1. Comparisons of NDVI values Dean Monroe

2. Location

3. Field

4. Field with N-rich Strip

5. N-rich Strip

6. Distributional Assumptions

7. Comparing NDVI Values Assumption: 1.Strip NDVI is Equal to Whole Plot NDVI Findings: 1.There is a 99.998 % confidence in the falsehood of the assumption of equality 2.This test was performed using standard t and Welch Modified t

8. Correlation by Longitude Assumption: 1.Row to row correlation Findings: - Correlation is low from row to row

9. Variogram Interpretation Whole field reaches sill in approx. 22 m whereas strip reaches sill in approx. 17 m.

10. Variogram Assumptions Data is continuous between sample points Tobler’s First Law of Geography: “everything is related to everything else, but closer things are more closely related” (Tobler, W., 1970 Econ Geog 46)

11. Spatial Statistics (Classical) Geostatistics Continuous realizations between samples in continuous space Lattice Data Continuous realizations in a discrete vector space Point Distributions Binomial in continuous vector space

12. Lattice Data in Space Assumption of countable and finite occurrences of realization Realizations occur in discrete space Correlation structure depends on the “Neighbor” concept Is the spatial equivalent of regular time series analysis Uses a similar class of “auto” models and the Markov Property A Lattice has the following assumptions Translation Invariance (Location is not a factor) Pairwise-Only Dependence (Simplifying Assumption) Positivity (All possible neighborhood system exist)

13. Attributes of Lattice Data Has a multi-variable extension Utilizes multiple Neighborhood configurations (five in common use) Performs on both regular and irregular lattices as long as:

14. Reasons for using a Lattice No assumption of data between points Better suited for separation of large and small scale effects (e.g. Median Polish)  Preferential Clustering  The Proportional Effect

15. Statistics on lattice Spatial auto-correlation (SAC) Moran’s (I) –Similar to Pearson’s Moment Geary’s Index (C) E(I) = (-1)/(n-1)  0 for large n J. Lee and D. Wong 2001

16. Example Subset whole plot into rectangular grid the length of the N-rich and wide as provided by complete rows Perform SAC on raw and polished grid Perform similar analysis on N-rich strip Compare degree of spatial relatedness

17. Before Median Polish

18. After Median Polish

19. Results E(I)=-1.86 EE-4 - The Polished data yields better correlation values - Both Indices show a moderate degree of clustering Whole Plot Strip E(I)=-1.0 Approx -Little to no Clustering -Median Polish failed

20. Interpretation Results are based on first-order neighbor structure Neighborhood system of one unit lagged cells. No diagonals Values in Whole Field experiment are more clustered than those in the Strip Caveat: Narrowness of the strip could have contributed to correlation value being low. Ultimately, there is probably a better method for this data.

21. Extensions for this analysis Build second-order,hexagonal in, hexagonal out, and diagonal neighborhood systems Explore assumption of free sampling verses non-free sampling (Assumption of how the data is distributed) Use irregular grid where nearest neighbor systems are defined by distance or nearest (k) neighbors (nonparametric approach) If yield data can be obtained, use NDVI to regress yield with spatial correlation adjustment (similar to regression with auto- correlated error terms