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• • ~« Department of Range Science Reclamation Research Lab 303/491-6541 Colorado State Unlverslty Fort Collins, Colorado 80523 ~~ ~ q r: ~+r--C \l . .. _ 20 September 1982 f'+~~Y'~ ~ x:;83 Mr. Wayne Sowards Trapper Mine Inc. P.O. Box 187 Craig, Colorado 81626 Colo. Dept. of n:~,w~~ rsesource~ Dear Wayne: I have studied the excerpt from your permit application which deals with the use of linear regression to estblish a revegetation success standard. I have also asked Mario to look it over; from our discussion I have the following comments to offer, First of all, a basic assumption can be made that the reference area and the pre-mine area have a joint distribution (i.e., the changes over time in one are not independent of the other). In the case of Trapper, this is just common sense because you do not expect that the cover or biomass of the two areas to be independent since the same environmental forces are influencing both areas in the same way. If you were to try to develop a regression between the two areas in a ig'ven year (that is regress data in one area against data in the other area), then the procedure would be wrong because the samples would not be taken as tuples (i.e., samples taken jointly or each sample being a set of (X,Y) X = reference, Y = pre-mine) but they would be taken at random within each of the areas and as such they are independent as a consequence of the sampling rocedures. Now this is entirely different from considering each year as a tuple (X,Y in which X and Y are the means for the reference and pre-mine area because you are then looking at variations along a gradient, represented in this case by time (years) and trying to correlate the variation of Y as a function of X along this gradient. A similar example would be to look at the correlation between growth of shrubs and grasses in a given area for the purpose of determining how grass growth changes with shrub growth. For this you need a gradient. You can build this gradient by looking at areas with different shrub growth and regress them against each other or select one area and use yearly changes in shrub growth as your gradient (by the way this is the only way that you can set up a regression if you were establishing a reclaimed area and you want to look at the competition effect of shrubs over grasses). However, if I were you, I would first look at the yearly data between the two areas and run for each year an unpaired t-test to see if they are significantly different in any year. Three situations could arise: