Spatial Statistics A 15 minute Tour…

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

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)

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

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

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

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

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

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.

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

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

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

Cross Tabulation in TAS

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