Some preliminary information from:

Statistical workshop on experimental design and analysis

of turtle mitigation studies

November 7-8, 2007Villa Blanca

Alajuela, San Ramón, Costa Rica

Attendees:Mary Christman, University of Florida

Daniel Hall, University of GeorgiaPaul 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, JapanMichelle Sims, Duke University, North Carolina

Steven Thompson, Simon Fraser University, Canada

Funded by: OFCF, WPRFMC, NOAA/NMFS, IATTC, WWF

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.

Some general questions considered by the Some general questions considered by the groupgroup

1)1)What else can be done to determine how well your What else can be done to determine how well your results will represent the typical longline if hook results will represent the typical longline if hook changes are implemented?changes are implemented?

2)2)How could the data you have already collected be used How could the data you have already collected be used to determine what sample sizes you need to detect to determine what sample sizes you need to detect differences in hooking rates and if your sampling differences in hooking rates and if your sampling methods could be improved?methods could be improved?

3)3)What are the best statistical methods to use to What are the best statistical methods to use to determine if there is a significant difference in hooking determine if there is a significant difference in hooking rates between C and J hooks?rates between C and J hooks?

J J JJ JC C C C

The hook experiment design:The hook experiment design:

This is a reasonable way to compare hook performance This is a reasonable way to compare hook performance because you can control for potentially important because you can control for potentially important variables (e.g., environmental characteristics).variables (e.g., environmental characteristics).

Typically fishermen would not alternate hook types; Typically fishermen would not alternate hook types; therefore, this experimental design is not therefore, this experimental design is not representative of how the fishermen will actually fish.representative of how the fishermen will actually fish.

1)1) Generalization of resultsGeneralization of results

C C C CCC C C C

When a fishermen switches to C hooks, the When a fishermen switches to C hooks, the longline becomes:longline becomes:

Will hook performance be the same when the Will hook performance be the same when the line consist of only one type of hook?line consist of only one type of hook?

That is, will the difference in catch rates (J, C) That is, will the difference in catch rates (J, C) be the same when the line has only C be the same when the line has only C hooks?hooks?

We don’t know.We don’t know.

This alternating hook design is sufficient for This alternating hook design is sufficient for testing the null hypothesis of no difference testing the null hypothesis of no difference between hook types and may be more between hook types and may be more powerful.powerful.

However, it may lead to bias estimates of the However, it may lead to bias estimates of the difference in hooking rates, and if the p-value difference in hooking rates, and if the p-value is significant, it may be artificially small.is significant, it may be artificially small.

What to do?What to do?

One suggestion from the workshop was to One suggestion from the workshop was to consider trying the following hook consider trying the following hook configuration:configuration:

If results are similar to those of longlines with If results are similar to those of longlines with alternating hooks, this strengthens alternating hooks, this strengthens conclusions.conclusions.

J J JJ JCC C J

A second suggestion was to consider continuing A second suggestion was to consider continuing to sample the boats that switch all their hooks to sample the boats that switch all their hooks from J to C.from J to C.

How do their hooking rates compare to boats How do their hooking rates compare to boats that are still part of the experiment (i.e., still that are still part of the experiment (i.e., still using J,C,J,C…)?using J,C,J,C…)?

Different experiments could be done in stages. Different experiments could be done in stages. First use the alternating hook design. If a First use the alternating hook design. If a difference is detected, then do additional difference is detected, then do additional experiments that are more likely to replicate experiments that are more likely to replicate an actual longline configuration.an actual longline configuration.

2)2) Sample size and how to sampleSample size and how to sample

What is the sampling unit for analyses? Number of What is the sampling unit for analyses? Number of hooks, turtles, sets, or trips? hooks, turtles, sets, or trips?

Is this sampling unit dependent on fishing areas Is this sampling unit dependent on fishing areas and animal distribution?and animal distribution?

Would it be preferable to sample more vessels Would it be preferable to sample more vessels and fewer trips per vessel or more trips per and fewer trips per vessel or more trips per vessel and fewer vessels?vessel and fewer vessels?

Can try to answer these questions with the data Can try to answer these questions with the data you have using simulations.you have using simulations.

Simulation details will be forthcoming…Simulation details will be forthcoming…

3)3) Statistical methods to compare hook Statistical methods to compare hook performance between J and C hooksperformance between J and C hooks

Some of the issues:Some of the issues:

- The turtle (fish) hooking data have many zeros The turtle (fish) hooking data have many zeros and occasional large values, and statistics and occasional large values, and statistics computed from these data may not conform to computed from these data may not conform to assumptions of many statistical tests.assumptions of many statistical tests.

- There are many variables that may affect There are many variables that may affect hooking rates, but using a complex model that hooking rates, but using a complex model that includes all these variables is difficult.includes all these variables is difficult.

Several different types of statistical tests were Several different types of statistical tests were discussed, of various levels of complexity.discussed, of various levels of complexity.

The simplest to implement and interpret, and the The simplest to implement and interpret, and the least dependent on assumptions is the least dependent on assumptions is the randomization testrandomization test..

For these reasons, the randomization test is a For these reasons, the randomization test is a good first start. More complex analyses could good first start. More complex analyses could follow.follow.

How does the randomization test work?How does the randomization test work?

The question of interest: Is there a difference in the The question of interest: Is there a difference in the hooking rates between J and C hooks? hooking rates between J and C hooks?

To answer this question we compare a summary statistic To answer this question we compare a summary statistic of the observed data, such as the mean difference, to of the observed data, such as the mean difference, to the same statistic based on permutations of the data. the same statistic based on permutations of the data.

Permutations of the data are generated to reflect the Permutations of the data are generated to reflect the study design (e.g., alternating J and C hooks within a study design (e.g., alternating J and C hooks within a set), assuming no hook effect.set), assuming no hook effect.

How unusual the observed statistic is compared to those How unusual the observed statistic is compared to those from the permutations is a measure of the evidence of from the permutations is a measure of the evidence of a difference between hooks types.a difference between hooks types.

For simplicity, assume equal numbers of J and C For simplicity, assume equal numbers of J and C hooks on the longline (can make adjustments if hooks on the longline (can make adjustments if not true).not true).

Summary statistic = sum of differences in # Summary statistic = sum of differences in # animals (may not be most powerful statistic, animals (may not be most powerful statistic, but provides an example).but provides an example).

““Original” data:Original” data:

Set J: # animals

C: # animals

Diff.

1 11 13 -2

2 34 21 13

3 9 3 6Sum of Sum of

diff. = 17diff. = 17

Randomization # 1Randomization # 1

Set J C Diff.

1 13 11 2

2 21 34 -13

3 9 3 6

Sum of Sum of

diff. = 21diff. = 21

Randomization # 2Randomization # 2

Sum of Sum of

diff. = -5diff. = -5

Set J C Diff.

1 13 11 2

2 34 21 13

3 9 3 6

Compute all permutations (…there are only 8).Compute all permutations (…there are only 8).

Below are the ordered difference values:Below are the ordered difference values:

2121

1717

99

55

-5-5

-9-9

-17-17

-21-21

P-value for one-sided test = 2/8 = 0.25 P-value for one-sided test = 2/8 = 0.25

For larger data sets, you would do 1,000’s of For larger data sets, you would do 1,000’s of randomizations on a computer.randomizations on a computer.

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

Some options for software that implement some Some options for software that implement some forms of randomization tests:forms of randomization tests:

Excel has an add-on packageExcel has an add-on package

GenStat Discovery Edition 3 may be available GenStat Discovery Edition 3 may be available free to scientists in Latin America and ‘non for free to scientists in Latin America and ‘non for profit’ organizations (www.genstat.co.uk)profit’ organizations (www.genstat.co.uk)