de Silva and Condrey: Patterns in patchy data discerned from Brevoortia patronus bycatch 
201 
200 
150 
100 
(D 
E 
mean: 0.1685 
median: 0.0333 
n = 257 
50 
L. 
0.5 
1.5 2 2.5 
Bycatch percentage 
3.5 
Figure 4 
Distribution of the bycatch percentage in fishing sets sampled during the 1995 gulf menhaden fishing 
season. 
where n high \ ik = the probability of observing a set 
with high bycatch given area i and 
season k; and 
n [ow | ik = the probability of observing a set 
with low bycatch given area i and 
season k. 
This model, in loglinear and logit forms, had a 
G 2 =17.82, with 12 df and a P-value=0.1213. Exami- 
nation of the standardized residuals of the logit form 
revealed that none of the residuals had an absolute 
value greater than 1.45 and thus showed no evidence 
of lack of fit. 
For the logit model, there was a significant inter- 
action between season and area (Wald chi-square 
(X 2 )=14.65, df=6, P=Q.Q232). This interaction is re- 
flected in the plot of probabilities of high (greater 
than 0.033%) bycatch for the area-season combina- 
tions (Fig. 5). 
Contrasts The contrasts of the odds of high bycatch 
between seasons for a given area indicate that the 
hypothesis of spring and summer seasons being the 
same for all four areas could not be rejected. Wald x 2 
Table 3 
Estimated odds ratios and Wald chi-square (y 2 ) values of 
contrasts of observing high bycatch between seasons, given 
a set was made in a certain area. For example, the odds of 
observing high bycatch is 11.761 times greater during the 
spring season than during the fall season for area 11-12. 
* indicates a ratio significantly different from 1. Wald y 2 
values are in parenthesis. For all contrasts, Wald y 2 df = 1. 
Season Area Spring Fall 
Fall 
Summer 
11-12 
11-12 
11.761* 
1.142 
(10.03) 
(0.05) 
0.097* 
(9.25) 
Fall 
Summer 
13-14 
13-14 
4.444 
0.555 
(2.24) 
(0.19) 
0.125 
(2.41) 
Fall 
Summer 
15-16 
15-16 
0.699 
0.414 
(0.48) 
(4.29) 
0.592 
(0.97) 
Fall 
Summer 
17-18 
17-18 
0.312 
0.218 
(2.11) 
(2.47) 
0.899 
(0.02) 
values are presented in Table 3. The contrasts of the 
spring and fall seasons suggest that the only signifi- 
