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Replication and Effect Size

March 19, 2015

I am asked pretty often by my students the following question:

“How many replicates do I need for experiment X?”

I always ask them a series of question trying to get at what they think the effect size will be relative to underlying variation without asking them, “What do you think your effect size will be given your underlying within-treatment variation?”

I could quote my graduate experimental design professor, Patrick Phillips, who said, “30 is closer to infinity than it is to zero.” but they generally don’t get that if they have not taken my Applied Statistics course.

I could also direct them to calculators that allow them to calculate necessary sample sizes needed to detect a given difference given a set amount of within sample variation. Once again, not very satisfying. I want them to have an intuitive feel for how these things relate to one another and this week in the field, because of a recent experiment and priceless weather here in Puerto Rico, I have a good illustration that any of you may steal if you find it useful.

I work in collaboration with the Luquillo Experimental Forest LTER and we have been conducting a Canopy Trimming Experiment that allows us to experimentally decouple the effects of canopy opening (microclimatic changes) and green litter inputs (fresh litter has different nutrient levels than senesced litter), two effects that normally occur concurrently in hurricanes and which are hard to decouple then because you did not plan it and you are rebuilding your life post-hurricane and don’t have time to move 66,000 kilos of litter around the forest. The LUQ LTER just published a set of papers on this in the november issue of Forest Ecology and Management. The second part of the experiment was supposed to look into the effects increasing hurricane frequency and a group of volunteers and arborists just did the cut. When the experiment was put in, we dealt with all the practical issues having to do with setting up what was for us a large scale experiment in a tropical rain forest. We decided that all we could afford, in terms of money and human power, was 3 blocks. That’s right: n=3. You might ask, why only three? The sites look like this:

The Control Plot to Block B of the Canopy Trimming Experiment, El Verde Field Station.

The Control Plot to Block B of the Canopy Trimming Experiment, El Verde Field Station.

In addition, you have to hike there (no roads) and the trail is steep and slippery, even in the “dry” season (really more like the “less wet” season in what is a pretty seasonal rain forest). So, the forest after being trimmed looks like this:

The Block B plot with canopy cut and litter applied to the forest floor, about 5 months post-cut.

The Block B plot with canopy cut and litter applied to the forest floor, about 5 months post-cut.

If you are studying just about anything ecological, the treatment effect is going to be huge and detectable even with significant amounts of within-treatment variation. In this way, we can get away with low levels of replication and still detect the effect of the treatment because that effect is so huge. Now, there is a lot of variation due to elevation (seen as a block effect) and seasonality, but it works in the long run.

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