Deciphering the Cathedral Stats

The Church of England’s Research and Statistics Department (OK, technically the Archbishops’ Council’s Research and Statistics Department) has released figures for the past decade or so’s attendances at Cathedrals. The headline figures are encouraging, showing a growth in attendance of approximately 3% a year. However, scratch below the surface and some interesting trends (or rather lack of them) become apparent.

Sunday Attendance

The main reason for these impressive growth figures is the rise in midweek attendance. Last year, almost half of those attending a Cathedral for worship did so during the week rather than on Sunday. This sub-section of attendees is the main driver for growth and whilst impressive, masks what’s actually going on at a Sunday level.

In order to get to the bottom of the Sunday attendance figures I ran some linear regressions on the data available to see what the underlying trends were. The data used was below. For those who are pedants in this field, I also ran logistic regressions but they gave very similar outcomes, and for the ease of describing the results to the widest audience I will report the linear regression results.

Adult Minor Combined
2001 15500 2400 17900
2002 15100 2400 17500
2003 15600 2500 18100
2004 16000 2500 18500
2005 16000 2500 18500
2006 15800 2800 18600
2007 15900 2500 18400
2008 15800 2500 18300
2009 15600 2500 18100
2010 15800 3100 18900
2011 15900 2200 18100

The aim of a regression is to create a statistical  model that helps us understand what the underlying trends in a data series are telling us. The regression creates a formula that is the “line of best fit” to the actual data and a number of other useful bits of information (as we will see).

The first regression on the Over 16s produced an intercept of -62689 and a coefficient on the year variable of 39.09 recurring. What this is telling us is that, on average, each consecutive year brought in an extra 39 adults on a Sunday. That’s across ALL the cathedrals of England.

The second regression on the Under 16s produced an intercept of -30289 and a coefficient on the year variable of 16.36 recurring. What this is telling us is that, on average, each consecutive year brought in an extra 16 or so minors on a Sunday. That’s across ALL the cathedrals of England.

Looking at the data set, the 2011 Under 16s figure appears to be quite out of line with the rest of the data. If we remove 2011 from the data set and repeat the regressions we get coefficients of 40.6 and 44.2 for Adults and Minors respectively, slightly better then before but still indicating that on average, each Cathedral sees an increase over the year of just one adult and one child attending worship on a Sunday.

However, there is more in the figures from the regression then this. Here’s the full table from the Adults regression (i.e. trying to see what the relationship between year and adult attendance is).

SUMMARY OUTPUT
Regression Statistics
Multiple R 0.450925
R Square 0.203334
Adjusted R Square 0.103751
Standard Error 258.1109
Observations 10
ANOVA
df SS MS F Significance F
Regression 1 136030.3 136030.3 2.041847 0.190884
Residual 8 532969.7 66621.21
Total 9 669000
Coefficients Standard Error t Stat P-value Lower 95% Upper 95%
Intercept -65725.5 56990.49 -1.15327 0.28209 -197146 65694.85
Year 40.60606 28.41707 1.428932 0.190884 -24.9238 106.1359

Do you see that value “t-stat”? That’s a crude measure of how confident we are that any relationship we pick up in the regression (in our case, that on average each year the attendance increases by 39) isn’t just “random noise” but is a real trend that’s worth pointing out. You compare the t-stat to an upper (and in our case lower) bound as to whether we can be x% certain that a trend really exists. The standard certainty is 95% and reading off a t-table we can see that the relevant t-value to be 95% confident is 2.228 (two 2.5% tails).  Our t-stat is 1.4289 which is way lower, so we can’t say that we are 95% certain we have a real trend. In fact, we’re not even close to saying we’re certain there’s a real trend.

What does this mean? It means that although annual adult attendance across English Cathedrals is going up by about 1 per cathedral per year, there is a significant chance (i.e. more than 5%) that the real trend is actually downwards and that if we waited a year or two we would see that (though equally it could be much higher). By comparison, the t-stat for the Minors was 2.231, taking us past the 95% confidence interval. We’re pretty sure that the observed trend in Minors attending is real.

Let’s summarise. The massive increases in weekly attendance for Cathedrals are driven by mid-week attendance. When we look at Sunday attendance we see that there is a slight increase in Adult attendance, but it is not statistically significant. This is a very important point to get across – yes, adult attendance is increasing but it is too early to say whether that is a real trend or just random fluctuation.

Christmas Attendance

The Church of England Paper highlights that Christmas attendance rose over the past ten years, but by how much and is it significant? Once again we perform a regression, this time on Christmas Attendees and Christmas Communicants.

The figures show an upward trend but not a significant one. The coefficient for Year when regressing to Attendance is 1316 (so an average increase of 1316 per year), but the t-stat is 1.8839, too small to meet our 95% criteria. When we regress Year to Communicants we get a coefficient of 43.6 (not a lot) and a t-stat of 0.1656. That’s so low that we would reject any attempt to argue that the slight upward trend in Christmas Communicants is anything but a random trend.

Baptisms

Here for once the trend is clear. The coefficient of 11.45 regressing year to baptisms is accompanied by a t-stat of 3.2474. We can be really confident that the trend is an upwards one and it is genuine.

Summary

Some of this hesitancy in saying that the trends observed are real ones is down to sample size. We only have a decade or so’s data from Cathedrals and therefore the degrees of freedom are low. That said, in some instances the t-stats are so low that they would fail a 5% tail test (or in this case two 2.5% tails) whatever the number of observations.

The results are clear. While there is an observable upward trend in varying attendance and participation figures for Cathedral worship, there is too little data to be certain about the reality of such a trend. In particular, the Christmas attendance figures indicate no significant trend and the Sunday figures reveal that we can be confident that the trend for minors attending is a real increase, but not for adults.

Where the data is abundantly clear though is that mid-week attendance has exploded! The real follow-up to this research should not be to celebrate that Sunday attendance is increasing (it is, but not statistically significantly) but rather to find out why mid-week attendance is growing so rapidly. What do these mid-week services look like? What models can be adopted and put into practice elsewhere. By being realistic about how this data doesn’t tell us anything exciting about Sunday and Festival worship at Cathedrals, we can concentrate on getting our missiological teeth stuck into the real success stories.

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  • http://davidkeen.blogspot.in/ david keen

    And we’d probably need to see a breakdown by Cathedral, to find out which were doing well and which weren’t. Could the rise in midweek attendance be anything to do with the Cathedrals charging for entrance, so now ‘worship’ is the only way of getting into York Minster, St. Pauls etc. for free?

    • Si Hollett

      Indeed. A couple of years ago, I helped with a UCCF mission in Canterbury, and while the locals said that us guests could sneak in the back way (as residents of the Diocese they get in free anyway), we thought that was dishonest, so went to the front gate, said who we were (guests of the students of the churches of Canterbury), what we were going to do (have a quick look around and pray as a break before our evening events) and theological reasons why we shouldn’t have to pay for visiting our Father’s house (the low church non-conformist sympathies coming out of us). We weren’t going to be let in to look around, despite the offer of concessionary (student-rate) payment which was a fair price for entry, rather than the unaffordable full rate and opted instead to go to the Evensong service starting soon, joined only by the sides-people, choir, clergy and a group of French schoolchildren with their teachers.

      The service was sung well, though not our cup of tea, but stank of “we’ve always done this, so can’t give up” duty rather than “isn’t Jesus great” pleasure (not to put feelings in the heart of the people performing the service as we sat there being treated like an audience, but that was the vibes that were being given). That seems to me (though not with any evidence, just intuition) that the typical midweek Cathedral service is there as a tradition, a tourist attraction, a choral performance to put on.

      Interesting also that these small rises are billed by the CofE to be a 3% rise in Sunday attendance – just how small are the congregations in these massive churches?

      • nowconcerned

        I think you’re being a bit uncharitable towards the clergy who run cathedrals.  In my experience they don’t tend to be entirely comfortable with charging for entrance to a place of prayer.  Remember, it’s high church people that put the most store by holy spaces.  They have to charge or they simply wouldn’t be able to keep the roof on, and they stick very strongly to the principle of not charging for services.

        Also, I think the services are rather more than simply a tourist attraction.  There’s a lot of symbolism in high church services, that goes over the heads of us low church people, and I find choral music very moving.  Also, have you never noticed that there are always candles lit for prayers when you go into a cathedral?  I often say a prayer and light one myself so that people can see that this is still a place of prayer.

  • nowconcerned

    BTW Peter, numbers are meaningless to me, so I’ve no idea what you’re on about in this post. My own idea is that maybe if cathedrals are in the centre of commercial city areas people are fitting midweek services around work, whereas family parishes are in more residential areas?  Just guessing.  I’ve no idea why midweek services would be up.

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