{20}

Appendix 3.  Non-uniformity in the distribution of the 396 churches on Sheet 188

A crude but effective way to test the uniformity of the distribution is via a grid square analysis. If the sites were uniformly distributed with respect to area, then the number of churches in a 1km grid square would follow a Poisson distribution with mean 396/1600 = 0.2475. The expected numbers of grid squares containing 0, 1, 2, 3 etc. churches are shown in Table 6a, with the observed frequencies for comparison.

Table 6. Distribution of churches on Sheet 188

(a) Distribution of 396 churches among the 1-km grid squares

Churches in squareFrequency
 Obs.Exp.
013161249
1215 309
246  38
313   3
45   0.2
52   0.01
62   0.0004
70   0.00001
81   0.0000004
 

 16001600

(b) Grid squares with a large number of churches

No. of churches45678
 535576567061nil5839
 594758407655
 5742
 5130
 7530

As can be seen, with a uniform distribution we should not really expect any grid square to contain 4 or more churches, yet several do. They are shown in Table 6b. As might be expected, all these correspond to parts of towns or villages.