Well, I see that the U.N. Secretary General has declared that today, October 20, is the first Worldwide Statistics Day.  Now, I am not sure if that is a recognition of worldwide statistics, or a worldwide recognition of statistics, but I am only too happy to add my contribution in the spirit of the latter interpretation.

As regular readers are aware I am a bit, OK a lot, of a PresbyGeek or PresbyNerd when it comes to denominational statistics.  And I have the Presbyterian Church (U.S.A.) office of Research Services to thank as by “enabler.”  If you are not aware, they put out a daily Tweet with some tidbit or factoid of information.  I sometimes think that what they tweet is superficial or incomplete, but just like I do the best I can with Presbyterian History in 140 characters, they do the best that they can in that space as well.

Back about three weeks ago they put out the following tweet –

Membership increased in 2009 in 13 presbyteries. Does that include yours? http://bit.ly/cxn1mn #pcusa

That factoid got me wondering about what growth rates were long-term, and not just for 2009.

So, time to dig out some data.  Presbytery size for 2008 and 2009 came from the annual Comparative Research reports, Table 4.  The oldest edition of Table 4 that I am aware of is 1996, so turning to the trusty WayBack Machine, that data is also available.  So all of that was fed into a spreadsheet and the annualized growth rate over the 13 year period 1996-2009 was calculated along with the annual rate for 2009.

Now, looking at the data, two presbyteries (Atlantic Korean-American, Eastern Korean) were excluded because they were formed after 1996 so there is not a long-term growth rate for them over the same time period as the other presbyteries.  Two more presbyteries were seen as significant outliers and removed from the analysis as well.  In the long-term growth category Midwest Hanmi had a growth rate of 4.4%, over twice the growth rate of its next closest presbytery.  In the short-term column San Joaquin dismissed several churches in 2009 and so had a growth rate of -24.3%, ten percentage points higher than the next closest presbytery.  The concern was that when the correlation was calculated these significant outliers would leverage the correlation result.

So what do we get for these 169 presbyteries?  Here are the descriptive statistics:

As you can see there is generally good agreement in each distribution between the mean and median.  Between the two distributions the mean and median are significantly lower and the standard deviation of the short-term is significantly higher indicating a much broader distribution.  Visually, here are the two distributions.  Both horizontal and vertical axes are scaled the same to facilitate direct comparison of the charts.

The broader nature of the short-term distribution is now apparent but without other short-term distributions to compare it to drawing specific conclusions from this is a bit more challenging.  If fluctuations have a random nature to them stacking multiple broad annual distributions to produce the long-term distribution will generally result in a decrease in the standard deviation.

The left-ward shift in the distribution, or higher rate of decline, is statistically significant, and whether this represents a one-time higher decline or the end-member of a trend towards increasing rate of decline can not be told from this graph alone, my previous analysis of the decline rates suggests the latter.

But my main interest is in a comparison of short-term and long-term rates and particularly looking at specific presbyteries.  So, here is the graph of the correlation of short-term versus long-term growth rates.

As you can see there is noticeable scatter in the data but a general positive trend.  However, with an R-squared correlation coefficient of 0.14 the correlation is not strong.  With a slope of >1 there is the suggestion that for all presbyteries the short-term rate is of greater magnitude than the long-term rate.

But here is what I really wanted to get at:  The Research Services tweet pointed out that in 2009 13 presbyteries increased in size. (And the three with the largest percentage membership increases were excluded from this analysis as described above.) Over the long-term the membership has increased in five presbyteries (Charleston-Atlantic, Middle Tennessee, Northwest, Seattle, and the excluded Midwest Hanmi).  Of those, only Northwest (Puerto Rico) and Midwest Hanmi have shown an increase in membership over both the 13 year long-term and 2009 short-term periods.  In fact, it was probably not necessary to exclude Midwest Hanmi since for a long-term growth rate of 4.4%, the trend-line calculated above predicts a short-term rate of 6.0%, reasonably close to the actual of 5.4%.  The leverage would not have been too great.

Well, lots more could be done with this but that is enough for Worldwide Statistics Day.  If you looked carefully at the spreadsheet you can see that what I really prepared it for was my own tracking of the presbytery voting trends in the next few months.  In particular, I am very interested to see how the votes on the three big issues, the Belhar Confession, the new Form of Government, and Amendment 10-A correlate, or don’t as the case may be.  You are welcome to check back but I don’t intend it to be the “up to the minute latest and greatest source of news.”  I’ll probably update it weekly with what I can find and it will be my base for further statistical analysis.  If you are interested in that feel free to follow along.  Stay tuned…