Some preliminary information from: Statistical workshop on experimental design and analysis

1. Some preliminary information from: Statistical workshop on experimental design and analysis of turtle mitigation studies November 7-8, 2007 Villa Blanca Alajuela, San Ramón, Costa Rica

2. Attendees: Mary Christman, University of Florida Daniel Hall, University of Georgia Paul Kinas, Fundacáo Universidad Rio Grande, Brazil Bryan Manly, Western Ecosystem Technology, Inc, U.S. Marti McCracken, NMFS/NOAA-Hawaii Mihoko Minami, Institute of Statistical Mathematics, Japan Michelle Sims, Duke University, North Carolina Steven Thompson, Simon Fraser University, Canada Funded by: OFCF, WPRFMC, NOAA/NMFS, IATTC, WWF

3. Workshop purpose To provide the Eastern Pacific Regional Sea Turtle Program with suggestions for: • Analysis of existing data; • Improving sampling design and analysis of future studies. Workshop discussions are being summarized and will be made available.

4. Some general questions considered by the group • What else can be done to determine how well your results will represent the typical longline if hook changes are implemented? • How could the data you have already collected be used to determine what sample sizes you need to detect differences in hooking rates and if your sampling methods could be improved? • What are the best statistical methods to use to determine if there is a significant difference in hooking rates between C and J hooks?

5. Generalization of results The hook experiment design: C J C J C J J C J This is a reasonable way to compare hook performance because you can control for potentially important variables (e.g., environmental characteristics). Typically fishermen would not alternate hook types; therefore, this experimental design is not representative of how the fishermen will actually fish.

6. When a fishermen switches to C hooks, the longline becomes: C C C C C C C C C Will hook performance be the same when the line consist of only one type of hook? That is, will the difference in catch rates (J, C) be the same when the line has only C hooks?

7. We don’t know. This alternating hook design is sufficient for testing the null hypothesis of no difference between hook types and may be more powerful. However, it may lead to bias estimates of the difference in hooking rates, and if the p-value is significant, it may be artificially small.

8. What to do? One suggestion from the workshop was to consider trying the following hook configuration: C C J J J J J C J If results are similar to those of longlines with alternating hooks, this strengthens conclusions.

9. A second suggestion was to consider continuing to sample the boats that switch all their hooks from J to C. How do their hooking rates compare to boats that are still part of the experiment (i.e., still using J,C,J,C…)? Different experiments could be done in stages. First use the alternating hook design. If a difference is detected, then do additional experiments that are more likely to replicate an actual longline configuration.

10. Sample size and how to sample What is the sampling unit for analyses? Number of hooks, turtles, sets, or trips? Is this sampling unit dependent on fishing areas and animal distribution? Would it be preferable to sample more vessels and fewer trips per vessel or more trips per vessel and fewer vessels? Can try to answer these questions with the data you have using simulations. Simulation details will be forthcoming…

11. Statistical methods to compare hook performance between J and C hooks Some of the issues: • The turtle (fish) hooking data have many zeros and occasional large values, and statistics computed from these data may not conform to assumptions of many statistical tests. • There are many variables that may affect hooking rates, but using a complex model that includes all these variables is difficult.

12. Several different types of statistical tests were discussed, of various levels of complexity. The simplest to implement and interpret, and the least dependent on assumptions is the randomization test. For these reasons, the randomization test is a good first start. More complex analyses could follow.

13. How does the randomization test work? The question of interest: Is there a difference in the hooking rates between J and C hooks? To answer this question we compare a summary statistic of the observed data, such as the mean difference, to the same statistic based on permutations of the data. Permutations of the data are generated to reflect the study design (e.g., alternating J and C hooks within a set), assuming no hook effect. How unusual the observed statistic is compared to those from the permutations is a measure of the evidence of a difference between hooks types.

14. For simplicity, assume equal numbers of J and C hooks on the longline (can make adjustments if not true). Summary statistic = sum of differences in # animals (may not be most powerful statistic, but provides an example). “Original” data: Sum of diff. = 17

15. Randomization # 1 Sum of diff. = 21 Randomization # 2 Sum of diff. = -5

16. Compute all permutations (…there are only 8). Below are the ordered difference values: 21 17 9 5 -5 -9 -17 -21 P-value for one-sided test = 2/8 = 0.25 For larger data sets, you would do 1,000’s of randomizations on a computer.

17. If your data come from longlines with unequal numbers of J and C hooks……stay tuned for the workshop proceedings.

18. Some options for software that implement some forms of randomization tests: Excel has an add-on package GenStat Discovery Edition 3 may be available free to scientists in Latin America and ‘non for profit’ organizations (www.genstat.co.uk)