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<br />Mr. Gregg Squire 3 June 9, 1987 <br />Colo. Mined Land Recl. Div. <br />Where: C = 0.9}i the revegetation standard (90% of historic record) <br />}~ = standard mean determined from historic record <br />z =sample mean at year 9 or 10 <br />Sx = standard error of the mean defined as SZ/n <br />tcalc is then compared with t [able at aC = 0.10, <br />and n-1 degrees of freedom <br />If tcalc is greater than or equal to t table, <br />Ho is rejected and the revegetation is not successful. <br />Response: <br />I've reviewed Mr. Savage's response to our proposal. Ais suggestion of a Stu- <br />dents t test would be acceptable if the data were analyzed using an unpaired <br />Students t test. Based upon a review of statistical theory, an unpaired Stu- <br />dents [ test would be appropriaCe if the means on an annual basis were com- <br />pared against a reference area(s) on an annual basis. However, since the test <br />would be a mean based on the annual means for seven years against a single <br />annual mean or, in actuality, a single datum point, then an unpaired test <br />should be used. Also, the data cannot be considered to be paired since the <br />postmine annual mean is not obtained concurrently with the premine annual <br />means. <br />The following example, Table 4, demonstrates how the unpaired Students t test <br />formula could be applied using a one [ailed t table value. The formulas are <br />from Zar, Sec.9.4 (1984). <br />As an alternative to the above method, Trapper Mine proposes [o use [he Lower <br />confidence limit as a target production standard for reclamation. Table 5 <br />provides the production standards for each range site and shows how the values <br />were calculated. The standard is a rework of our May 7, 1986, proposal. Data <br />for 1979 has been added [o provide seven years of historic production data and <br />the summary statistics have been revised accordingly. Also, since Che pro- <br />posed standard is based upon a confidence Limit and not a mean, the basic <br />formula has been changed from: z.9 -t^-Led .1(s'x) <br />to: z - t^-L, d •OS (sz) <br />This properly represents the confidence limit concept. What is being proposed <br />by the revised formula is that the true unknown premine range site mean lies <br />somewhere above the lower confidence limit, and that we are 95% sure it is not <br />less than [he lower limit. This implies that on occasion an annual premine <br />mean (data point) may be less than the lower confidence limit, but that the <br />historic mean has a 95% probability of being somewhere above the lower limit <br />of confidence. <br />cont. <br />