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Fishery Bulletin 96(2), 1998 
observing a set with bycatch to that of observing a 
set with no bycatch in area 2: 
is 0.33/0.67 - 0.5. 
The odds ratio, 0, is computed as 
Q fl /Q f2 is 0.67/0.5= 1.34. 
Thus, the odds of observing response j 1 (presence of 
bycatch ) is 1.34 times more likely for row i, ( area 1) 
than for row i 9 (area 2). An odds ratio of 1 indicates 
that you are equally likely to observe response 
j ^presence of bycatch) for row i 1 (area 1) and row i 2 
(area 2) and thus indicates independence between 
the rows and columns of the table. 
The logit model has two forms. One form occurs 
where the explanatory variables are continuous and 
is the logistic regression model. The second occurs 
where the explanatory variables are categorical. The 
logistic regression model is analogous to a regres- 
sion model, whereas the second type is analogous to 
an ANOVA model. 
For the previous example, a model with a single 
categorical explanatory factor (area), the logit form 
of the model is 
\og(n jVl /n j2U ) = a + [3 f rea , 
where a = the mean of the logits; and 
pArea _ deviation from the mean for row i. 
(5, describes the effects of the factor on the response. 
For this model the higher /J, becomes, the higher the 
logit in row i, and the higher the value of Kjm The 
constraints on this model are I /3, = 0. In this case 
the right-hand side of the equation resembles the cell- 
means model of a one-way ANOVA. This logit model 
would be equivalent to log ( m yl ) - log ( m lj2 ) = 2Xj Area 
+ 2Xji Bycatch + 2 X i j 1 AreaBycatch in loglinear form. 
Bycatch sampling and data set description 
Bycatch from the gulf menhaden fishery was sampled 
April through October 1995 by two to three onboard 
samplers on a total of twenty-seven week-long trips 
aboard vessels operating from menhaden processing 
plants in the U.S. Gulf of Mexico. To maximize cover- 
age of the Gulf, samplers boarded vessels from ports 
in the western, central, and eastern regions in a given 
week as often as possible. During each sampling trip, 
all sets made by the vessel were alternatively 
sampled, either for releasable bycatch or automati- 
cally retained bycatch. For all sets sampled, the pres- 
ence of dolphins in the vicinity was also noted by the 
observers. In addition, the boat captains visually es- 
timated catch in standard menhaden (1,000 standard 
menhaden [-305 kg]) and recorded the latitude and 
longitude of a set location. The location was used to 
identify in which National Marine Fisheries Service 
(NMFS) statistical zone (Fig. 1) the set was made 
(after Kutkuhn, 1962). 
To collect releasable bycatch data, samplers ob- 
served the purse seine from the time it was brought 
alongside the carrier ship and throughout the pump- 
ing procedure, until the net was emptied and cleaned. 
During this time, the species, number, and fate of 
the releasable bycatch were recorded. The seven cat- 
egories of bycatch fate were as follows: gilled in the 
net (gilled); kept by the crew for consumption (kept); 
released with no apparent harm (released healthy ); 
released seriously injured or dead (released dead); 
released after being bruised or after being kept in 
the set for a long time (released disoriented); collected 
by the crew from the net or deck and put into the 
hold (caught and put in hold); and observed in the 
net but fate unknown (unknown). 
Statistical analysis 
Preliminary analysis For the variables bycatch num- 
ber, bycatch percentage, and estimated catch, we cal- 
culated a series of commonly used statistical descrip- 
tors, namely the mean, standard deviation, 95% con- 
fidence intervals, median, skewness, and kurtosis. In 
addition, we also calculated the winsorized mean and 
its standard deviation. 
We initially attempted to examine spatial and tem- 
poral patterns in the bycatch with a two-way ANOVA 
model. For the analysis, data were classified into sea- 
son (S) consisting of three groups: 1) spring (April 
through June), 2) summer (July through August), and 
3) fall (September through October). Adjacent NMFS 
zones (Fig. 1) were combined to form four area (A) 
groups: 11-12, 13-14, 15-16, and 17-18. 
Bycatch patterns were examined with two response 
variables: 1) bycatch numbers; and 2) bycatch per- 
centage ([bycatch number/total catch] x 100). For each 
of these two response variables, spatial and tempo- 
ral patterns were examined by using the ANOVA 
model with season, area, and their interaction term 
as independent variables. Because we anticipated 
that neither model would satisfy the model assump- 
tions of normality of residuals and homogeneous vari- 
ances, we also examined the models by using the log 
and square-root transformations for both response 
variables. In addition we also used 2 arcsin V (by- 
catch/menhaden catch) suggested by Neter et al. 
(1990) for transformation of proportions. All seven 
