6. Knox Statistic for Space-Time Clustering
The Knox approach is used to test whether there is a significant cluster during a defined
distance and time period. First it counts the number of point pairs as either close or
distant in space and /or time, then calculates the P-value.
Formula
For a certain distance
d
and time period
t
, the Knox statistic calculates the following
number:
d(i, j)
is the distance of point i and j,
t(i, j)
is the time interval of point i and j,
: the number of point pairs
(i, j)
with
d(i, j)
d
, and
t(i, j)
t
,
: the number of point pairs
(i, j)
with
d(i, j)
d
, and
t(i, j) > t
,
: the number of point pairs
(i, j)
with
d(i, j) > d
, and
t(i, j)
t
,
: the number of point pairs
(i, j)
with
d(i, j) > d
, and
t(i, j) > t
,
N
is the total number of point pairs (
)
The P-value is:
where
,
Input
1. Input data file, which should record X, Y coordinates of points and T the times
attached to each points (time elapsed in days, or years or minutes, etc).
2. The time interval.