[Federal Register Volume 62, Number 171 (Thursday, September 4, 1997)]
[Rules and Regulations]
[Pages 46679-46680]
From the Federal Register Online via the Government Publishing Office [www.gpo.gov]
[FR Doc No: 97-23404]


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DEPARTMENT OF COMMERCE

National Oceanic and Atmospheric Administration

50 CFR Part 622

[Docket No. 961226370-7074-02; I.D. 111896A]
RIN 0648-AI15


Fisheries of the Caribbean, Gulf of Mexico, and South Atlantic; 
Shrimp Fishery Off the Southern Atlantic States; Amendment 2; 
Correction

AGENCY: National Marine Fisheries Service (NMFS), National Oceanic and 
Atmospheric Administration (NOAA), Commerce.

ACTION: Final rule; correction.

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SUMMARY: NMFS published in the Federal Register of April 16, 1997, the 
testing protocol for bycatch reduction devices (BRDs). The statistical 
approach section of that appendix contains errors. This document 
corrects those errors.

DATES: Effective September 4, 1997.

FOR FURTHER INFORMATION CONTACT: Peter J. Eldridge, 813-570-5305.

SUPPLEMENTARY INFORMATION: The shrimp fishery off the southern Atlantic 
states is managed under the Fishery Management Plan for the Shrimp 
Fishery of the South Atlantic Region (FMP). The FMP was prepared by the 
South Atlantic Fishery Management

[[Page 46680]]

Council and is implemented under the authority of the Magnuson-Stevens 
Fishery Conservation and Management Act by regulations at 50 CFR part 
622.

Background and Need for Correction

    Amendment 2 to the FMP, among other things, requires the use of 
certified BRDs in all penaeid shrimp trawls in the exclusive economic 
zone in the South Atlantic. The final rule to implement Amendment 2 
contained as an appendix the Testing Protocol for BRD Certification. 
The Statistical Approach section of that appendix contained errors, 
primarily in the formulas for computing whether the BRD tested achieves 
the minimum required reduction rate for weakfish and Spanish mackerel.
    For clarity and ease of use, this correction restates the entire 
corrected Statistical Approach section of the Testing Protocol for BRD 
Certification.

Correction of Publication

    In FR Doc. 97-9816 published on April 16, 1997 (62 FR 18536), make 
the following correction. On page 18542, in the appendix to the 
document, which will not appear in the Code of Federal Regulations, 
remove the text beginning five lines from the bottom of the first 
column with the heading ``Statistical Approach'' and ending with the 
text on line 11 of the third column and replace it with the following:

Statistical Approach

    You should start with the assumption that the BRD to be tested 
does not achieve the minimum required reduction rate, say 
R<INF>0</INF>. This assumption will be rejected if the data provide 
sufficient evidence to do so. Hence, the hypotheses to be tested are 
as follows:

H<INF>0</INF>: BRD does not achieve the minimum required reduction 
rate,
[GRAPHIC] [TIFF OMITTED] TR04SE97.008

H<INF>a</INF>: BRD does achieve the minimum required reduction rate,
[GRAPHIC] [TIFF OMITTED] TR04SE97.009

    Here R denotes the actual reduction rate (unknown), 
R<INF>0</INF> denotes the minimum required reduction rate, 
<greek-m><INF><greek-ps></INF> denotes the actual mean CPUE with the 
control, and <greek-m><INF><greek-b></INF> denotes the actual mean 
CPUE with the BRD.
    With any hypothesis testing, there are two risks involved, known 
as type I error (rejecting the true H<INF>0</INF>) and type II error 
(accepting a false H<INF>0</INF>). The probabilities of committing 
these errors are denoted by alpha and beta, respectively, and those 
are inversely related to each other. As alpha increases, beta 
decreases, and vice versa. The above test will be conducted with an 
alpha to be specified by the RA. The above hypotheses should be 
tested using a ``modified'' paired t-test.
    The CPUE values for the control and BRD nets for each successful 
tow should be computed first and these will be used in the following 
computations. The test statistic to be used is given by:
[GRAPHIC] [TIFF OMITTED] TR04SE97.010

Where:
x is the observed mean CPUE for the control,
y is the observed mean CPUE for the BRD,
s<INF>d0</INF> is the standard deviation of 
d<INF>i</INF>={(1-R<INF>0</INF>)xi-yi} values, n is the number of 
successful tows used in the analysis, and i=1, 2, . . . , n.

    The H<INF>0</INF> will be rejected if t>t<INF>alpha,n-1</INF>,
where t<INF>alpha,n-1</INF> denotes the (1-alpha) 100th percentile 
score in the t distribution with (n-1) degrees of freedom.

    The computation of beta (for various assumed reduction rates, 
R<INF>1</INF>>R<INF>0</INF>) is somewhat involved and requires the 
knowledge of unknown parameters (or at least good estimates) of 
<greek-m><INF>c</INF> and 
<greek-s><SUP>2</SUP><INF><greek-d>0</INF>. Note that 
<greek-s><SUP>2</SUP><INF><greek-d>0</INF> is dependent on the 
R<INF>0</INF> specified (under H<INF>0</INF>) and equals:
    (1-R<INF>0</INF>)<SUP>2</SUP> 
<greek-s><SUP>2</SUP><INF><greek-kh><greek-i></INF>+<greek-s><SUP>2</SUP>
<INF><greek-u><greek-i></INF>-2(1-R<INF>0</INF>) <greek-r> 
<bullet><greek-s><INF><greek-kh><greek-i></INF><bullet><greek-s><INF><greek-u><greek-i></INF>
,

where <greek-r> is the population correlation coefficient between 
x<INF>i</INF> and y<INF>i</INF> values. The computation of beta in 
advance (in the absence of any preliminary data, i.e., without good 
parameter estimates) is almost impossible. More work in this 
direction is still needed. However, it is clear that beta could be 
reduced by increasing alpha or n or both.
    A (1-alpha) 100% two-sided confidence interval on R consists of 
all values of R<INF>0</INF> for which
    H<INF>0</INF>: R=R<INF>0</INF> (versus H<INF>a</INF>: 
R<not-eq>R<INF>0</INF>) cannot be rejected at the level of 
significance of alpha. One-sided confidence intervals on R could 
also be computed appropriately.

    Dated: August 27, 1997.
David L. Evans,
Deputy Assistant Administrator for Fisheries, National Marine Fisheries 
Service.
[FR Doc. 97-23404 Filed 9-3-97; 8:45 am]
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