clus.mean {fishmethods}

Estimation of Population Attributes and Effective Sample Size for Fishes Collected Via Cluster Sampling

Description

Calculates mean attribute, variance, effective sample size, and degrees of freedom for samples collected by simple random cluster sampling.

Usage

clus.mean(popchar = NULL, cluster = NULL, clustotal = NULL, rho = NULL,
 nboot = 1000)

Arguments

popchar

vector of population characteristic measurements (e.g., length, weight, etc.). One row represents the measurement for an individual.

cluster

vector of numeric or character codes identifying individual clusters (or hauls).

clustotal

vector of total number of fish caught per cluster.

rho

intracluster correlation coefficient for data. If NULL, degrees of freedom are not calculated.

nboot

number of bootstrap samples for calculation of bootstrap variance. Default = 1000

Details

In fisheries, gears (e.g., trawls, haul seines, gillnets, etc.) are used to collect fishes. Often, estimates of mean population attributes (e.g., mean length) are desired. The samples of individual fish are not random samples, but cluster samples because the "haul" is the primary sampling unit. Correct estimation of mean attributes requires the use of cluster sampling formulae. Estimation of the general mean attribute and usual variance approximation follows Pennington et al. (2002). Variance of the mean is also estimated using the jackknife and bootstrap methods (Pennington and Volstad, 1994; Pennington et al., 2002). In addition, the effective sample size (the number of fish that would need to be sampled randomly to obtained the same precision as the mean estimate from cluster sampling) is also calculated for the three variance estimates. The total number of fish caught in a cluster (clustotal) allows correct computation for one- and two-stage sampling of individuals from each cluster (haul). In addition, if rho is specified, degrees of freedom are calculated by using Hedges (2007) for unequal cluster sizes (p. 166-167).

Value

Matrix table of total number of clusters (n), total number of samples (M), total number of samples measured (m), the mean attribute (R), usual variance approximation (varU), jackknife variance (varJ), bootstrap variance (varB), variance of population attribute (s2x), usual variance effective sample size (meffU), jackknife variance effective sample size, (meffJ), bootstrap variance effective sample size (meffB) and degrees of freedom (df) if applicable.

Author(s)

Gary A. Nelson, Massachusetts Division of Marine Fisheries [e-mail]

References

Hedges,L.V. 2007. Correcting a significance test for clustering. Journal of Educational and Behavioral Statistics. 32: 151-179.

Pennington, M. and J. J. Volstad. 1994. Assessing the effect of intra-haul correlation and variable density on estimates of population characteristics from marine surveys. Biometrics 50: 725-732.

Pennington, M. , L. Burmeister, and V. Hjellvik. 2002. Assessing the precision of frequency distributions estimated from trawl-survey samples. Fish. Bull. 100:74-80.

Examples

data(codcluslen)
temp<-codcluslen[codcluslen$region=="NorthCape" & codcluslen$number>0,]
temp$station<-c(paste(temp$region,"-",temp$tow,sep=""))
total<-aggregate(temp$number,list(temp$station),sum)
names(total)<-c("station","total")
temp<-merge(temp,total,by.x="station",by.y="station")
newdata<-data.frame(NULL)
for(i in 1:as.numeric(length(temp[,1]))){
  for(j in 1:temp$number[i]){
    newdata<-rbind(newdata,temp[i,])
  }
}
clus.mean(popchar=newdata$length,cluster=newdata$station,
         clustotal=newdata$total)