i want to find the relationship between two raster file (eg: ndvi and lst) is there any solution in arcgis? or in any other software?
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You may be interested in this thread that discusses the creation of a scatter plot using two rasters as input: Scatter plot of two rasters
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You may also find the Band Collection Statistics GP tool useful (requires Spatial Analyst). It works on two or more rasters of same extent, etc.
The help describes it's functionality as: "The Band Collection Statistics tool provides statistics for the multivariate analysis of a set of raster bands. When using the Compute covariance and correlation matrices option is enabled, the covariance and correlation matrices are output as well as the basic statistical parameters, such as the values of minimum, maximum, mean, and standard deviation for every layer."
Do see these two sites for more details:
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As long as the 'lst' raster is not representing 'categorical' data, otherwise non-parametric tests of association are appropriate as suggested
my goal is to represent the result in raster. eg. which part of Germany has positive relation and which part of the Germany has negative relation (both in one raster ).
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Combine then.... you are simply showing association and not the strength or degree or association. In order to go further to test the degree of association statistically, then you would have to see whether the data conform to the descriptive characteristics of the data. Chi-squared testing is non-parametric and hence makes no assumptions about the nature or distribution of the data. Parametric statistics have limitations in their application... sadly, often ignored.
If you are interested in where the attributes of two rasters co-locate, you can use Combine. This would serve as the basis for chi-squared testing as a minimum. As for other expressions of 'significance' you will have to elaborate on why you expect there to be a spatial association between the two.
Other ideas combine-data-classification-from-raster-combinations