Compare Results

Two tools are provided in the Spatial Data Modeller as aids to comparing results obtained from the different analytical methods. They are:

• the calculation of an Area Weighted Spearman's Rank Correlation Coefficient
• the generation of a Map of Rank Differences

How to use the Compare Results tool

Comparison of Ranks

The ranks of values are compared rather than the raw values because the results from different methods may be scaled over a different range. For example, weights of evidence will typically generate higher probabilities than logistic regression, particularly for the areas predicted to be most favourable. When results are compared relatively, eg. using ranks, the results are very similar. So, for example, in the prediction of mineral favourability, the 5% of are study area predicted to be most favourable by one method is compared with the 5% predicted to be most favourable by the other method rather than the absolute probabilities generated by either method.

Ranks are generated by sorting the data in ascending order and assigns integer values R = 1, 2, ..., n. Spatial Data Modeller defines 20 ranks, or the maximum possible if the data set is too small to generate 20. The area weighting is built in to the equations for the Spearman's Rank Correlation, while an equal area classification is used to rank the data for the Map of Rank Differences.

Area Weighted Spearman's Rank Correlation Coeffiecient

If data in one data set are being compared to data in another data set, the two data sets are combined to create a unique conditions grid so that ranks can be compared for the same areas or "polygons". (If data from two fields in the attribute table of the same data set (grid them) are being compared this step is not necessary.) The data is transformed to ranks. The mean rank is calculated and the area associated with unique condition or polygon determined. An algorithm to calculate the following equation is used to calculate the coefficient:

r_s is reported in a table based on a dBase file.

r_s varies from 1 (perfect correlation) through 0 (no correlation or independence) to -1 (perfect negative correlation).

Map of Rank Differences

Ranks are generated using an equal area classification. The grid themes being compared are reclassified by rank and a unique conditions grid is generated that is the basis of the map of rank differences. For each unique condition, the difference between the source ranks is calculated and appended to the attribute table. It is this difference that is mapped. The map is primarily a visual tool: areas where the input maps match are coloured grey; the greater the first ranked data is than the second, the greater the saturation of blue; and the greater the rank of the second map is than the first, the greater the saturation of red.

How to use the Compare Results tool

1. Select 'Compare Results...' from the SDM menu. The following dialog box is displayed:

The box labelled 'Select layers:' lists all of the "theme-field" combinations available for comparison. The format for each item is [theme name . field name]. Valid inputs for comparison are all the grid themes in the active view and the numeric fields in any integer grid theme attribute tables. If a grid theme is based on a floating point grid, the field name is specified as 'Value' (although technically there is no field).

1. Select two theme-field combinations to compare by clicking on one and holding down the shift-key and clicking on a second.
2. Check the comparison techniques(s) you want to use.
3. Click OK.
4. If the area weighted Spearman's rank correlation is calculated, specify the filename and location of the dBase file when prompted. The default name is wsr#.dbf
5. If the map of rank differences is generated, specify the name and location of the source grid when prompted. The default name is diff#.

When processing is complete, the location of the table containing the Spearman's rank correlation coefficient and the name of the view containing the map of rank differences is reported: