Archive for the ‘statistics’ Category

Banned! Minority tyrrany! (Perspective?)


There’s been a ruling in an English High Court that, instead of praying at the start of council meetings (when everyone must be there), the Bideford town council should instead pray just before the start of council meetings (when attendance is optional). The case was introduced by a local councillor, and supported by the National Secular Society (NSS). Michael Langrish, the Bishop of Exeter, tells us in that story that this is an attack on the religious freedom of Christians. “I think it’s a great pity that a tiny minority are seeking to ban the majority, many of whom find prayers very, very helpful, from continuing with a process in which no-one actually has to participate.”

It seems to me that there is a whole lot of wrong wrapped up in the Bishop’s words. I’ll take some time to review the two main bits of wrong: the demographics involved, and the injury done.

For the demographics, I’m drawing on a 2011 poll commissioned by the British Humanist Association (BHA), and a 2007 poll conducted by Why Church, a Christian group. I do not know how biased either of these polls might be, so I will also throw in numbers from the recurring British Social Attitudes Survey. The numbers differ, but the overall story is basically the same.

The BHA study found that 53% of people in England and Wales claim to be Christian (7% claim other religions), but only 29% claimed to be religious. For how many of those is the message of their church important? The Why Church study finds that regular attendance is declining steadily – at the time of the report, it was at 15%. That’s how many in the UK attend at least once a month. In particular, compare this section from the executive summary of their report to the bishop’s statement above (my emphasis):

Two thirds of UK adults (66%) or 32.2 million people have no connection with church at present (nor with another religion). These people are evenly divided between those who have been in the past but have since left (16 million) and those who have never been in their lives (16.2 million). This secular majority presents a major challenge to churches. Most of them – 29.3 million – are unreceptive and closed to attending church; churchgoing is simply not on their agenda.

The BHA study supports this, reporting that 63% of respondents had not been to church in more than a year.

It looks like the good bishop’s claim to speak for the majority is, at best, barely true and soon to be outdated. More likely, he’s thinking about a Britain that is several decades in the past.

The BHA poll reports that while 53% claim to be Christian, 65% of people in England and Wales claim to be non-religious. Clearly, some see themselves as “non-religious Christians” – a category which reminds me of “secular Jews”. A Scottish poll gave similar results: 58% claiming some religious affiliation, and 56% saying they were not religious. Even the Why Church survey shows agnostics and atheists at 33% of the population. Langrish’s claim that it is a “tiny minority” imposing these onerous restrictions is therefore ridiculous. It is no stretch to say that, if they don’t already, non-believers are likely to soon outnumber believers in the UK.

The British Social Attitudes Survey shows a drop in Church of England affiliation from 22.50% in 2008 to 19.98% in 2009. Christians overall went from 49.70% to 43.83%, and total religious affiliations from 56.38% to 48.86%. The “no religion” category grew over the same period from 43.19% to 50.67%. Call me crazy, but it looks to me like the bishop’s C of E flock is less than half the size of those whose interests the NSS seeks to protect – Langrish’s “tiny minority”. Probably, he meant all religious people when referring to the “majority” – but even so the numbers are close, and moving in favour of the non-religious.

I’ll let you sift through the statistics yourselves for further insight – there is obviously a lot of scope for picking different numbers, depending what aspect of the issue is important to you. The British Social Attitudes Survey releases their data to registered users; the Why Church people have a number of informative graphics on their website, as well as an in-depth report (PDF). The BHA provides downloadable statistical summaries of their poll on their website.

What wiggle room do we have in interpreting the demographics for this issue?

On the bishop’s side, we could include only regular attenders of the Church of England? That would be somewhere well south of 15%. It’s tempting, but of course other Christians and religious people more generally may also claim an interest in making prayers part of the official council business. That would put the number up as high as 61% – but only, mark you, if the prayers are inclusive of all religious perspectives. And what about people who only attend services rarely or not at all? Is it reasonable to think that they would be upset by a law that allows councillors to opt out of pre-meeting prayers? Counting regular (monthly or more) attenders from all religions, we get something closer to the 15%.

On the secular side, should we only look at members of the NSS, the BHA, and other organizations promoting non-belief? If so, we’ll have a very low number – perhaps appearing to justify Langrish’s “tiny minority”. The BHA has 28000 paying members and supporters; the HSS (Humanist Society of Scotland) has around 6500 members; and the NSS is estimated to have fewer than 10000 paying members. Some individuals will be members of more than one of these groups, and there are many smaller groups that I have left off of this list, but this indicates that something like 40000 people – a fraction of a percent of the UK population, are card-carrying, dues-paying secularists. Should we also include the “de-churched” – the 33% of UK adults who used to attend church, but no longer do? They seem to have made a pretty solid vote for reducing the influence of church in their daily lives. Should we include everyone who claims to be non-religious? Again, it’s tempting, but not all of this group (depending on the survey, somewhere from 33% to 65%) will agree with the secularization of Britain (just as not all religious people agree with the establishment of church power and rituals in government institutions).

Regarding the specific issue at hand – religious prayers before council meetings – a couple of questions about politics on the British Social Attitudes Survey are also relevant. A growing number of people think that churches have too much power in the country (10.58% in 1991, 29.76% in 2008), and people increasingly object to religious leaders influencing government (56.64% in 1991, 67.26% in 2008).

Goodness, what a mess of numbers! Over all, the bishop’s appeal to democratic sensibilities seems to backfire. If the will of the people is important, then the British people seem to be saying that the church should back off. (Of course, an obvious rejoinder from Langrish’s camp would be to bemoan the fact that people are turning their backs on religion – but that becomes more paternalistic and less democratic. Besides, I wouldn’t want to put words in the good reverend’s mouth.)

But let’s back up a little. What did the court rule, exactly? It ruled that prayers are okay in a pre-meeting context, but not as part of the minuted, mandatory-attendance part of council meetings.

So when we hear people complain that their voices are being silenced, their rights trampled on, bear that in mind. They are being pushed perhaps a few minutes earlier, so that people who object to the practice of prayer in council meetings have more freedom to absent themselves while the religious folks carry on thanking and invoking and praising as they always have. That is the great secular imposition which Langrish and others are wailing about.

This is the point where I would typically want to extract some broader lesson. Perhaps about people’s tendency to inflate perceived injuries against them. Or I would congratulate myself on my humility by noticing that we also tend to minimize perceived injuries against others when we identify – by creed or otherwise – with those accused of the attack. (It’s true that I think the Bishop is being alarmist. On the other hand, he is right in his statement in the Guardian that ” the agenda of the National Secular Society is inch by inch to drive religion out of the public sphere.”)

But I think I’ll leave it there, and see what you think. Is there an obvious demographic perspective that makes this all clear? Should we be worried about how many of us there are and how many of them, or is secularization about something more than just one side beating another side with brute numbers? What is the significance of the (apparently overlooked) fact that it was the High Court, attempting to interpret the laws of the land, that handed down this ruling (and not the NSS or one disgruntled atheist councillor)?

Exploring language


Thanks to Steve Novella of the Neurologica blog, I have discovered a new toy to play with: the Google Ngram Viewer. I’d like to share it with you, and encourage you to play as well.

You may have heard of all the books that Google has been digitizing for their Google Books project. (It caused some stir among publishers and writers – it seems to have been sorted out now.) Well, the Ngram Viewer is a very Google-esque* way of looking at word count statistics from that huge collection of books.

Let’s say you’re curious about the relative popularity of two words – say, “humanist” and “atheist“. Well, you enter them as search terms, and voila:

humanist/atheist unigram graph, 1800 to 2000

Relative frequencies of "humanist" and "atheist" in the Google Books corpus, from 1800 to 2000.

We can watch the relative frequencies of these words over time. Unexpectedly (to me at least), we see “humanist” (blue) overtake “atheist” (red) during the first half of the twentieth century, following a couple of decades (20s and 30s) tracking together.  I’ll leave it up to readers to try to infer the reason for this inversion.

The term “n-gram” (yes, pronounced the same as “engram”, but there’s no connection to neuropsychology or Scientology) is used in corpus-based linguistics to denote sequences of words. A unigram is a sequence of 1 word; in the graph above, we compare the frequencies of two unigrams (relative to the total number of unigrams in the corpus). A bigram is a sequence of 2 words. Trigram: 3 words. From there on, it is common just to use the number: 4-gram, 5-gram, etc.

One more unigram comparison that I thought was interesting: function words. Check out this graph comparing “the”, “and”, “of”, “for”, “a”:

Unigram frequencies for selected function words, 1800 to 2000.

Unigram frequencies of "the", "of", "and", "a", "for", from 1800 to 2000.

What is interesting here is that the relative (and even the absolute) frequencies show very little change over two centuries. Think about all of the change in the language that those two centuries represent – from shortly after the founding of America to around the time of the latest millennial fever. And these five words have shown such amazing constancy. Sure, there is some change, but compare those to the changes in other graphs, and the difference is clear.

So, let’s check out a bigram comparison. Here’s a chart of “national debt” and “social security”:

Bigram frequencies for "national debt" and "social security"

Bigram frequencies for "national debt" and "social security" from 1800 to 2000.

I’m no political scientist, but it looks like interest in social security leaped onto the scene in the late 30s, and has been slowly climbing ever since, while talk about national debt (in the English-speaking world) has steadily declined basically since the earliest samples in this corpus.

I could go on all day about this, but I’d rather leave it to you now. Before you take off to do your own informal surveys of this delicious data repository, let me offer a couple of caveats.

First, the numbers are only as reliable as the sources. What are the sources? Google gives some information on this. They note some sources of error; they also acknowledge some inherent biases. For example, there are more computer books in recent years than in the 1800s. Whether this is a problem or not depends on the sort of question you’re asking, and how you are interpreting it.

Second, there are different numbers of books in different time periods. They actually go back as far as 1500, but you get problems when, say, a particular year only has one book published. (Check out the results for that nice constant graph of function words, if you go back to 1500.)

Third, always always keep in mind what it is that you’re measuring. These graphs do not measure belief (search “bigfoot, ufo, unicorn“). They do not measure popularity or approval (search “murder, charity“, or the “national debt, social security” illustration above). They simply measure how often people mention the words (or bigrams, trigrams, etc) in published books. (Periodicals are excluded.)

Having said that, it is still a delightful way to while away a day. If you’re stuck for ideas, here are a couple of classic sources of interesting patterns:**

  • What are the relative frequencies of different number words? Is there anything systematic here? Any surprises?
  • What are the relative frequencies of gender-marked pronouns (“he, she”, for example)? How about gender-marked nouns (“man, woman”)?***

Have fun, my merry scientists!


* Google-esque: powerful, easy to use, with the potential to distract me from real work with its endless possibilities to explore.

** Before doing any search, see if you can guess what the results will be. Form a hypothesis, give a reason for your expectation. If the results agree with your expectation, congratulations! If not, see if you can explain why. Does this new explanation generate predictions about some other word frequency pattern that you could now test?

*** There is at least one pair of gender-marked nouns that seems to reverse the general trend. Can you find them? Why would they be different?

What are the odds?


I have just learned that tomorrow, the 20th of October 2010, is the first ever World Statistics Day – officially designated by the UN!

As a scientist, I directly use statistics every day, analysing and reporting results of experiments, and reading and evaluating the research of others.  As a regular person, I indirectly use statistics every day.

Some are statistics that I have gathered, consciously or unconsciously.  (When is the bus due?  How likely am I to catch it if I wait another 5 minutes?)

Some are statistics that I’ve been explicitly exposed to – in advertisements, media reports, or conversations with people I know.  (Will dressing like this help me get the job?  Will this candidate’s policies really improve the economy?  Will this candidate really implement these policies?  How bad is my lack of regular exercise for my long-term health?)

Responsible use of statistics is one of the greatest boons to modern science – from the development and evaluation of medical innovations (yay, Florence Nightingale!) to the examination of global climate (it’s changing).

Irresponsible use of statistics is an increasing threat.  From frauds misusing the numbers to promote quack alternatives to medicine, to news outlets misrepresenting results for the sake of a headline, to politicians and industry executives lying with a veneer of scientific credibility.

Without (responsible) statistics, we would be at the mercy of our appallingly bias-laden intuitions.  (Be honest, did you get the Monty Hall problem right when you first came across it?)  Without a basic understanding of statistics, we are at the mercy of people who will distort the data to try to convince us of anything.

A tiny side-note here:  despite the popular aphorism, it is not true that you can prove anything you want with statistics.  You can claim anything you want.  If your audience is ignorant enough you might get away with it.  But only by lying and distorting.  Statistics don’t lie to people; people lie to people (and often to themselves.) If you understand statistics – and I mean the basic concepts, not the fancy mathematical equations – then it is much harder for someone to lie to you with statistics.

Okay, I’d love to go on at greater length.  But I have some data to analyze.

In celebration, here are some things to check out.  Enjoy!

  • R, the best way to do statistics.  It’s free and it’s friendly.  It’s used in beginners courses, and it’s used by professional statisticians.  Give it a try.  You know you want to!
  • Ben Goldacre’s Bad Science blog and book, with loads of tips about what to look out for in popular portrayals of science and statistics.  (That book would serve as a good introduction to statistical thinking, among other things.)
  • Hans Rosling’s presentation of beautiful statistics (YouTube) – proving that stats don’t have to be boring and opaque.


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