clus.t.test {fishmethods}

Correcting a Two-Sample Test for Clustering

Description

Calculates Hedges (2007) t-statistic adjustment and degrees of freedom for a t-test assuming unequal variances and clustered data with clusters of unequal size.

Usage

clus.t.test(popchar = NULL, cluster = NULL, group = NULL,
      rho = NULL, alpha = 0.05, alternative = c("two.sided"))

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).

group

vector of group membership identifiers.

rho

common intra-cluster correlation for groups.

alpha

alpha level used to calculate t critical value. Default=0.05

alternative

a character string specifying the alternative hypothesis, must be one of "two.sided" (default), "greater" or "less".

Details

A two-sample t-test with unequal variances (Sokal and Rohlf, 1995) is performed on clustered data. The t-statistic and degrees of freedom are corrected for clustering according to Hedges (2007).

Value

List with null hypothesis of test and matrix table with mean of each group, rho, ntilda (Equation 14 of Hedges 2007), nu (Equation 15), degrees of freedom (Equation 16), uncorrected t-statistic, cu (Equation 18), the t-statistic adjusted for clustering, critical t value for degrees of freedom and alpha, and probability of significance.

Author(s)

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

References

Sokal,R.R.and F.J.Rohlf. 1995. Biometry, 3rd Edition. W.H. Freeman and Company, New York, NY. 887 p.

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

Examples

   data(codcluslen)
   temp<-codcluslen[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$number[i]){
     newdata<-rbind(newdata,temp[i,])
    }
  }
 newdata<-newdata[,-c(5)]
 clus.t.test(popchar=newdata$length,cluster=newdata$station,
            group=newdata$region,rho=0.72,
            alpha=0.05,alternative="two.sided")