4 
Fishery Bulletin 99(1 ) 
Figure 2 
Internal otolith morphometric variables that were measured for 
stock identification of haddock on Georges Bank. 
by the area of its enclosing rectangle oriented along the 
length of the section (Media Cybernetics, 1996). 
Data analysis 
Internal otolith morphometries were compared between 
eastern and western Georges Bank haddock for stock 
identification. All variables were first examined for 
assumptions of normality and homoscedasticity and were 
subsequently log e -transformed prior to statistical analysis 
if these assumptions were not satisfied. Following trans- 
formation, all variables conformed to statistical assump- 
tions. Analysis of covariance (ANCOVA) was then used to 
determine the effect of fish length on the magnitude of 
each variable. Those variables found to have significant 
interactions (P<0.05) between sampling region and fish 
length (i.e. samples with unequal slopes) were excluded 
from further statistical analyses. In contrast, those vari- 
ables found to have samples with equal slopes, but that 
significantly correlated with fish length, were corrected for 
fish length by using their respective common within-group 
slope ( 6 ) to standardize the samples. 
Potential confounding sources of variation among sam- 
ples, such as sex, age, and year-class differences, were 
examined and accounted for in the analyses before in- 
terpreting stock differences. Such confounding variables 
need to be examined to ensure interpretations of stock dif- 
ferences are real and not simply the result of sample vari- 
ation (Castonguay et al., 1991; Begg and Brown, 2000). 
Consequently, multivariate analysis of variance (MANO- 
VA) was used to examine differences between the sexes 
in their internal otolith structure, for samples from the 
same region and year class, and of the same age, by using 
the appropriate length-corrected internal otolith morpho- 
metric variables. One-way, fixed effects, unbalanced anal- 
ysis of variance (ANOVA) was then used to examine in- 
dividual variables to interpret any significant differences 
detected by the MANOVAs. Significance levels were cor- 
rected for multiple testing by using the Bonferroni adjust- 
ment factor (Sokal and Rohlf, 1995). The same tests were 
then used to examine the internal otolith structure of dif- 
ferent-age fish (sampled from the same region and year), 
and fish originating from different year classes (same 
region and age). Tukey’s honestly significant difference 
(HSD) tests were used for a posteriori comparisons for 
each significant variable. The same multi- and univari- 
ate tests were then used to examine the internal otolith 
structure of haddock sampled from eastern and western 
Georges Bank. These analyses were used to determine if 
there was any evidence for stock separation of haddock 
across the Bank. 
Principal component (PC) analysis of the length-correct- 
ed internal otolith morphometric variables was conduct- 
ed for samples of the same age and year class to provide 
an unbiased indication of separation between eastern and 
western Georges Bank haddock (i.e. there were no a priori 
assumptions of group membership). ANOVA was used on 
the significant principal components to examine differenc- 
es in the PC scores between the proposed groups. Forward 
stepwise canonical discriminant analysis was then used to 
detect differences in the internal otolith structure of east- 
ern and western Georges Bank haddock samples. The sig- 
nificant (P<0.05) canonical variate (CV) derived by each 
analysis represented the optimal combination of morpho- 
metric variables that provided the best overall discrimina- 
tion between the samples. ANOVA was used to examine 
differences in the CV scores. Jack-knifed cross-validation 
procedures were used to give unbiased estimates of clas- 
sification success (SPSS, Inc., 1997). 
Results 
All the internal otolith morphometric variables, except for 
Al and rectangularity, were log^-transformed prior to sta- 
tistical analysis to correct for nonnormality and inequality 
of variances. ANCOVA indicated a significant correlation 
between fish length and region for otolith width (homoge- 
neity of slopes test, P<0. 0222) (Table 2). Significant region- 
specific differences in the correlation between fish length 
and otolith width (i.e. regional differences in growth rate) 
made it necessary to remove otolith width as an analysis 
