################################# ### How can sensR help us analyzing sensory similarity test data? ################################# library(sensR) discrim(40, 100, pd0=0.25, conf.level=0.90, method="triangle", test="similarity") #Compare with the difference test data analysis: (only the test info changes - NOT CIs) discrim(40, 100, conf.level=0.90, method = "triangle") # SAME data may provide non-significant results for BOTH difference and similarity tests: discrim(40, 100, pd0=0.2, conf.level=0.90, method="triangle", test="similarity") discrim(40, 100, conf.level=0.90, method = "triangle") # SAME data may provide significant results for BOTH difference and similarity tests: discrim(80, 200, pd0=0.25, conf.level=0.90, method="triangle", test="similarity") discrim(80, 200, conf.level=0.90, method = "triangle") # What if similarity is defined as dprime < 0.5: mypd0=pc2pd(psyfun(0.5,method="threeAFC"),Pguess=1/3) #Or the same: mypd0=rescale(d.prime=0.5,method="threeAFC")\$coefficients[1,2] mypd0 discrim(40,100,pd0=mypd0,conf.level=0.90,method="threeAFC", test="similarity") ################################# ### How can sensR help us planning sensory similarity tests? ################################# # Assuming true pd to be zero: discrimPwr(pdA=0,pd0=0.25, sample.size=100, alpha=0.05,pGuess =1/3,test="similarity") # Assuming true pd to be 0.2: discrimPwr(pdA=0.2,pd0=0.25, sample.size=100, alpha=0.05,pGuess =1/3,test="similarity") # The critical value for the similarity test can be found by findcr: cr=findcr(sample.size=100, alpha = .05, p0 = 1/3, pd0 = 0.25, test = c("similarity")) cr discrim(41, 100, pd0=0.25, conf.level=0.90, method="triangle", test="similarity") discrim(42, 100, pd0=0.25, conf.level=0.90, method="triangle", test="similarity") # The power can be now explained as follows: # First for pdA=0: pbinom(cr,100,1/3) # Nextfor pdA=0.2: pdA=0.2 pcA=pd2pc(pdA,Pguess=1/3) pcA pbinom(cr,100,pcA) # Power of similarity tests when similarity is defined on d.prime scale: d.primePwr(d.primeA=0,d.prime0=0.5, sample.size=100, alpha=0.05, method="triangle", test="similarity") # Sample size computations to meet required power: # First on pd-scale with pd0=0.25, best case: discrimSS(pdA=0,pd0=0.25, target.power=0.9, alpha=0.05,pGuess =1/3, test="similarity") # Still on pd-scale with pd0=0.25, "bad" case: discrimSS(pdA=.2,pd0=0.25 , target.power=0.9, alpha=0.05,pGuess=1/3, test="similarity") # Then on d.prime-scale with d.prime0=0.5, best case: d.primeSS(d.primeA=0, d.prime0=0.5, target.power=0.9, alpha=0.05,method="triangle", test="similarity") # Then on d.prime-scale with d.prime0=0.5, "bad" case: d.primeSS(d.primeA=0.4, d.prime0=0.5, target.power=0.9, alpha=0.05,method="triangle", test="similarity") ################################# ### How can sensR help us analyze replicated sensory difference tests? ################################# discrim(11,12,method="triangle") discrim(70,180,method="triangle") # First we look at possible outcomes of replicated triangles: # First a case where individuals are "clones" - they are NOT really different, # AND there is NO product difference: rs windows() par(mfrow=c(1,1)) rs=discrimSim(20, replicates = 12, d.prime = 0,method = "triangle",sd.indiv=0) barplot(rs[order(rs)],col="blue",ylim=c(0,12),main="dprime=0, sd.indiv=0", names.arg=1:20,cex.names=0.8) abline(h=mean(rs)) # Next a case where individuals are "clones" - they are NOT really different, # but there IS a product difference, d.prime=2: rs=discrimSim(20, replicates = 12, d.prime = 2,method = "triangle",sd.indiv=0) barplot(rs[order(rs)],col="blue",ylim=c(0,12),main="dprime=2, sd.indiv=0", names.arg=1:20,cex.names=0.8) abline(h=mean(rs)) # Finally a case where individuals are really different, (sd.indiv=2) # AND there IS a product difference, d.prime=2: rs=discrimSim(20, replicates = 12, d.prime = 2,method = "triangle",sd.indiv=2) barplot(rs[order(rs)],col="blue",ylim=c(0,12),main="dprime=2, sd.indiv=2", names.arg=1:20,cex.names=0.8) abline(h=mean(rs)) # Analysis for the Table 7.4 data from the book: x <- c(2, 2, 3, 3, 4, 4, 4, 4, 4, 4, 4, 5, 6, 10, 11) X2 <- cbind(x, 12) X2 summary(betabin(X2,method="triangle")) # Naive analysis: sum(x) discrim(70,180,method="triangle") # Exercise 5 # Set the situation: (make your own choices) myN=15 #Number of individuals myK=10 #Number of replications myd.prime=1 # Level of product difference mysd.indiv=1 # individual heterogeneity # Simulate and plot some data: rs=discrimSim(myN, replicates = myK, d.prime = myd.prime,method = "triangle",sd.indiv=mysd.indiv) barplot(rs[order(rs)],col="blue",ylim=c(0,myK), names.arg=1:myN,cex.names=0.8) abline(h=mean(rs)) # Put the simulated data on the form needed for the betabin analysis: X=matrix(c(rs,rep(myK,myN)),ncol=2) X # Do the betabin analysis: summary(betabin(X,method="triangle"))