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TEACHING GEOG 385.02/GTECH 785.02 |
GIS SG course homepage |
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CLASS DEMO 6. STATISTICS DEMO
If you have not done so yet, download Demo6.exe. Downloading class demo data.
NOTE: This demo focuses on crosstabulation of qualitative data. Using regression in derivative mapping of quantitative data is demonstrated in the competency exercise 8.
Inferential Statistics
Qualitative Data and Crosstabulation
In this example we will use two landuse images for the same territory but for different dates: 1971 and 1985. This information is qualitative or categorical data and the objective is to describe the relationship between these two images. In particular, to measure the degree to which they are the same or, alternatively, the degree to which change in the landscape as occurred between 1971 and 1985.
DISPLAY LAND71 and LAND85 with WESTLUSE palette. We can see that some changes occurred between these dates. However, it would be useful to measure the change and know which categories changed.
To do this, this exercise uses only a very small window from the upper right of these images. DISPLAY LAND71W and LAND85W with legend and WESTLUSE palette. We can see changes here as well.
Run CROSSTAB; specify both cross classification image and cross tabulation; call the output image CROSSW; and choose to print KAPPA for each category…
To analyze the change in statistical terms we’d use Crosstabulation.
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Cropland_1971 |
Pasture_1971 |
Urban_1971 |
Transport_1971 |
Water_1971 |
Total |
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Cropland_1985 |
49 |
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49 |
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Pasture_1985 |
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178 |
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178 |
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Urban_1985 |
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22 |
17 |
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39 |
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Transport_1985 |
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37 |
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37 |
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Water_1985 |
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9 |
9 |
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Total |
49 |
200 |
17 |
37 |
9 |
312 |
- CHI –squared statistic estimates likelihood that there is a relationship between these variables (landuse75 and landuse80).
- Cramer’s V – estimates strength of association (0-1) : in this case 0.92
- K (Kappa) – index of agreement between the two images: 0.88 – pretty high. Kappa ranges from -1 to 1, where 1 = full agreement.
- Kappa for each category is also computed (these numbers are for 1985 referent, look across rows):
Cropland (1) 1.0 - unchanged (full agreement)
Pasture (2) 1.0 - all 178 pixels here in 1985 were in the same category in 1971
Urban (9) 0.4 – 39 pixels in 1985 but 22 of them were pasture in 1971
Transportation (10) 1.0 – unchanged (full agreement)
Water (12) 1.0 – unchanged (full agreement)
With 1971 as the referent, all Kappa statistics are 1.0 except for Pasture (.74).
To create a map of change for the same area we use Crossclassification. This image (CROSSW) was created when we ran the module the first time.
DISPLAY CROSSW with Qual16 palette and legend.
This image shows were all possible combinations of the categories of the two images occur. Note that a new category has been formed for the 22 pixels moving from pasture to urban.