1. Spatial Statistics
A 15 minute Tour…

2. Descriptive Statistics
Describe aspects of the dataset
Frequency (histogram)
Central tendency (mean, median)
Range (max, min, percentiles)
Variability (standard deviation)

3. Descriptive Statistics in TAS
Data image is the layer attribute you want to calculate stats for (e.g. slope)
Feature definition image is the feature(s) for which you want to calculate attribute statistics (eg. Average slope for a watershed, watershed is the feature definition image)

4. Cross Tabulation
Useful for change detection and quantification of spatial coincidence
Comparing maps of Land use/land cover over different time periods
Testing correlation between modelled and observed phenomena

5. Cross Tabulation 1978 1998 Cropland Pasture Urban Transport Water
Total 49
178 22 17 39 9
200 37
312
1998

6. Cross Tabulation
1978
Cropland
Pasture
Urban
Transport
Water
Total 49
178 22 17 39 9
200 37
312
1998
All 49 cells that were cropland in 1998 were also cropland in 1978

7. Cross Tabulation
1978
Cropland
Pasture
Urban
Transport
Water
Total 49
178 22 17 39 9
200 37
312
1998
All 178 cells that were pasture in 1998 were also pasture in 1978

8. Cross Tabulation
1978
Cropland
Pasture
Urban
Transport
Water
Total 49
178 22 17 39 9
200 37
312
1998
However, 22 cells that were pasture in 1978 are urban in 1998

9. Statistical Measures
Chi-squared stat. estimates likelihood that the two variables are related
Cramer’s V estimates the strength of association (0-1)
Kappa is an index of agreement between the two images (-1 to 1), where 1= full agreement and -1=no agreement. 0 indicates that agreement is random.

10. Kappa Analysis Kappa can be computed for each category
For our example, with 1998 as the referent (look across rows)…

11. Cross Tabulation 1978 1998 1998 as referent Cropland Pasture Urban
Transport
Water
Total
kapa 49
1.0
178 22 17 39
0.4 9
200 37
312
1998
1998 as referent

12. Kappa Analysis 1978 1998 1978 as referent Cropland Pasture Urban
Transport
Water
Total 49
178 22 17 39 9
200 37
312
Kappa
1.0
0.74
1998
1978 as referent

13. Cross Tabulation in TAS

14. Output
Image with concatenated values of input maps (e.g. map 1 = 7, map 2 = 3, output map = 73)
Cross tabulation table (text file)
Chi-square, Kramer’s V and Kappa statistics (in text file)
Kappa index requires that both files have the same number of categories