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~`,~ <br />Gregg Squire and Mike Long <br />-2- <br /> <br />April 25, 1986 <br />Trapper correctly asserts that data collected by point-intercept methods for <br />vegetative cover is binomial in nature (either one "hits" vegetation or one <br />doesn't) yielding distinct non-continuous data and a binomial distribution <br />rather than the normal distribution yielded by continuous data (e. g. <br />productivity data from harvested plots). Trapper then asserts that there is <br />an intrinsic relationship between the average cover of the affected area and <br />that of the reference area through their proposed use of binomial analytic <br />methods. In reality this is not so. Binomial properties presume that one <br />knows something of the nature of the population, in this case the average <br />vegetative cover of the sampled area (which is a proportion of the total <br />sample, i. e. the proportion p). Since there are two proportions in our <br />sampling (vegetation cover and no vegetation cover) one can presume the <br />relationship vegetation cover + bare earth = total sample or p + q = 1, and <br />p = 1-q. It is crucial to note that this mathematical axiom applies only <br />within one sampling population unit, that is reference area or affected area, <br />not between the two. Trappers employment of the proposed binomial evaluation <br />techniques violates the mathematical axiom and the premises on which binomial <br />sampling is founded (Zar, 1974), rendering the proposed usage of the technique <br />inappropriate. <br />I would propose the following resolution. Since binomial samples of size 25 <br />or greater usually approximate the normal distribution very closely it is <br />appropriate to use those statistical methods in evaluation of the cover data <br />for reclamation success purposes. <br />The Division should require Trapper to test success of reestablisfiment of <br />cover using the same method employed for production as outlined in my November <br />25, 1985 memo and stipulate that a minimum of 25 sample units be undertaken <br />prior to comparison. <br />Zar, Jerrold N. 1974. Biostatistical Analysis. Prentice-Hall, Inc., <br />Englewood Cliffs, N. J. 619 pg. <br />/tmb <br />9550E <br />