3/9/2015. Overview. Introduction - sampling. Introduction - sampling. Before Sampling

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1 PLP 6404 Epidemiology of Plant Diseases Spring 2015 Lecture 19: Spatial variability, sampling and interplotinterference Prof. Dr. Ariena van Bruggen Emerging Pathogens Institute and Plant Pathology Department, IFAS University of Florida at Gainesville Overview Introduction: Spatial variability What is sampling? why sampling? Before How many samples? designs Sequential sampling Bulking samples for experimental design inter-plot interference Summary Introduction: Spatial variability Introduction - sampling is that part of statistical practice concerned with the selection of a subset of individual observations within a population of individuals intended to yield some knowledge about the population of concern, especially for the purposes of making predictions based on statistical inference. Regular pattern Random pattern Aggregated 2 < 2 = 2 > var. less than mean variance = mean variance>mean Introduction - sampling Goals of sampling Describe a population (get true estimate of mean and variance) Monitor an event (ie temperature change) Minimize variance due to sampling Minimize effort and costs Before Before sampling you need to decide: What you are going to do with the data Describe population mean/variance Compare to other populations (treatments) What you want to sample Decide on species or phenomena (disease?) Unit (field vs plant vs leaf vs cell) Qualitative (+/-) or quantitative Environmental variables How much time and money you have 1

2 Before Good to know: Spatial distribution Mean of population Variance (time and space) of population How to process samples Best time to sample How hard is it to sample a population? The lower the mean (more rare the event) and the more aggregated the populations (higher the variance), the harder it is to get a true estimate of the population. What is small and what is aggregated? If disease is above 10%, most sampling systems work If variance/mean ratio less than 5, most sampling will work Unfortunately, these are usually outside of our experiences with disease in the field How many samples do you need? What is the coefficient of variance of a population? solve for n to get the desired sample size as a function of CVx- CV is inversely proportional to sample size n: as sample size increases, CV will be smaller (decrease). How many samples do you need? We can estimate the sample size with a confidence interval equal to a proportion of the parameter µ, using the following formula (for n>30): where the confidence interval is expressed in terms of D, a fixed proportion of the mean. For a 95% CI, Z P/2 = 1.96 (from a standard normal Z-table). Then n = 4S 2 /L 2 where n = number of samples, S is standard deviation, and L is acceptable error (ie 0.05*40 = 2 bushels if mean yield is 40 bushels) So, if standard deviation is 10 and accuracy needed is 2 bushels, you need to take 100 samples (100 = 4(10 2 )/2 2 ) for rare events: Don t take a representative sample Look for likely spots Region, field, plant, plant part over time: Minimize variance by sampling at the same location Sample at consistent time units If possible sample with same observer Sample at end of experiment may be most important product of integration of season Sample designs: Systematic sampling Diagonal W; Better to increase number of arms (directions) than number of samples on an arm Random sampling Cluster Size Analysis Stratified Random Sample Zonal Sequential sampling 2

3 Systematic sampling Start at random position on field edge, then take a sample every 10 paces as go across field Easy to do (only one random event to deal with) Built in stratification, but may not cover clusters Can not estimate standard error of mean May be badly biased if chosen interval is equal to cluster interval Random sampling Simple random sampling - selecting n units without replacement from the population of N such that every one of the units has an equal chance of being sampled removes possibility of bias on the part of the evaluator requires designation of every sampling unit (cumbersome but unbiased) 3

4 Cluster size analysis for stratiefied sampling Little variance among quadrats: quadrat size not equal to cluster size Examine size and position of clusters When variance is highest, cluster sample size and actual cluster are equal Thus, quadrat size needs to be equal to cluster size High variance among quadrats: quadrat size equal to cluster size Stratified Random Sample Stratified random Sample Design Stratified random sampling Every plant (unit) has the possibility of being sampled Samples are dispersed over the entire field Provides estimates of within field variance Provides data on spatial relationships Percent error is inversely related to disease incidence and directly related to disease aggregation Delp, B. R., Stowel, L J., Marois, J. J Evaluation of field sampling techniques for estimation of disease incidence. Phytopathology

5 Zone sampling Especially when using GIS Incorporates known geographic features into sampling (ie soil type, plant density, etc) Sample size in a zone Take more samples where variance in zone is higher Take more samples when zone is larger Apply a weight according to zone size Bulking samples, e.g. in zones Reduces processing costs Loses information especially variance Reduces variance Reduces degrees of freedom Be careful once bulked cannot go back Sequential sampling It is an alternative to taking a fixed number of samples by evaluating population density of a disease after each sample, and deciding to continue sampling or not At every sampling population levels are evaluated relative to some pre-defined threshold The basic concept of sequential sampling is that the cumulative number (Tn) of the sampled entity (i.e., lesions) is determined after each sample Express, rearrange Substitute in equation for Generated values of Tn are known as stop line When observed Tn exceeds generated Tn, the desired reliability has been achieved; no additional samples are necessary Sequential sampling - example Sequential sampling plan to determine whether the incidence of fruit infected by Monilinia in loads of blueberries is above or below a threshold of 0.5% The maximum number of samples, nmax, that needs to be collected if the cumulative number of infected fruit stays between the two stop lines, was calculated with precision D=0.25. for experimental design Determine spatial aggregation of inoculum of root diseases Use knowledge of crop rotation history and previous disease history in a field Collect soil samples from each area (stratified random sampling) based on crop and disease history to provide knowledge of background levels of a soil-borne pathogen Determine cluster size and locations Randomize treatments within each inoculum density level Use inoculum density clusters as blocks 5

6 Experimental design What is inter-plot interference? Negative inter-plot interference net loss of inoculum out of a plot, resulting in less disease than expected Positive inter-plot interference net gain of inoculum into a plot, resulting in more disease than expected Minimize inter-plot interference Use border rows (same crop or a taller intercrop) Plot spacing (distance large enough to avoid inter-plot dispersal; don t include the margins of each plot) Plot size (large enough to minimize negative interference) Vector control Summary Introduction: Spatial variability What is sampling? why sampling? Before How many samples? designs Sequential sampling Bulking samples for experimental design inter-plot interference 6

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