Jagielo et al.: Demersal groundflsh densities in trawlable and untrawlable habitats off Washington 



549 



Fish were enumerated by identifying and counting only 

 those fish observed in the lower portion of the video moni- 

 tor screen (counting area), below the imaginary line con- 

 necting the laser spots. Lighting and visibility was greatest 

 in this zone, and we assumed that the probability of observ- 

 ing and counting fish in this portion of the video image was 

 1009f (i.e. g=l). Afish was counted if any portion of the fish 

 was visible in the counting area. The distance obsei-ved be- 

 tween the two laser spots was used as a reference to classify 

 fish into two size categories; large (>20 cm) and small (<20 

 cm). Fish were identified to the lowest taxonomic level pos- 

 sible. We recognized that fish detection and identification 

 were subject to observer error The variability describing 

 that error was obtained by conducting a repeat counting 

 of a sample of transects by the same observer. Additional 

 validation checks were made between multiple observers. 



where Zj^ = the percentile of the unit normal which gives 

 power; 

 Zj^ = the percentile of the unit normal for the 

 significance criterion; for a two-tailed test, 

 a = a^2/2; 

 d = the standardized effect size index for the 

 two-tailed <-test calculated as 



<i = ^ ^. (2) 



where «;, and m^^ - the true densities in trawlable and 

 untrawlable habitat, respectively; 

 and 

 s^ = the true pooled variance of the sub- 

 mersible survey density estimator. 



Analytical methods 



Fish density estimates (number/10^ m^) were computed 

 by dividing the total number of fish counted by the total 

 estimated area-swept at each sample-unit site. Statistical 

 comparisons of fish density estimates between the traw- 

 lable and untrawlable habitat types were limited to the 

 level of classification (e.g. species or species group) where 

 identifications were considered to be reliable. Estimates of 

 the sample variance of fish density for the trawlable and 

 untrawlable habitats (s,^ and sj^, respectively) were esti- 

 mated as the sample variance of the fish density estimates 

 among sites within each habitat type. 



We used a power analysis for detecting differences in 

 fish density between habitat types to generate sample 

 size requirements to describe the sampling power of the 

 submersible survey. The greater the sampling power, the 

 fewer samples needed. Statistical power (i.e. the probability 

 of correctly rejecting a false null hjrpothesis) is inversely 

 related to the significance criterion (a) and is positively cor- 

 related with sample size and effect size (Peterman, 1990). 

 The significance criterion is the rate of rejecting a true null 

 hypothesis (the probability of type-I error) and was fixed at 

 0.05 for our analysis. Effect size can be thought of as the 

 degree to which a phenomenon exists (Cohen, 1988). In our 

 study, the effect size was the hypothesized true difference in 

 fish densities between trawlable and untrawlable habitats. 

 Given a significance level and effect size, power is a function 

 of sample size. Because the effect size is the quantity being 

 tested, it is unknown. Therefore a power analysis is a theo- 

 retical "what if exercise, which asks the question: "If the 

 effect is this big, would the test be likely to detect it with this 

 sample size?" Although the choice of effect size values used 

 for a power analysis are arbitrary, they should be set at some 

 meaningful threshold level, such that if the true effect is less 

 than this threshold, it would not be important to detect it. 



In our power analysis we used the approximation 



(/()i-l)V2;j 



2(H-l)-i-1.21(Z,_„-1.06) 

 (Dixon and Massey, 1957; Cohen, 1988), 



(1) 



By design, our study drew independent samples of equal 

 size from each of the two habitat types, and s^ ={s'^i+s'^J. 



The power approximation procedure was convenient to 

 use, in lieu of an exact method, because it was dependent 

 only on the effect size-index (d) and sample size. Note from 

 Equation 2 that d is unitless, so that statistical power and 

 sample size could easily be compared across a range of spe- 

 cies groups, where the absolute density differences between 

 trawlable and untrawlable habitats can vary considerably 

 (Cohen, 1988). 



For the analysis, we derived a standardized effect size- 

 index for the density comparison (J^). The derivation was 

 based on the relationship between density, abundance, and 

 an effect size-threshold selected for abundance (Appendix 

 II). The effect size-threshold for the abundance estimator 

 was arbitrarily chosen to be equal to its standard error 

 under the assumption that a lesser effect size would be 

 difficult to detect. Under this assumption, the standardized 

 effect size index is given by 



d,= 



— SD(D,)ls^ 



(3) 



where A^ = the area of untrawlable habitat; 

 A = the total area; 

 SD(Di) = the standard deviation of the trawl survey 

 abundance estimator; and 

 s = the pooled standard deviation of the submers- 

 ible survey density estimates. 



The standardized effect size index (di,) depends on 1) the 

 proportion of untrawlable habitat in the total area (A^IA), 

 and 2) the variability in the trawl survey density estimator 

 in relation to the variability in the submersible survey den- 

 sity estimator (SD{ D,)ls ) (Eq. 3). One can see that as A„ I A 

 increases, d^ decreases; conversely, as SD(D^)ls increases, 

 d^ increases. 



The relationship between the standard deviations (SD 

 ( DgVs ) and <i^ creates an apparent paradox. Greater uncer- 

 tainty in the trawl survey estimator {SD{ D^)) in relation to 

 the submersible survey estimator (s ) causes cf^ to increase, 

 and thus the power of the submersible survey. Because 



