Optimum Sample Size to Detect Perturbation Effects: The ...

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Table 1. Power values (probabilities) for an ANOVA design with a = 0.05. For 2 to 25 N° of treatments and for each one of the habitats analysed by Mouillot et al. (1999). A small effect size is 0.1, medium effect is 0.25 and a large effect is 0.4 (sensu Cohen, 1988). power (with Type I error = 0.05) N° marine habitats treatment - 1 seagrass west rocky bottoms south rocky bottoms east (k-1) variability coefficient variability coefficient variability coefficient 10 % 25 % 10 % 25 % 10 % 25 % (comparisons) sample size sample size sample size n = 118 n = 19 n = 112 n = 18 n = 130 n = 21 effect size effect size effect size 0.1 0.25 0.4 0.1 0.25 0.4 0.1 0.25 0.4 0.1 0.25 0.4 0.1 0.25 0.4 0.1 0.25 0.4 1 34 97 99 9 33 68 29 94 99 8 31 66 36 98 99 9 36 73 2 38 99 99 9 36 76 32 98 99 9 34 73 41 99 99 9 40 80 3 43 99 99 9 41 83 36 99 99 9 39 80 46 99 99 10 45 87 4 47 99 99 10 45 88 40 99 99 9 43 86 50 99 99 10 50 91 5 52 99 99 10 49 92 44 99 99 10 47 90 55 99 99 11 54 94 6 56 99 99 11 53 94 47 99 99 10 51 93 60 99 99 11 58 96 8 63 99 99 11 60 97 54 99 99 11 57 97 67 99 99 12 66 99 10 69 99 99 12 67 99 60 99 99 12 64 98 73 99 99 13 72 99 12 74 99 99 13 72 99 65 99 99 12 69 99 78 99 99 14 77 99 15 81 99 99 14 78 99 71 99 99 13 76 99 83 99 99 15 84 99 24 92 99 99 21 97 99 85 99 99 16 89 99 94 99 99 18 94 99 Note: n = average sample size and coefficient of variability per habitat from Mouillot et al. (1999) 4 Ortiz
Power analysis for sample size estimations 5 Fig. 1. Power curves for ANOVA design for seagrass west habitat with a. 10 % (n = 118) and b. 25 % (n = 19) of variability (dispersion coefficient). Dotted line represents the minimum acceptable power of 0.80. Re-evaluation of data Figures 1, 2 and 3 show that for the seagrass, rocky shores south and rocky shores west habitats, respectively, independent of the coefficient of variability, the magnitude of a possible perturbation (effect size) must always be large, that is ³ 0.40, to ensure a high robustness of the statistical test (ANOVA) in assessing the hypothesis. In a situation where the putative perturbation is small (effect size = 0.10), no sample size proposed by Mouillot et al. (1999) is sufficient. Additionally, if the effect size is < 0.10, more than 1000 samples must be taken for an ANOVA design.
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Optimum Sample Size to Detect Perturbation Effects: The ...

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