Find the nearest neighbor statistic for the following pattern, assuming a study area of 15 by 15 km. Test the null hypothesis that the pattern is random by finding the z statistic.
What will be an ideal response?
First we calculate the distances to the nearest neighbor for every point, and find that the distances are:
6, 6, 5, 5, 4, 4, 2, 2, 8. The mean of these values is 4.667, and with the area being 15 by 15, the
density of points p is given by n/A = 9/225 = 0.04.
Thus, R = 2 * 4.667 * sqrt(0.04) = 1.867.
Next, we calculate V[R] = (4 - pi) / pi*n = (4 - pi) / pi*9 = 0.030.
From this
z = (R - 1) / sqrt(V[R]) = (1.867 - 1) / sqrt(0.030) = 4.974
This is greater than the critical value of 1.96, so that we reject the null hypothesis of no pattern. The
data show strong evidence of uniformity.
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