Applied Sampling for Wildlife
Applied Sampling for Wildlife FW 580
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BIOL 1305 - 003
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This 3 page Class Notes was uploaded by Maximilian Lynch on Monday September 21, 2015. The Class Notes belongs to FW 580 at Colorado State University taught by Staff in Fall. Since its upload, it has received 48 views. For similar materials see /class/210053/fw-580-colorado-state-university in FISH at Colorado State University.
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Date Created: 09/21/15
FW580 IAny questions IImportant points from last time JSimple Random Sample Excel ISRS is no guarantee of a representative sample ITradeoffs in design Let us start with a Simple Random Sample SRS Conceptual example we have a known opulation of birds 6 possi e plots Number of birds B What is the probabilitg of y particular sample What is the probability of any one plot being Included 39 mple 15 possible samples Sample Elrst Secund Elrst Secund Sample Apsulute Number Member Member Value Value Average Devlatlerr i A 3 2 3 4 4 2 A c 2 3 5 3 3 A D 2 i3 3 2 4 A E 2 i3 3 2 5 A E 2 i2 7 i 3 3 c 3 3 7 i 7 3 D 3 l3 3 3 3 3 E 3 i3 3 3 3 3 E 3 i2 3 i in c D 3 i3 3 i ii c E 3 i3 3 i i2 c E 3 i2 i3 2 i3 D E in in i 2 i4 D E in i2 ll 3 i5 E E i2 ll 3 Average 3 Sampling distribution of the sampled average Sarrple Sarrple Deviance 55 pie Relativ Expected yumbgg V V V 39 39h Average Frequenc FFeMHC Avg rel fre 7 l 4 4 4 l o 07 o 27 2 5 3 5 l o 07 o 33 3 3 2 6 2 0 is 080 4 3 2 7 2 0 is 093 5 7 l 8 2 dis lo7 3 7 l 9 3 0 20 l 80 7 3 El i0 2 0 l3 Ha I 3 3 3 ll 2 MS l47 3 3 El Total is l in 3 El Expectation sum 8 00 ii 3 El l2 l3 72 3 i3 72 5 l4 ll 73 3 l5 ll 73 i Average n blas 3 5 7 x v in ii swam Sampling distribution of the estimator ISample average is a random variable Value has a distribution and varies from sample tn sample as a result ofsampling process lSampleaverage formula is an estimator of population average parameter Each sample average outcome is an estimate ICompare sampling distribution of a SRS with n r itrary samp ing scheme39 IEstimator has a samplin distribution with nown outcomes and re ative frequenCIes We base much upon this Sampling distribution Judge an estimator by examining its sampling distribution as a whole lWhat properties do we desire Estimator does not systematically mislead us concerning true value average ofall possible samples equals true al or ue Average deviance 0 Therefore unbiased Correspondence principle IStates best estimator is the same function of the sample as the parameter is of the population Not generally true either in terms of unbiasedness see example later o Orin terms of being the best39 case of supplementary information Supplementary information ISay you knew the range of number of deer in each plot was 212 Decide on a rule that if a 2 is in the sample a 1 is added to the sample average if a 12 is in the sample a 1 is subtracted from the average ICan supplemental information can be valuable come back to later Rule add 1 to 2 subtract 1 from 12 3 stgnm s ie ri se rid sa pie oe l l Nu e We VueAvEgeVsleleleZA nntnea Sampling distribution variance I Estimation unbiasedness is not enough U Want the best estimator among all unbiased estimators I Insist upon sampling distribution being concentrated around average precision Measured with variance Average difference deviation ofsample means from the mean of the distribution 2 gt673 n Need m square the deviations because half are positive and half are negative 2 x s a n xpecte popu ation an sampe distribution variance nuvvn Population Deviation Deviation DEWZJ Relative Pm Number reeuenev reeuenev me Avg seuevee neirvee 2 i on s as sun 5 i on 2 v osv a i oiv o o ooo to i on 2 v osv to i on 2 v osv i2 i on v is 257 5 tom Sampling Distributlun Relative Deviation Deviation DeWZV Average reeenev rie enev meAvg seveee neirvee Oupsll v 7 e is iov 5 7 3 9 men s 3 2 2 D53 7 3 i i D13 5 3 o o ooo s o i i o2o to 3 2 2 D53 ii 3 3 s i2o Tmel i Expected sennine Variance v 27
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