{20}
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.
(a) Distribution of 396 churches among the 1-km grid squares
| Churches in square | Frequency | |
|---|---|---|
| Obs. | Exp. | |
| 0 | 1316 | 1249 |
| 1 | 215 | 309 |
| 2 | 46 | 38 |
| 3 | 13 | 3 |
| 4 | 5 | 0.2 |
| 5 | 2 | 0.01 |
| 6 | 2 | 0.0004 |
| 7 | 0 | 0.00001 |
| 8 | 1 | 0.0000004 |
| 1600 | 1600 | |
(b) Grid squares with a large number of churches
| No. of churches | 4 | 5 | 6 | 7 | 8 |
|---|---|---|---|---|---|
| 5355 | 7656 | 7061 | nil | 5839 | |
| 5947 | 5840 | 7655 | |||
| 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.