the team said neighbourly cohesion could encourage physical activities such as walking, which counter artery clogging and disease.

That could be true, but is it really more likely that talking to your neighbours makes you walk around the neighbourhood or work in the garden, or that walking around the neighbourhood and working in the garden leads to talking to your neighbours? On top of that, the correlation with neighbourly cohesion was rather stronger then the correlation previously observed with walking.

July 22, 2014

Lack of correlation does not imply causation

From the Herald

Labour’s support among men has fallen to just 23.9 per cent in the latest Herald-DigiPoll survey and leader David Cunliffe concedes it may have something to do with his “sorry for being a man” speech to a domestic violence symposium.

Presumably Mr Cunliffe did indeed concede it might have something to do with his statement; and there’s no way to actually rule that out as a contributing factor. However

Broken down into gender support, women’s support for Labour fell from 33.4 per cent last month to 29.1 per cent; and men’s support fell from 27.6 per cent last month to 23.9 per cent.

That is, women’s support for Labour fell by 4.2 percentage points (give or take about 4.2) and men’s by 3.7 percentage points (give or take about 4.2). This can’t really be considered evidence for a gender-specific Labour backlash. Correlations need not be causal, but here there isn’t even a correlation.

June 23, 2014


My attention was drawn on Twitter to this post at The Political Scientist arguing that the election poll reporting is misleading because they don’t report the results for the relatively popular “Undecided” party.  The post is making a good point, but there are two things I want to comment on. Actually, three things. The zeroth thing is that the post contains the numbers, but only as screenshots, not as anything useful.

The first point is that the post uses correlation coefficients to do everything, and these really aren’t fit for purpose. The value of correlation coefficients is that they summarise the (linear part of the) relationship between two variables in a way that doesn’t involve the units of measurement or the direction of effect (if any). Those are bugs, not features, in this analysis. The question is how the other party preferences have changed with changes in the ‘Undecided’ preference — how many extra respondents picked Labour, say, for each extra respondent who gave a preference. That sort of question is answered  (to a straight-line approximation) by regression coefficients, not correlation coefficients.

When I do a set of linear regressions, I estimate that changes in the Undecided vote over the past couple of years have split approximately  70:20:3.5:6.5 between Labour:National:Greens:NZFirst.  That confirms the general conclusion in the post: most of the change in Undecided seems to have come from  Labour. You can do the regressions the other way around and ask where (net) voters leaving Labour have gone, and find that they overwhelmingly seem to have gone to Undecided.

What can we conclude from this? The conclusion is pretty limited because of the small number of polls (9) and the fact that we don’t actually have data on switching for any individuals. You could fit the data just as well by saying that Labour voters have switched to National and National voters have switched to Undecided by the same amount — this produces the same counts, but has different political implications. Since the trends have basically been a straight line over this period it’s fairly easy to get alternative explanations — if there had been more polls and more up-and-down variation the alternative explanations would be more strained.

The other limitation in conclusions is illustrated by the conclusion of the post

There’s a very clear story in these two correlations: Put simply, as the decided vote goes up so does the reported percentage vote for the Labour Party.

Conversely, as the decided vote goes up, the reported percentage vote for the National party tends to go down.

The closer the election draws the more likely it is that people will make a decision.

But then there’s one more step – getting people to put that decision into action and actually vote.

We simply don’t have data on what happens when the decided vote goes up — it has been going down over this period — so that can’t be the story. Even if we did have data on the decided vote going up, and even if we stipulated that people are more likely to come to a decision near the election, we still wouldn’t have a clear story. If it’s true that people tend to come to a decision near the election, this means the reason for changes in the undecided vote will be different near an election than far from an election. If the reasons for the changes are different, we can’t have much faith that the relationships between the changes will stay the same.

The data provide weak evidence that Labour has lost support to ‘Undecided’ rather than to National over the past couple of years, which should be encouraging to them. In the current form, the data don’t really provide any evidence for extrapolation to the election.


[here’s the re-typed count of preferences data, rounded to the nearest integer]

June 3, 2014

Are girl hurricanes less scary?

There’s a new paper out in the journal PNAS claiming that hurricanes with female names cause three times as many deaths as those with male names (because people don’t give girl hurricanes the proper respect). Ed Yong does a good job of explaining why this is probably bogus, but no-one seems to have drawn any graphs, which I think make the situation a lot clearer. (more…)

January 14, 2014

Causation, counterfactuals, and Lotto

A story in the Herald illustrates a subtle technical and philosophical point about causation. One of Saturday’s Lotto winners says

“I realised I was starving, so stopped to grab a bacon and egg sandwich.

“When I saw they had a Lotto kiosk, I decided to buy our Lotto tickets while I was there.

“We usually buy our tickets at the supermarket, so I’m glad I followed my gut on this one,” said one of the couple, who wish to remain anonymous.

Assuming it was a random pick, it’s almost certainly true that if they had not bought the ticket at that Lotto kiosk at that time, they would not have won.  On the other hand, if Lotto is honest, buying at that kiosk wasn’t a good strategy — it had no impact on the chance of winning.

There is a sense in which buying the bacon-and-egg sandwich was a cause of the win, but it’s not a very useful sense of the word ’cause’ for most statistical purposes.

November 7, 2013

Why you should eat in crowded food halls

There’s a couple of posts being promoted on the internet about an important and relatively subtle form of selection bias.  Epidemiologists know it as Berkson’s Paradox, in modern causal inference terminology it’s ‘conditioning on colliders’, and for an economist it’s a consequence of production-possibility frontier.

The basic issue is very simple. As Gabriel Rossman puts it at The Atlantic

 There is no ontological reason why we can’t have shoes that are both hideous and uncomfortable but rather there is a practical reason in that nobody wears shoes that are terrible in every way and so such shoes don’t make it unto the market. 

In the same way, there’s no necessary reason why cricketers who are good at bowling have to be bad at batting.  Being able to deliver the ball so it misleads or outpaces the batsman doesn’t make it any harder to spot bowling trickery or to react fast. And in fact, if you look at 12-year-olds, often the same kids are good at batting and bowling.  In international-level cricket, though, all-rounders are pretty rare, and someone who can take 5 wickets in an Test innings is very unlikely to be able to score a Test century.  The slight positive correlation you see in kids turns into a strong negative correlation in adults. The reason is that getting into an international cricket team requires you to be very, very good at batting or very, very good at bowling. Since it’s more likely that you’re very, very good at one thing than two, most international cricketers are either batsmen or bowlers, but not both. Among those who are selected, there’s a negative correlation.

There are examples in the social sciences: opposition to marijuana legalisation is positively correlated with opposition to government wealth redistribution in the US as a whole, but uncorrelated among Republican voters.

There are examples in medicine: the genetic variant Factor V Leiden is strongly associated with deep-vein thrombosis in the population in general, but not at all predictive of recurrence in people who have already had one.

And there are examples in dining: for a given price, a successful restaurant has to do well enough on some combination of food quality, pleasant ambience, trendiness, etc. So these will end up negatively correlated, and if you want good inexpensive food in downtown Auckland, try one of the Asian food courts.

(via @gnat, who points to one of the posts and notes: Anyone who thinks it’s possible to draw truthful conclusions from data analysis without really learning statistics needs to read this.)

October 27, 2013

Fast-food outlets and obesity

Everyone knows that areas with more fast-food stores have more overweight people, and it certainly makes sense that fast food is bad for you. Like almost everything else, though, it gets more complicated when you start looking carefully.

Firstly, earlier this year Eric Crampton wrote in NBR about some research by an economics PhD student, Rachel Webb, who was trying to take advantage of this well-known relationship to unpick some aspects of correlation vs causation in the relationship between mother’s weight and infant’s birthweight. She found that, actually, areas in New Zealand with more fast-food outlets didn’t have more obesity to any useful and consistent extent.

Secondly, there’s new research on diet and fast food using data from the big NHANES surveys in the USA.  It confirms, as you might expect, that people who eat more fast food also eat less healthily at other times.