Il s'agit d'un message multivolet au format MIME. --------------C0537FDC865FD3C817DF4132 Content-Type: text/plain; charset=iso-8859-1 Content-Transfer-Encoding: 8bit
Dear all, I am a french Ph.D. student, I am working on ecological risk assessment of oil exploitation on deep-sea benthic communities. Part of my work is to look at sampling strategies. So, I have used retrospective power analysis to determine the sampling size required to detect a predefined effect size. However, I am quite surprised by the results. Since I am not fair with power analysis I am looking for some advice on the background and results of my analysis. Perhaps could someone help me? Here is the description of the analysis, the results and questions: >From the data we have obtained on macrofaunal densities at 2 deep-sea stations I am trying to determine the effect size that could be detected with our sampling design and the number of sample that should be needed to detected a pre-specified effect size. We have taken 3 samples on each of the 2 stations, one of it was sampled in 2000 and the other one in 2000 and 2001. For the purpose of the analysis, I have used scenarii based on a Before After Control Impact design and inferred that in a 2 way ANOVA, a significant effect of oil activities should be detected if the interaction between the 2 factors (location and time) is significant. One of the station we have sampled was my control, the second one my impacted station. The "control" station was sampled in 2000 and 2001 so I have used these data to take into account the natural temporal variations. First, for the "impact" station, I have regularly increased observed densities of 10%, 20%, .30%,� in each of the 3 samples. I have performed for each effect size a two-way ANOVA and then calculated the noncentrality paramater as lambda = SSinteraction/MSerror and determined the power of the analysis. With this process I found that a 60% increase in densities gave a type I error of 0.04 and power of 0.55. In a second step I have tried to look at the sample size needed to detect a 30% increased in densities. For the purpose of the test, I have assumed that the densities in all further samples should be between the range of already observed densities. So, I have created 30 random data sets with randomly chosen densities for each sample size from n=4 to n=9 samples. I have then computed the 2 way ANOVA and power for each data set. Finally, I have used the mean alpha and mean power per sample size to estimate the sample size needed to detect a 30% increase in densities. >From this analysis, I have observed that the mean alpha and confidence interval constantly decreased until n=7 samples. The inverse relation was found for power (see figure 1 in attached file). My first interrogation is why the mean alpha and mean power values became so abruptly constant and not continuously decreased as sample size increased ? I have also plot from these results each value of power according to the value of alpha and found always the same kind of correlation (figure 2 in attached file) (I have plot values of alpha and power from others completely different data sets and always found the same correlation). According to this correlation, a power of 0.8 could only be achieved with an alpha of 0.0075. I am surprised by these results. I am then wonder if in retrospective power analysis, the alpha level should actually be more informative than the value of power. The results of simulation actually suggest that a mean alpha below 0.05 (which is good enough) could be achieved with 7 samples per time per location with a mean power of 0.68 (which is not so good!). Could you please told if the concepts behind the analysis are valid (or if I am totally wrong) and help me in the interpretation of these results ? I hope that someone can find time and interest in helping me. I also hope that my explanations in English were clear enough. Thank you very much for reading this message until the end. 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