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Dri an Afvn son 6 Sue ~rrl • <br />June 12, 1981 <br />Page 2 <br />Relative values obtained were: <br />H-G Formula: 1.41.I <br />Acceptable Division Formula: 1.699 <br />< Preferred tJ. D.E.(J. Formula: 3.287 '~ <br />It is obvious that the N-G formula is the least conscrvati•/e estimator of <br />minimum adequate sample size, though relatively close to an accepted Division <br />value. The td. D.E.O. formula is the most conservative estimator of minimum <br />adequate sample size. <br />Since minimun sample size formulae are based on estimations of population <br />parameters to begin with, the values these formulae yield are at hest <br />estimations of an adequate sample size. Therefore, the Division is primarily <br />concerned with obtaining data For any given community and/or parameter which <br />reflects a reasonable level of accuracy and confidence. To this end, I am <br />more concerned with the provision of confidence IeveIs by applicants. <br />Mt. Duba's contention that t-values should exceed the critical value of 0.84 <br />to indicate statistical confidence of at least 80~u is erroneous since the 0.84 <br />value comes from a sample with infinite degrees of freedom, which is not the <br />case in this situation. The cwrfidence level analysis must be carried out <br />relative to the number of degrees of freedom for each data set (in this case <br />(sample size-1)). <br />In the utilization of the following formula, it can be determined that a given <br />sample size n, from a sample with a given variance 52, and agiven mean, z, <br />will yield a level of conficence, t; which is within the desired level of <br />accuracy, d. <br />t = n(dx)2 <br />~- <br />Zn layman's terms, if a value for t of 1.13 has been calculated from the <br />applicant's data, with a sample size of IS, one can make the following state- <br />ment fora two-tailed test: I am less than 80% confident, but greater than <br />SOe confident that my sampling has yielded a value which is within 10% of <br />the actual mean of the population. <br />It is the Division's position that vegetative sampling should he required to <br />meet an 80o minimum confidence level for woody communities and a 9U~ minimum <br />confidence level for herbaceous communities. <br />Under these minimal confidence 1e_vel requiremcrnts, 11-G has met sampling <br />adequacy for the fo.Ilowing communities and parameters: <br />