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Outline Some field sampling issues Overview of approach to understanding a system Example 1 – KPBS Example 2 – Xoo Example 3 – SIR model Through approach again with these three examples Karen A. Garrett Kansas State University

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Rust fungi Phytophthora infestans, an oomycete Wheat curl mite, vector of Wheat streak mosaic virus Cercospora apii infects both humans and… celery

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Designed experiments vs. observational experiments Designed experiments generally have a more straightforward analysis Observational experiments rely more on correlation, so that interpreting causality may be more difficult Many experiments in disease ecology have some designed elements and some observational elements

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Ratio of Phaeosphaeria nodorum to Mycosphaerella graminicola compared to sulfur dioxide emissions Bearchell et al. 2005 PNAS

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Defining an inference space The inference space of an experiment is the group to which the experimental conclusions can be correctly applied The pool from which the experimental units are randomly drawn will clearly be part of the inference space Logic outside statistical inference may be used to extend results to broader set of units Definition of this space allows definition of the appropriate experimental unit

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Pseudoreplication Pseudoreplication occurs when repeated observations of a subject are substituted for replicated applications of a treatment on different subjects In general, if it seems that the number of replicates can be increased indefinitely by splitting samples in increasingly smaller units, these are probably pseudoreplicates “What is objectionable is when the tentative conclusions derived from unreplicated treatments are given an unmerited veneer of rigor by the erroneous application of inferential statistics” - Hurlbert

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Classic example of pseudoreplication Pseudoreplicates True replicates Scenario in which an individual mite is the appropriate experimental unit

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Pseudoreplication – ex 2 – pseudoreplication in spatial samples Suppose that a treatment has been applied at the larger scale Pseudoreplication

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Suppose there is no treatment application or experimental design? Defining pseudoreplication in an observational study is more challenging The variance associated with sampling at different spatial scales or across different types of groups of individuals can be compared to determine what are the largest sources of variation

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Important note about correlation and newer statistical packages Recall the standard assumption for typical analyses of variance that observations are independent In the past, and sometimes in the present, people might disregard the possibility of using packages like SAS Proc GLM because they knew their samples were not truly independent Newer programs like SAS Proc Mixed (and programs in R?) make it easier to specify more complicated correlation matrices for the errors in an analysis of variance

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Statistical power Statistical power: the probability of detecting treatment effects that really exist Scientists have tended to emphasize controlling the Type I error rate (the probability of designating an effect as “significant” when it is not real) rather than maximizing power This seems to be based on the idea that journals should not be cluttered with reports of a lot of effects that are not real However, if you want to manage a disease, discarding an effect because the associated p-value is greater than 0.05 may lead you to leave out important effects Real effects may be difficult to detect because of noise Sensitivity analyses can be used to explore the implications of removing an effect when it is actually real

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Parsimony On the other hand, parsimony is a good general goal Statistical models need to strike a balance to avoid leaving out important predictors and also to avoid overparameterizing Mechanistic models can be applied to explore the potential impacts of many predictors

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Statistical power Power is increased by reducing measurement errors and by increasing sample size Just because a null hypothesis has not been rejected doesn’t mean that there are no treatment effects

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Testing for bioequivalence Bioequivalence tests can be used to formally test whether there is no difference between the effects of treatments (within some tolerance)

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Garrett 1997

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Defining a “biological tolerance level” A sensitivity analysis might be used to define a tolerance level for effects below which there is not expected to be any important impact Formal discrimination between statistical significance and biological significance BUT…you would need to have a great deal of confidence in your model to rely on this for management decisions

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Meta-analysis applications in plant pathology Comparisons across studies can be formalized in meta- analyses We have illustrated the application of meta-analysis to the large quantities of data available from plant pathology field trials Rosenberg, Garrett, Su, and Bowden 2004 Phytopathology

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Metadata The National Center for Ecological Analysis and Synthesis works with metadata and metadata standards as one of its many projects http://www.nceas.ucsb.edu/nceas- web/resources/metadata.htmlhttp://www.nceas.ucsb.edu/nceas- web/resources/metadata.html

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For discussing the disease data set analyses Here are some suggestions for pondering your data sets and projects You might consider addressing these questions in your discussions and final presentation

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Defining the goals of the project A. What is the motivation for the project? –Understanding the system better In what way in particular? –Learning to manipulate the disease What are the potential methods for manipulation? B. What are the hypotheses to be tested or parameters to be estimated? –Will the project be sufficient to test hypotheses? –Or will it more appropriately generate hypotheses to be tested in a more controlled context?

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Variables and parameters What are the potential predictor and response variables? What are the parameters to be estimated? When using parameter estimates from an experiment in a mechanistic simulation model, the estimates might be viewed as values to emphasize while considering a wider range of possible values

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Studying the distribution of variables It may be necessary to split variables into logical groups, such as by environment For example, if environment has a large effect, analyzing the disease severity for samples from all environments in the same analysis might produce a multi- model distribution

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What are sources of bias? Since samples may not have been collected specifically to answer later questions, estimates may be biased for some questions For example, rather than random sampling, specific individuals may have been sampled because of their observed characteristics (symptoms, family size, …) True random sampling is often a challenge, anyway

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Deciding what to average prior to analysis Once the appropriate experimental unit is identified, you might average the subsamples within a unit Possibly the subsample variance is interesting in its own right and you would like to include it in analyses You can keep all the individual subsample measures in the analysis if you are careful to use the correct error estimates for testing effects

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Is there a widely accepted model for this system already available? Can your data be used to further validate this model or perhaps as an example of a case in which the model does not hold? Does your data add a new component to this model, such as considering the effects of a novel environmental parameter?

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If there are not already accepted models for your system… Is there a related system that has been studied more, modeled, and might be used as a starting point for considering your system? For example, SIR models might be generally applied for many types of disease

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Iteration between input from experimental analyses and input from modeling Modeling Construction of new hypotheses and predictions Empirical experimentation: Testing of hypotheses in experiments; generation of new parameter estimates; generation of new hypotheses Modeling Construction of new hypotheses and predictions Empirical experimentation: Testing of hypotheses in experiments; generation of new parameter estimates; generation of new hypotheses

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Sensitivity analysis Analysis of model output for a range of parameter and variable inputs – analysis of the sensitivity of outputs to changes in the inputs The distribution of outputs for a particular set of inputs can be evaluated in terms not only of the mean or median, but also the maxima and minima

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Model validation A data set might be split by location, so that a model developed based on one subset of locations is validated using another subset A data set might be split by time, so that a model developed based on earlier time points is validated using later time points

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