design-eng

# Design-eng - Data collection and statistics Sampling Statistics descriptive Experimental setup analysis of variance correlation regression

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Data collection and statistics Sampling - descriptive - analysis of variance -corre lat ion - regression - ordination - classification Experimental setup Statistics Websites : www.statsoft.com => electronic statistic textbook

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Sampling Qualitative Semi-quantitative Quantitative Ecologiscal research Per unit of surface or volume - Sample size ? - Number of samples ? time and space - Number of replicates ? - location ? Time ? Determinant factors : size and life strategy of organisms patchiness type of ecosystem - gradients
Distribution patterns : “ patchiness” RANDOM UNIFORM AGGREGATED Variance = < > mean Poisson + binomial - binomial

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Random pattern => Poisson distributie Assume N cells and 1 individual and no forces acting on the individual Probability that individual is present in one particular cell is 1 / N Equal probability for individual to be present in any of the cells or process of repeated dichotomy (presence- absence) If data are distributed according to a poisson distribution, it means there is no influence from the organisms on each other, or from the environment . Therefore in ecology or ethology it is first tested if there is a poisson distribution before interactions are investigated
Chi quadrate test for goodness of fit If sample is large enough => one can test if observed frequency distribution pattern is similar to one of the three possibly expected distributions. = ² χ (observed* - expected*)² observed* * values for each frequency interval The calculated value is then compared with tabullated values of ² df = number of frequency intervals - number of estimated parameters -1 Poisson 1 + binomiaal 2

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Scale to investigate a population is important A : random B : aggregated C : random D : regular Not always visual obvious=> correct sampling , counting and calculation of parameters is necessary
NR OF REPLICATES DEPENDENT ON PATCHINESS Î statistical minimum of 3 A : random B : aggregated C : random D : regular Aggregated pattern gives underestimation with low nr of replicates

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Alternative method to test distribution patterns : “Taylor’s Power law” based upon 2 statistical parameters μ and ² σ Assume we estimate the mean and variance of a population based upon several samples that are characterised by different densities Due to sample size time, environmental conditions Next we plot both parameters in an XY scatter plot
Y = 3.7 X^2. .3 0 100 200 300 400 500 600 700 800 02468 1 0 1 2 Next we look for the best fit for the relation between μ and ² by a “power curve” σ Regression-analysis with the relation between 2 variabels described by a known function By means of the method of the least squares, a and b are calculated that best describe the relation between μ en ².

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## This note was uploaded on 05/28/2010 for the course WE BIBI010000 taught by Professor Marnikvuylsteke during the Spring '10 term at Ghent University.

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Design-eng - Data collection and statistics Sampling Statistics descriptive Experimental setup analysis of variance correlation regression

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