Dat's 0-1 matrix test

  • temporal
  • global
  • multiple time series
    • Indications/Recommendations for use: Use Dat's test with counts, not rates, on 5-10 time intervals. You cannot use the method when the expected number of cases in each interval is smaller than 2 (consider using the empty cells test instead, otherwise). The test is more sensitive than the Ederer-Myers-Mantel test in detecting multiple clusters within a space sub-unit. Within a time series the method assumes population size does not change through time. When cases cluster in one or a few time periods, A will be small (more).
    Description: Dat's 0-1 matrix test (Dat, 1982) is used to detect clustering in time. The test statistic, A, is the number of cells containing more than the number of cases expected in the absence of clustering. A large test statistic indicates cluster avoidance such that some of the time intervals have slightly more than the expected number of cases. The test statistic is small when cases cluster in a few time intervals. Stat! provides two tests for temporal clustering under Dat's method; within a single time series (using the z-score) and across several time series simultaneously (using the chi-square). It answers two questions: `Is there an unusual pattern over time in one time series' and `Is there an unusual pattern over time in several time series?'
    Test statistic: Define t to be the number of time periods (e.g. months) and n to be the number of cases summed over the t time periods. A, is the number of time periods with at least the number of cases expected in the absence of clustering, [n/t-0.5] cases (where the brackets represent the "least greater integer function: e.g. [1.3]=2). A can be written as a normal deviate which is expected to be normally distributed with a mean of 0 and unit variance:

    Null Hypothesis: Cases occur at random over the t time periods.

    Alternative Hypothesis: Cases do not occur randomly through time.
    GeoMed Inputs: Counts of the number of cases over several time periods. For example, the number of measles cases in a census district over six months. This test can only be used when there are from 5 to ten time periods. Dat's 0-1 matrix test requires the name of a file containing the time series (TIM file).
    GeoMed Outputs:
    • For each time series:
      • A, and its expectation E(A) and variance Var(A)
      • z-score and its one-tailed p-value
    • For multiple time series: a chi-square statistic testing for simultaneous clustering in several time series.
    • Plot of A against its expectation (dashed line of the function A=E(A) describing where observations would be plotted under the null hypothesis of cases occuring at random over the t time periods)
    Example Analysis Reference: Dat, M. V. 1982. Tests for Time-Space clustering of Disease. Ph. D. dissertation, Dept. of Biostatistics, SPH, University of North Carolina, Chapel Hill, NC.
    Website maintained by Andy Long. Comments appreciated.
    longa@nku.edu