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R mode measures for environmental data

Note: Environmental data should not suffer from the double-zero problem. That is, "0" should indeed mean "0" in a numeric sense rather than "not observed" or "no information".

Q Are you dealing with...

Quantitative variables with linear relationships?
My variables express quantitative values and have linear relationships to one another.

Semi-quantitative or ordered variables with monotonic relationships?
My variables contain semiquantitative or ordered categorical values which either increase or decrease together, although not necessarily in a linear fashion.
Qualitative variables or quantitative variables without monotonic relationships?
My variables contain qualitative variables with no particular order or non-monotonic variables.