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Fishery Bulletin 103(3) 



Scheaffer et al., 1996). If poststratification is applied to 

 data from a multispecies survey, 1) abundance data for 

 each species can be poststratified with different habitat 

 variables or 2) abundance data for every species can 

 be poststratified with the same variables, but different 

 stratum boundaries can be used for each species. 



Many large-scale multispecies groundfish surveys are 

 conducted by using a stratified random sampling design 

 (Azarovitz, 1981; Halliday and Koeller, 1981; Pitt et 

 al., 1981; Martin 1 ; Weinberg et al. 2 ). Depth, distance 

 from or along shore, latitude, distance along depth 

 contours, or broad geographic features (such as bays, 

 capes, banks, gullies, and slopes) are used as stratum 

 boundaries in trawl surveys because they have been 

 shown to be related to species distributions. These fac- 

 tors are fixed spatially, allowing samples to be allocated 

 to strata prior to sampling. The same boundaries are 

 used for all species, and boundaries generally remain 

 the same over years. 



When conducting a multispecies survey with a strati- 

 fied random sampling design, optimal stratification for 

 one species may not be optimal for others (Koeller, 1981; 

 NRC, 2000). Because the placement of strata boundar- 

 ies is critical for precise stratified estimates (Cochran, 

 1977), use of a stratified sampling design for a multispe- 

 cies survey may result in only small gains in precision 

 for some or all species. Poststratification is possible for 

 data that have been collected under a stratified design. 

 It can be used to stratify data more finely for individual 

 species. Under stratified random sampling, a simple 

 random sample is taken in each stratum. Thus, data 

 within each stratum can be poststratified separately 

 with additional variables and the abundance estimates 

 from each of the strata can be summed. The resultant 

 estimator is unbiased and likely will be more precise 

 than that of the original stratified design if sample 

 sizes in poststratified strata are large enough. 



Often, researchers need to estimate abundance from 

 data sets that were not recorded under a probability 

 sampling design (a design in which randomness is built 

 into the survey design, such as simple random sampling 

 or stratified random sampling). Finances and logistics, 

 for example, may make it impossible to collect data 

 under a probability sampling design, researchers may 

 want to estimate species abundance from commercial 

 fisheries or other nonsurvey data, or previously collected 

 data sets that were not recorded under a probability 



1 Martin, M. H. 1997. Data report: 1996 Gulf of Alaska 

 bottom trawl survey. NOAA Tech. Memo. NMFS-AFSC- 

 82, 235 p. National Technical Information Service, U.S. 

 Department of Commerce, 5285 Port Royal Road, Springfield, 

 Virginia 22161. 



2 Weinberg, K. L., M. E. Wilkins, R. R. Lauth, and P. A. Ray- 

 more jr. 1994. The 1989 Pacific west coast bottom trawl 

 survey of groundfish resources: Estimates of distribution, 

 abundance, and length and age composition. NOAA Tech. 

 Memo. NMFS-AFSC-33, 168 p., plus appendices. National 

 Technical Information Service, U.S. Department of Com- 

 merce, 5285 Port Royal Road, Springfield, Virginia 22161. 



sampling design may be used for retrospective studies. 

 In this article, we refer to data collection without a 

 probability sampling design as "haphazard sampling." 

 The use of haphazardly collected data for estimating 

 abundance is undesirable because they cannot be eval- 

 uated by the theorems of probability theory (Krebs, 

 1989). Although undesirable, it is often necessary to 

 analyze haphazardly collected data and effective meth- 

 ods are needed to do so. 



Poststratification can be applied to data that were 

 not collected with a probability sampling design. When 

 poststratification is applied to data not collected under 

 a probability sampling design, the poststratification es- 

 timator, a design-based estimator, may be biased. When 

 analyzing such data, it is important both to maximize 

 the precision and to minimize the bias. Poststratifica- 

 tion has been applied to nonprobability samples in other 

 studies to increase the precision (Hall and Boyer, 1988) 

 and decrease the bias of estimators (Buckland and An- 

 ganuzzi, 1988; Hall and Boyer, 1988; Anganuzzi and 

 Buckland, 1989). 



Poststratification can be useful, but has some draw- 

 backs. With poststratification, sample sizes within 

 strata are random variables — which are an additional 

 source of variability over that of a stratified sampling 

 variance estimator (Thompson, 1992; Scheaffer et al., 

 1996). The variance of a poststratified estimator can 

 be estimated by using standard stratified sampling 

 variance equations and by incorporating an additional 

 approximate term to account for the random sample 

 sizes present with poststratification (Scheaffer et al., 

 1996). Alternatively, the variance of a poststratified 

 estimator can be estimated by conditioning on samples 

 sizes and by applying the standard stratified sampling 

 variance equation (Thompson, 1992). For accurate post- 

 stratification estimates, the proportion of total possible 

 samples in each stratum (for this study the propor- 

 tion of the total survey area included in each stratum) 

 must be known or approximated closely enough that 

 the error in the approximation is negligible (Cochran, 

 1977). Error in estimates of stratum sizes causes bias 

 in poststratified estimates of abundance. Because error 

 in the estimation of stratum size is unaccounted for in 

 the estimated variance of poststratified estimates, the 

 estimated variances may be underestimates of the true 

 error (Cochran, 1977). 



This study had two goals. The first goal was to evalu- 

 ate the benefits and drawbacks of using poststratifica- 

 tion to incorporate habitat and fish-density information 

 into estimates of abundance from multispecies survey 

 data that were not collected under a probability sam- 

 pling design. To achieve this goal, this study compared 

 three estimates of total abundance and variance (un- 

 stratified, poststratified by habitat, poststratified by 

 habitat and estimates of fish density in neighboring 

 years) for each of four species. The comparison was 

 made to determine whether poststratification of hap- 

 hazardly sampled data with habitat and fish-density 

 information increases the precision and helps account 

 for possible bias in abundance estimates. 



