In the last week the news on Amendment 08-B includes: (1) Five more presbyteries have voted with one a repeat “yes,” three switching from “no” to “yes,” and one repeat “no.”  This puts the unofficial vote at 73-90.  (2) The official count at the Office of the General Assembly now confirms Amendment 08-B as being the only Amendment to be defeated in this round.

While the dominant “yes” vote this week has resulted in some minor changes in the summary statistics I discussed last time, the basic conclusions still hold and I will update those statistics later related to the overall conclusions.

I now want to turn to the numbers that first caught my attention and that probably stand by themselves with the least need of dissection or interpretation.

Presbytery vote counts
Much has been made of the change in the percentage of “Yes” votes between the Amendment 01-A vote and the 08-B vote.  This “vote swing” has been pointed at as an indicator of changes in the denomination, primarily changes in attitude concerning this issue.

But as I pointed out in the first part of this series, in the total vote numbers the actual number of “Yes” votes is substantially unchanged from the previous vote while the number of “No” votes has decreased by about 3000 or roughly 14%.  Now, I do believe it is more complex than just saying the “No” votes are not showing up for presbytery meetings or leaving the presbyteries, but if you want to reduce the changes in the vote numbers to a single cause that would be it — no changed attitudes just changed demographics.  (See the first post for a more detailed discussion of possible factors and combinations of those factors.)

Viewing this on a Presbytery level is when you see that it is a more complex situation.  (Again, my previous post on every presbytery is different.)  But as would be expected the general trend is the same as the combined numbers.

As before, my data comes from the usual sources, PresbyWeb and Presbyterian Coalition.  I am still considering 01-A and 08-B as similar amendments so that their voting records can be compared.  (As I will show in the second post from now this may not be valid for 100% of the presbyteries, but it looks like a good working hypothesis for most.)  And in the analysis I am about to present I use the ratio of the number of votes on 08-B to the number of votes on 01-A.  This can result in a divide by zero error if there were no votes in that category for 01-A and can produce large ratios when there were a small number in 01-A.  The number of instances of each of these are limited.

So here we go with the charts and graphs and the 27 8×10 color glossy photographs with circles and arrows and a paragraph on the back of each one…  Or something like that.

The three frequency distribution graphs below illustrate what caught my attention from the very beginning of the voting on Amendment 08-B.  They are the distributions of the ratio of the number of votes in each category (yes votes, no votes and total votes).  The red arrow is the average and the solid line running vertically through all three is the value of 1.0. (no change)  As you can see they are aligned with the same horizontal scale for visual comparison.  Frequency count bins are 0.05 wide and the number listed on the x-axis is the upper inclusive value of the bin.  For the “yes” votes there are six more presbyteries off the right hand side of the scale but I do not show them so all three graphs can be scaled equally. (The large ratios are mostly due to changes in small numbers.)  Those presbyteries are included in the statistics.  For the two presbyteries that had no yes votes on either vote their ratio for “yes” is fixed at 1.0.  For the one presbytery that changed from no “yes” to one “yes” it was entered as 2.0.  (Yes, I probably should have discarded them but I haven’t.)

For the “Yes” votes the average is 1.06, the median is 1.00 and the standard deviation is 0.42.  For the “No” votes the average is 0.76, the median is 0.75, and the standard deviation is 0.21.  For the total number of votes the average is 0.87, the median is 0.86 and the standard deviation is 0.20.  For all three groups the number of presbyteries counted is 147.  While the distributions have the general appearance of being normally distributed and follow the central limit theorem I’ll address the exact nature of the distributions later in this series.

For those who are looking for the bottom line — The number of “Yes” votes in the presbyteries shows a slight to no increase, the number of “No” votes shows a significant downward shift, and the total number of commissioners voting show a more moderate decrease.  In fact, only 12 presbyteries, 8%, have an increase in the number of commissioners voting no and 43 presbyteries, 29%, show a ratio greater than 0.95 for the ratio of total number of votes cast on 08-B versus 01-A.  That would be a low probability of just being random variation.

Another interesting feature is how much wider the spread of values is on “Yes” votes than “No” votes with a standard deviation of 0.42 for the former and 0.21 for the latter.  Some of this can be attributed to presbyteries that have very low numbers of “Yes” votes so a change of one or two votes can produce a very large ration.  But in spite of that a visual comparison of the “Yes” and the “No” distributions shows a markedly wider distribution for the “Yes” differences.  So it can be said that the number of “No” votes more uniformly declined while the “Yes” vote showed no decline in the average but more variability in the changes.

Changes in vote percentages
As I mentioned above the percentages of yes and no votes, without regard to the changing size of the populations, has been a focus in this voting round.  So here for your viewing pleasure are those frequency distributions for the presbyteries.

For 01-A the average “Yes” vote was 0.42 and for 08-B it was 0.48.  While the average shifted upward the standard deviations were relatively close at 0.16 on the first and 0.19 on the second.  In this view the distributions show somewhat different shapes but the upward shift is still visible.

Total vote ratio with time
I throw in the following graph for fun.  It shows how the ratio of the total number of votes changed as voting proceeded.

It is tempting to attribute higher turnouts later in the voting to increased awareness, get-out-the-vote campaigns, or people getting nervous/hopeful about the outcome.  But note that the scatter also increases.  This slight, and maybe statistically insignificant (R-squared is only 0.01)
increase can be nearly completely accounted for by the fact that “No” presbyteries voted earlier and “Yes” presbyteries generally voted later so the sustained level of “Yes” votes late in the process tilts the trend line.

Well, now that I have gotten your eyes to glaze over properly today I will leave you with that data to ponder until next time.  No further discussion or conclusions now — I’ll leave that until I’ve spread a bit more data before you.  Having now looked at the numbers as the whole group of presbyteries next time I’ll split the presbyteries apart into a couple of different groupings and see if that shows anything interesting.  After that I’ll expand the study to include all four votes and ask whether any given year is different, or different enough.