Simulation Study to Detect the Existence of Spatial Patterns: An Application of Randomization Test

• Activity Number: 526
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Computing
• Author(s): Denise Nunes Viola*+
• Companies: UFBA
• Keywords: Randomization test ; Spatial pattern ; Semivariogram ; Mantel test

Abstract

Often the researcher's interest is to model the spatial distribution in different areas. In Geostatistics, semivariogram is commonly used to verify the existence of spatial patterns, but eventually it should not be used. An alternative to identify the existence of spatial patterns when the assumptions are not met is to use an adaptation of the Mantel Randomization Test. The randomization test is appropriate for small samples and can be used for non random samples. This test compares the value of an observed statistic for the original data with the values of the statistic after randomizing the observations, where the p-value is given by the proportion of times the randomized data was statistically greater than or equal to statistics obtained from the original data. To test it, was generated a thousand sets of 250 observations. Data was generated with spatial dependence of 7 meters of range in a 20x20 meters area. The matrix of distances from the location of collection was randomized 10,000 times to get the p-value. In 81.20% of the randomizations it was confirmed the existence of spatial pattern. Additional studies will be conducted to confirm the results.