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.

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).

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.