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<br />• Brian Munson & Sue Mowry <br />June 12, 1981 <br />Page 2 <br />Relative values obtained were: <br />H-G Formula: 1.4II <br />Acceptable Division Formula: 1.644 <br />Preferred C9. D.E.Q. Formula: 3.287 <br /> <br />It is obvious that the H-G formula is the least conservative estimator of <br />minimum adequate sample size, though relatively close to an accepted Division <br />value. The W. D.E.Q. 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 best <br />estimations of an adequate sample size. Therefore, the Division is primarily <br />concerned with obtaining data for any given community and/or para;reter which <br />reflects a reasonable level of accuracy and confidence. To this end, I am <br />more concerned with the provision of confidence Levels by applicants. <br />Mr. Duba's contention that t-values should exceed the critical value of 0.84 <br />to indicate statistical confidence of at Least 80% 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 confidence level analysis must be cairied out <br />relative to the number of degrees of freedom for each data set (in this case <br />(sample size-1)). i <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 S2, and a given mean, z, <br />will yield a level of conficence, t; which is within the desired level of <br />accuracy, d. <br />t n(dz)2 <br />~- <br />In layman's terms, if a value for t of I.13 has been calculated from the <br />applicant's data, with a sample size of 15, one can make the following state- <br />ment for a two-tailed test: I am less than 80~ confident, but greater than <br />50~ 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 be required to <br />meet an SOo minimum confidence level for woody communities and a 90o minimum <br />confidence level for herbaceous communities. <br />Under these minimal confidence level requirements, H-G has met sampling <br />adequacy for the following communities and parameters: ' <br />