Harvey et al.: Improving the statistical power of length estimates of reef fish 
75 
was specified as a random factor. The silhouette vari- 
ance component was used as an estimate of <j\. Note 
that for the stereo-video estimates, we took a 2 d . This is 
because there should be no variation in the accuracy 
and precision of measurement made with a stereo-vid- 
eo system operated by different divers over different 
dives. Operators either swim the system along a tran- 
sect or locate it in one area to record point counts. The 
operator has no control over the configuration of the 
camera system and cannot change any of the param- 
eters; both these features of the system would preserve 
measurement accuracy and precision. Over the dura- 
tion of one dive, and between several dives, the small 
variations in calibration stability that occur have mini- 
mal effect on the accuracy and precision of measure- 
ments (Harvey and Shortis, 1998). Harvey et al. (2000) 
have shown that very small variations in measure- 
ment accuracy (mean error -0.25 cm) may occur de- 
pending on the level of experience of the operators with 
the software used for making measurements from the 
images in the laboratory. To minimize this error, mea- 
surements where made where the orientation of a fish 
was less than 50 degrees perpendicular to the camera 
rig (Harvey and Shortis, 1996). 
Results 
The estimates of the variance components used in the pow- 
er analysis are shown in Tables 1 and 2, together with their 
90% confidence limits. Figure 2 shows the predicted power 
of visual estimates made by novice and experienced sci- 
entific divers and the predicted power of estimates made 
by a stereo-video system to detect a 15% change in the 
mean length of populations of blue cod, snapper, and red 
cod based on recording 30 fish per sample. Fifteen percent 
has been selected as an effect size because it represents a 
5-cm change in the mean length of the population of blue 
cod used for our study. The results show that for each of the 
three species, the experienced scientific divers had greater 
power to detect changes than did novice scientific divers. 
However, for blue cod and snapper (Fig. 2), the stereo-video 
system had much greater power to detect changes in the 
mean length than either novice or experienced scientific 
divers. For example, we could achieve 90% power to detect a 
15% change in the mean length of blue cod by recording 10 
samples per site with the stereo-video system, with 27 sam- 
ples per site for experienced scientific divers, and with 28 
samples per site for novice divers. Similar conclusions apply 
to snapper with 11, 23, and 29 samples being required, 
respectively, under the same conditions. The advantage of 
the stereo-video system was not as good for red cod (30, 43, 
and 50 samples, respectively) as a result of the greater vari- 
ability in their true mean length between locations than 
that recorded for the other two species (Fig. 2). 
Influence of effect size 
Around the southern coastal waters of New Zealand, blue 
cod may reach a maximum size of 50 cm, averaging 20-30 
165.0 167.0 169.0 171.0 173.0 175.0 177.0 179. 0E 
Figure t 
Map of the distribution of sites where fish were collected. The 
mean lengths shown for each site are in cm. 
Table 1 
Estimates of the variance components a\ (between dive 
locations) and a\ (within dive locations) of the natural log- 
arithm of true fish length, for each of three species (90% 
confidence limits shown in parentheses). 
Between 
Within-dive 
Species 
dive locations 
locations 
Red cod 
0.025 (0.015,0.060) 
0.076 (0.068,0.084) 
Snapper 
0.008 (0.005,0.014) 
0.027 (0.025,0.029) 
Blue cod 
0.008 (0.004,0.060) 
0.019 (0.016,0.022) 
cm. (Ayling and Cox, 1982). The sample of blue cod on 
which our power analysis was based had a mean length 
of 33 cm. A 15% change in mean length would represent a 
change of 5 cm. Figure 3 shows how the advantages of ste- 
reo-video measurements over diver estimates diminish as 
the size of the change to be detected increases. For exam- 
ple, to detect a 30% change in the mean length of blue cod 
with 90% power 4 samples were needed per site with the 
stereo-video system, 9 samples were needed with experi- 
enced scientific divers, and nine samples with novice sci- 
entific divers. A 50% change would be detected with 90% 
power with three samples per site with the stereo-video 
system, five samples with experienced scientific divers, 
and five samples with novice scientific divers. 
The influence of numbers of fish per sample 
As the numbers of fish recorded per sample decreases 
(for example from 30 to 10 to 1), the number of samples 
that need to be recorded to maintain an equivalent level 
of power increases. For example, to detect an effect size 
