1. Applied Geostatistics Geostatistical techniques are designed to evaluate the spatial structure of a variable, or the relationship between a value measured at a point in one place, versus a value from another point measured a certain distance away

2. Ho in Spatial Statistics states that: events, highs, lows, differences between evenly distributed Randomly arranged Illustrated on directional trend Features are

3. We assume either: Randomization - the observed pattern is one of many possible arrangements of the population; or Normalization – the observations is a sample of a larger population and it was obtained randomly

4. We consider: Global statistics – pattern across the whole of the study area Local statistics – individual’s relationship with nearby features

5. Spatial Mean: The average x-coordinate and average y- coordinate for all features in the study area (or select set). Comparing changes in spatial distributions

6. Central Feature: The feature having the shortest total distance to all other features in the study area (or select set) Describes the most accessible feature Center Mean

7. Standard Distance, Standard Deviational Ellipse The extent to which the distances between the mean center and the features vary from the average distance. The standard deviation of the features from the mean center separately for the X and Y coordinates

8. Linear Directional Mean The angle of the line that represents the mean direction (or orientation )

9. A B C D E F G H I J First Order Neighbors Topology Binary Connectivity Matrix Distance Class Connectivity Matrix 1 11 101 1001 00011 001101 0000011 01100011 010000011 ABCDEFGHIJABCDEFGHIJ A B C D E F G H I J 1 12 121 1221 23211 221121 3222211 21123211 212332211 ABCDEFGHIJABCDEFGHIJ J I H B G C F D A E 1= connected, 0=not connected Join Count Categorical (nominal) data Are values clustered or dispersed Easy to construct

10. Moran’s I …Geary’s C Continuous data Similarity of nearby features Single statistics summarizing pattern Doesn’t indicate clustering of “highs” or “lows”

11. General-G Continuous data Concentration of “high/low” Not “so good” if both highs and lows are clustered

12. Nearest Neighbor Average distance between features Results may be biased by edge Evaluated with Z-score

13. K-function, Ripley’s-K Count of features within defined distances Concentration at a range of scale Edge plays an important role Evaluation through simulations for random distribution envelope