sampling_designs-2.pdf

-Sampling…part 2 - Scale and study plots (pp. 158-159) - Randomization - Kinds of sampling design  Scale and study plots Two aspects to consider – Focus: physical area represented by the actual unit of observation – Extent: physical area over which the units of ob...

-Sampling…part 2 - Scale and study plots (pp. 158-159) - Randomization - Kinds of sampling design  Scale and study plots Two aspects to consider – Focus: physical area represented by the actual unit of observation – Extent: physical area over which the units of observation are distributed Waide et al. 1999. The relationship between productivity and species richness, Annual Review of Ecology and Systematics 30:257-300. Jornada Konza Chalcraft et al. 2004. Scale dependence in the species richness-productivity relationship: the role of species turnover. 85:2701-2708. Need to determine appropriate balance between 1) Number of observations wanted for sample 2) Size of area representing an observation (not an issue if units are individuals; size should be appropriate for observation to be meaningful) 3) Inference space to which the collection (sample) of observations represent (want to represent as broad a space as possible)  Randomization - The random selection of observations from a statistical population - Essential to obtain an unbiased estimate of mean and variance of statistical population -fundamental assumption of many statistical tests - Several ways to determine which observations to randomly select (e.g., random number generator, random number table, stopwatch)  Sampling designs 1) Simple random - all possible observational units have the same probability of being selected - the probability of one unit being selected is not dependent on the selection of another unit (i.e., independence) -mean and variance calculated using traditional measures of mean and variances 1 6 11 16 21 2 7 12 17 22 3 8 13 18 23 4 9 14 19 24 5 10 15 20 25  You can seldom go wrong using simple random sampling but it could be less efficient (need more observations) if there are spatial patterns in the environment Potential danger of observation locations to be clumped; does not adequately represent statistical population X X X X X 2) Stratified random sampling - sampling space is divided into subunits (strata) and then observations are randomly selected from within each strata. X X X X X X - Be sure to select strata that are likely to be important - More strata, more observations; identified strata may not be meaningful 5 10 10 10 5 25 35 25 30 30 65 50 55 60 60 70 75 75 65 70 100 90 95 90 85   51.6 x  35 5 10 10 10 5 25 35 25 30 30 65 50 55 60 60 70 75 75 65 70 100 90 95 90 85   51.6 x  52  X X X X X X X X X X X X X X If different number of samples/strata (or area of strata differs) need to weight observations to calculate mean and variance  Where: σLh=1 𝑛h ylj h L = number of strata ylj st = nh = total number of [area] units in strata h N N = total number of [area] units in all strata Strata # Average within Variance samples strata (dbh) 1 7 20 9 2 5 15 4 3 2 10 4 Standard error from stratified random (SE weighted by proportion of samples in each strata)  nh   s  2 2 SEST      h  N   nh  3) Systematic sampling -equal spacing of sample units (initial point selected randomly) X X X X X X 90 10 80 10 95 15 85 5 90 10 𝜇 = 49.4 95 90 85 45 30 25 15 10 𝑥ҧ = 56.25 95 90 85 45 30 25 15 10 𝑥ҧ = 62.5 CANNOT estimate SE with one systematic sample (regardless of # observations). Can’t use typical equations to estimate SE with systematic sampling because typical equations assume all entities selected with equal probability (i.e., are independent). To get unbiased mean and SE estimate from systematic sampling need to have MULTIPLE systematic samples – In other words your unit of replication (systemic sample rather than individual observation) is changing so your sample size is changing.  x  x  m 2 xi x SY   i 1 m SESY  i m(m  1) SY M is # of systematic samples and NOT # observations within sample - Provides good spatial coverage BUT Gives poor estimates of parameters if cyclical variation Requires multiple systematic samples