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x = the mean of the estimate as calculated from the initial samples. <br />If the initial samples do not provide a suitable estimate of the mean (i.e., the inequality is <br />false), additional samples should be collected until the inequality (n.j. < n) becomes <br />true. However, where sampling is for managerial (monitoring) information, adequacy is <br />not necessary and is calculated for informational purposes only. <br />If reverse-null testing will be utilized to document success, then in accordance with Rule <br />4.15.11 (2) (c) a minimum of 30 samples must be collected and a demonstration of <br />sample adequacy is not necessary. In this circumstance a two-sample reverse null t-test is <br />mandated along with Satterthwaite approximated degrees of freedom and standard error. <br />However, if an adequate sample can be obtained from the reference area, then a less <br />complex one-sample t-test may be utilized. With the reverse null test, the smaller the <br />variance (given by extra sampling) the better the chances of passing closely matched <br />parameters. <br />For certain statistical demonstrations of woody plant density, documentation of sampling <br />adequacy is often problematic, hence Rule 4.15.11 (3) may be used in lieu of Rule <br />4.15.11 (2). Rule 4.15.11 (3) (a) is a reverse-null approach based on the median and <br />requires a minimum of 30 samples. Rule 4.15.11 (3) (b) allows direct comparison with <br />standards if a statistically adequate sample cannot be demonstrated in accordance with <br />Rule 4.15.11 (2) (a), however, a minimum of 75 samples with a minimum quadrat size of <br />100 m2 is required (equivalent to total enumeration of 1.85 acres). Rule 4.15.11 (3) (c) is <br />a standard-null approach based on determination of a "running mean" and a minimum of <br />40 samples is required. <br />Success Evaluation <br />To summarize, success evaluations involve either a direct or a statistical t-test <br />comparison of appropriate parameters for each variable of interest (cover, production, <br />diversity, or woody plant density). For monitoring efforts, comparisons shall be made <br />directly with either the reference area parameters or the permitted standards to facilitate a <br />determination of the progress of revegetation. In the case of ground cover and <br />production, comparisons shall be made against reference area data of the same year. <br />Diversity and woody plant density variables shall be compared against the standards <br />defined above. <br />For bond release efforts, direct comparisons are made when the revegetated area <br />mean value for a given variable is greater than either 90% of the standard or the reference <br />area mean assuming that a statistically adequate sample has been collected. If a <br />statistically adequate sample cannot be obtained, a "reverse-null" hypothesis test may be <br />employed as detailed in C.R.S. Rule 4.15.11 (2) (c). If an adequate sample is obtained <br />for a particular variable, but the mean is less than 90% of the reference area mean or <br />standard, a "standard-null" hypothesis t-test may be employed as detailed in C.R.S. Rule <br />4.15.11 (2) (b). <br />4.15-33 Revision Date: 3/14/08 <br />Revision No.: TR-72