###The following code outlines methods to calculate Hedges effect sizes and associated confidence intervals.
###Methods follow:
#Gurevitch, J., Morrison, J.A. & Hedges, L.V. (2000) The interaction between competition and predation: A meta-analysis of field experiments. American Naturalist, 155, 435-453.
#Hedges, L.V. & Olkin, I. (1985) Statistical methods for meta-analysis. Academic Press, Boston, Massachuessets, USA.
#Morris, W.F., Hufbauer, R.A., Agrawal, A.A., Bever, J.D., Borowicz, V.A., Gilbert, G.S., Maron, J.L., Mitchell, C.E., Parker, I.M., Power, A.G., Torchin, M.E. & Vazquez, D.P. (2007) Direct and interactive effects of enemies and mutualists on plant performance: A meta-analysis. Ecology, 88, 1021-1029.

###Basic parameters of the study required for four treatments (Control, A, B, A*B): number of replicates, mean, standard deviation

####Input parameters####

##Number of samples##
#No. replicates in Control
nc<-12
#No. replicates Treatment A
na<-12
#No. replicates Treatment B
nb<-12
#No. replicates Treatment A*B
nab<-12

##Means##
#Mean in Control
mc<-0
#Mean in Treatment A
ma<-0.3
#Mean in Treatment B
mb<-.13
#Mean in Treatment A*B
mab<-0.14


##Standard deviations##
#stdev in control
sc<-0.22
#stdev in treat A
sa<-0.51
#stdev in treat B
sb<-.52
#stdev in treat A*B
sab<-.52


###Calculate pooled standard deviations###

#calculate pooled standard deviation of Treatment A and Control
pooledAC<-sqrt(((na-1)*sa^2+(nc-1)*sc^2)/(na+nc-2))

#calculate pooled standard deviation of Treatment B and Control
pooledBC<-sqrt(((nb-1)*sb^2+(nc-1)*sc^2)/(nb+nc-2))

#calculate pooled standard deviation across all four groups
pooledAll<-sqrt(((na-1)*(sa^2)+((nb-1)*(sb^2))+((nc-1)*(sc^2))+((nab-1)*(sab^2)))/(na+nb+nc+nab-4))


###Calculate J(m) small-sample bias correction###

#for effect A
Jma<-1-(3)/((4*(na+nc-2))-1)

#for effect B
Jmb<-1-(3)/((4*(nb+nc-2))-1)

#for interaction
Jmi<-1-(3)/((4*(nc+na+nb+nab-4))-1)


###Calculate individual effects and their sampling variances###

#Calculate individual effect of A
da<-((ma-mc)/pooledAll)*Jma

#Calculate individual effect of B
db<-((mb-mc)/pooledAll)*Jmb

#Calculate sampling variance of individual effect A
sv_a<-((1/na)+(1/nc)+((da^2)/(2*(na+nc))))

#Calculate sampling variance of individual effect A
sv_b<-((1/nb)+(1/nc)+((db^2)/(2*(nb+nc))))

###Calculate confidence intervals for individual effects of A and B
CI_a_low<-da-(1.96*sqrt(sv_a))
CI_a_high<-da+(1.96*sqrt(sv_a))

CI_b_low<-db-(1.96*sqrt(sv_b))
CI_b_high<-db+(1.96*sqrt(sv_b))


###Calculate main effects of A and B

#Main effect of A
dA<-(((ma+mab)-(mb+mc))*Jmi/(2*pooledAll))

#Main effect of B
dB<-(((mb+mab)-(ma+mc))*Jmi/(2*pooledAll))
  
###Calculate interaction effect size and sampling variance

#Interaction effect
dI<-(((mab-mb)-(ma-mc))*Jmi/(pooledAll))

#Interaction variance 
vI<-((1/na)+(1/nb)+(1/nc)+(1/nab)+((dI^2)/(2*(na+nb+nc+nab))))

###Calculate interaction confidence interval
ICI_low<-dI-(1.96*(sqrt(vI)))
ICI_high<-dI+(1.96*(sqrt(vI)))