A test for time clustering in several time series simultaneously, this test is insensitive to differences in population size over the areas from which the time series originate

Data Requirements

Counts of cases in consecutive time periods for several time series

cannot use rates, counts are required, therefore the method is biased by changes in population size through time
the number of time intervals in the series must be between 2 and 5

Analysis

H₀: cases occur at random in each time series

H_a: cases do not occur randomly through time, they either cluster or occur uniformly within areas

Test Statistic: The test statistic is m₁, the maximum number of cases in a time series. When cases are clustered m₁will be large, it will be small when cases occur uniformly through time. The data from several time series (each time series represents an area such as a county) are used to construct a Chi-square statistic to test for time clustering in several areas simultaneously:

The summations are over the number of time intervals in the time series, is the sum of the maximum number of cases over all time series, and are sums of the expectation and variance of m_1i under the null hypothesis. If either m₁ is larger or smaller than expected, the chi-square statistic will be large.

Output

r, the total number of cases in a time series

f(r), the number of time series with that number of cases

E(m₁) and Var(m₁) under the null hypothesis for a time series of similar length and r

Chi square value and significance level

Plot of expected m₁ on the observed m₁

dashed line of the function m₁=E(m₁) describing where observations would be plotted under the null hypothesis of cases occurring at random over the t time series simultaneously
one symbol is plotted for each time series described for a total of S f(r) symbols

Reference

Jacquez, G.M. 1994, User manual for Stat!: Statistical software for the clustering of health events, BioMedware, Ann Arbor, MI.