Grimson's test

  • spatial/temporal
  • global
  • point-based
    • Indications/Recommendations for use: When high-risk items cluster there will be an excess of adjacencies and the test statistic will be large (more).
    Description: A versatile test used to detect space, time or space-time clustering in both time series and point data.
    Test statistic: Label a subset of the data as high risk. The labeled items might be cases (as opposed to controls) for point data, high-risk counties for area data or high-risk time periods (e.g. an exposure occurred) for time series data. Test Statistic: A, the count of the number of adjacent labeled objects.
    Null Hypothesis: The items have been labeled high risk at random. Under this hypothesis the expected number of adjacencies is given at right.

    Here x is the total number of items (both labeled and not labeled), n is the number of labeled items, and y is the average number of borders per item. When high-risk items cluster there will be an excess of adjacencies and the test statistic will be large.

    Alternative Hypothesis: High risk items tend to be adjacent.
    GeoMed Inputs: The test requires the following quantities:
    • x : the total number of items (both labeled and not labeled)
    • n : the number of labeled items
    • y : the average number of borders per item
    • var(y) : the variance in the number of borders per item
    • A : the value of the test statistic
    GeoMed Outputs:
    • E(A)
    • Var(A), including the regularity and variability components of the variance
    • z-score
    • Significance of A as a one-tailed test using the Poisson or the standard normal distribution (whether to use the Poisson or the normal approach depends on proportion of variance contributed by the variability component)
    • Graph of significance of A against the value of A under both Poisson and normal approaches. The expected number of pairs of high-risk objects is used to calculate the significance of Grimson's test.
    Example Analysis:
    		Reference: Grimson, R. C. 1989. Assessing patterns of epidemiologic events in space-time. In Proceedings of the 1989 Public Health Conference on Records and Statistics. National Center for Health Statistics.
    Grimson, R. C. 1991. A versatile test for clustering and a proximity analysis of neurons. Methods of Information in Medicine, 30:299-303.
    Website maintained by Andy Long. Comments appreciated.
    longa@nku.edu