R+script+for+sensory+analysis

Sample.A <- c(5,7,9,8,8,8,5,8,6,6,8,8,8,7,7,6,5,8,8,8,8,9,6,7,7,7,7,8,3,6,6,9,6,7,6,7,8,7,6,7,7,7,6,6,6,8,8,7,6,6,7) Sample.B <- c(5,8,8,9,8,8,8,7,6,8,8,8,8,8,7,6,7,6,7,9,7,7,8,8,8,6,7,8,6,8,5,9,6,8,8,7,8,6,5,7,7,6,6,6,6,7,7,7,7,7,6) Sample.C <- c(6,5,8,9,8,7,5,7,7,8,8,8,8,6,8,4,5,9,7,8,8,2,2,9,8,7,8,8,7,7,7,9,8,5,6,6,8,6,7,7,8,6,7,6,8,6,7,6,7,6,8) Sample.D <- c(6,6,7,8,8,7,8,6,8,6,8,9,8,9,7,7,7,7,8,8,6,3,8,8,8,7,7,8,5,5,8,8,8,8,7,7,8,6,8,7,7,7,7,8,6,7,7,7,7,8,7) Sample.E <- c(5,6,8,7,8,8,4,7,8,8,7,8,8,8,6,6,3,7,6,7,5,2,7,8,8,6,7,8,6,8,8,9,3,4,5,5,8,6,9,6,9,6,6,7,8,7,7,8,7,7,7) Sample.F <- c(6,6,7,8,8,8,6,9,7,8,7,9,8,8,8,7,3,8,8,7,8,2,8,8,8,5,7,8,5,7,8,7,7,8,6,6,8,5,7,6,8,8,7,6,7,7,7,6,6,6,7) Sample.G <- c(6,7,9,9,7,6,6,5,8,7,8,9,7,8,7,6,4,8,6,7,8,6,9,8,8,6,7,8,5,7,8,7,6,6,5,5,8,6,7,6,7,5,6,7,7,7,8,5,9,8,8) Sample.H <- c(8,7,9,9,7,8,4,8,8,9,7,9,6,8,8,7,5,8,7,7,7,7,9,8,8,7,7,8,3,8,7,6,5,7,4,6,7,5,7,6,8,6,6,7,9,7,7,7,8,7,8) > mean (Sample.A) [1] 6.941176 > mean (Sample.B) [1] 7.117647 > mean (Sample.C) [1] 6.882353 > mean (Sample.D) [1] 7.17647 > mean (Sample.E) [1] 6.705882 > mean (Sample.F) [1] 6.960784 > mean (Sample.G) [1] 6.921569 > mean (Sample.H) [1] 7.078431 > > Assessors <- factor(rep(c(1:51),times=8)) Samples <- factor(c(rep(c("0"),times=51),rep(c("1"),times=51),rep(c("2"),times=51),rep(c("3"),times=51),rep(c("4"),times=51),rep(c("5"),times=51),rep(c("6"),times=51),rep(c("7"),times=51))) Creaminess <- c(5,7,9,8,8,8,5,8,6,6,8,8,8,7,7,6,5,8,8,8,8,9,6,7,7,7,7,8,3,6,6,9,6,7,6,7,8,7,6,7,7,7,6,6,6,8,8,7,6,6,7,5,8,8,9,8,8,8,7,6,8,8,8,8,8,7,6,7,6,7,9,7,7,8,8,8,6,7,8,6,8,5,9,6,8,8,7,8,6,5,7,7,6,6,6,6,7,7,7,7,7,6,6,5,8,9,8,7,5,7,7,8,8,8,8,6,8,4,5,9,7,8,8,2,2,9,8,7,8,8,7,7,7,9,8,5,6,6,8,6,7,7,8,6,7,6,8,6,7,6,7,6,8,6,6,7,8,8,7,8,6,8,6,8,9,8,9,7,7,7,7,8,8,6,3,8,8,8,7,7,8,5,5,8,8,8,8,7,7,8,6,8,7,7,7,7,8,6,7,7,7,7,8,7,5,6,8,7,8,8,4,7,8,8,7,8,8,8,6,6,3,7,6,7,5,2,7,8,8,6,7,8,6,8,8,9,3,4,5,5,8,6,9,6,9,6,6,7,8,7,7,8,7,7,7,6,6,7,8,8,8,6,9,7,8,7,9,8,8,8,7,3,8,8,7,8,2,8,8,8,5,7,8,5,7,8,7,7,8,6,6,8,5,7,6,8,8,7,6,7,7,7,6,6,6,7,6,7,9,9,7,6,6,5,8,7,8,9,7,8,7,6,4,8,6,7,8,6,9,8,8,6,7,8,5,7,8,7,6,6,5,5,8,6,7,6,7,5,6,7,7,7,8,5,9,8,8,8,7,9,9,7,8,4,8,8,9,7,9,6,8,8,7,5,8,7,7,7,7,9,8,8,7,7,8,3,8,7,6,5,7,4,6,7,5,7,6,8,6,6,7,9,7,7,7,8,7,8) dfc <- data.frame(Samples,Assessors,Creaminess) > library (asbio) Loading required package: plotrix Loading required package: vegan This is vegan 1.17-8 Loading required package: MASS tukey.add.test(dfc$Creaminess,dfc$Samples,dfc$Assessors)
 * 1) CREAMINESS

Tukey's one df test for additivity data: dfc$Samples and dfc$Assessors on dfc$Creaminess F = 13.8805, num.df = 1, denom.df = 349, p-value = 0.0002271 creaminess <-matrix(c(5,7,9,8,8,8,5,8,6,6,8,8,8,7,7,6,5,8,8,8,8,9,6,7,7,7,7,8,3,6,6,9,6,7,6,7,8,7,6,7,7,7,6,6,6,8,8,7,6,6,7,5,8,8,9,8,8,8,7,6,8,8,8,8,8,7,6,7,6,7,9,7,7,8,8,8,6,7,8,6,8,5,9,6,8,8,7,8,6,5,7,7,6,6,6,6,7,7,7,7,7,6,6,5,8,9,8,7,5,7,7,8,8,8,8,6,8,4,5,9,7,8,8,2,2,9,8,7,8,8,7,7,7,9,8,5,6,6,8,6,7,7,8,6,7,6,8,6,7,6,7,6,8,6,6,7,8,8,7,8,6,8,6,8,9,8,9,7,7,7,7,8,8,6,3,8,8,8,7,7,8,5,5,8,8,8,8,7,7,8,6,8,7,7,7,7,8,6,7,7,7,7,8,7,5,6,8,7,8,8,4,7,8,8,7,8,8,8,6,6,3,7,6,7,5,2,7,8,8,6,7,8,6,8,8,9,3,4,5,5,8,6,9,6,9,6,6,7,8,7,7,8,7,7,7,6,6,7,8,8,8,6,9,7,8,7,9,8,8,8,7,3,8,8,7,8,2,8,8,8,5,7,8,5,7,8,7,7,8,6,6,8,5,7,6,8,8,7,6,7,7,7,6,6,6,7,6,7,9,9,7,6,6,5,8,7,8,9,7,8,7,6,4,8,6,7,8,6,9,8,8,6,7,8,5,7,8,7,6,6,5,5,8,6,7,6,7,5,6,7,7,7,8,5,9,8,8,8,7,9,9,7,8,4,8,8,9,7,9,6,8,8,7,5,8,7,7,7,7,9,8,8,7,7,8,3,8,7,6,5,7,4,6,7,5,7,6,8,6,6,7,9,7,7,7,8,7,8),nrow=51,byrow=FALSE, dimnames=list(1:51,c("A","B","C","D","E","F","G","H"))) result <- friedman.test(creaminess) > Friedman rank sum test data: creaminess Friedman chi-squared = 7.2871, df = 7, p-value = 0.3996 sample.A <- c(4,7,9,9,7,4,8,8,6,7,9,8,8,7,4,6,8,8,6,8,3,6,7,8,6,8,8,3,7,8,9,7,9,6,7,7,6,6,7,8,6,6,7,6,7,7,6,7,7,8) sample.B <- c(4,7,8,8,7,4,8,5,7,3,8,8,8,8,7,7,7,7,8,7,7,8,8,7,6,8,8,7,7,6,9,5,8,7,7,8,6,7,8,8,6,6,6,7,7,7,7,7,8,6) sample.C <- c(5,7,8,8,7,4,5,7,7,8,8,8,7,8,6,6,8,8,7,7,2,4,8,8,7,8,8,4,7,6,8,8,8,5,7,8,7,8,6,8,6,7,7,9,7,6,7,8,6,7) sample.D <- c(4,5,7,8,7,3,7,6,7,6,9,8,8,7,6,7,7,7,6,7,4,7,8,7,7,6,8,6,5,8,8,7,9,5,7,7,7,7,6,8,8,6,7,6,6,8,7,6,8,7) sample.E <- c(4,6,8,7,7,8,4,7,8,4,8,8,8,7,7,4,7,6,4,6,2,9,7,7,5,7,8,4,8,6,8,1,5,6,7,7,7,6,6,8,6,6,7,9,7,7,8,8,7,7) sample.F <- c(6,8,7,8,7,8,5,9,6,8,9,8,9,9,5,4,9,8,4,7,6,8,8,8,6,7,8,3,8,8,7,6,6,6,7,7,6,7,7,6,8,7,6,8,8,8,5,6,7,8) sample.G <- c(7,7,9,9,8,6,6,5,8,8,9,8,9,7,6,4,7,7,4,7,6,8,8,8,5,8,8,4,7,8,7,7,7,6,7,8,6,6,7,6,7,6,7,7,6,9,5,8,8,7) sample.H <- c(6,8,9,9,7,8,5,8,8,4,9,6,8,8,6,6,9,7,7,6,7,8,8,8,7,7,8,3,7,8,6,4,8,5,6,8,5,7,7,8,6,5,8,9,8,8,7,9,9,8) > mean (sample.A) [1] 6.88 > mean (sample.B) [1] 6.96 > mean (sample.C) [1] 6.88 > mean (sample.D) [1] 6.76 > mean (sample.E) [1] 6.48 > mean (sample.F) [1] 7 > mean (sample.G) [1] 6.96 > mean (sample.H) [1] 7.12 > Assessors <- factor(rep(c(1:50),times=8)) Samples <- factor(c(rep(c("0"),times=50),rep(c("1"),times=50),rep(c("2"),times=50),rep(c("3"),times=50),rep(c("4"),times=50),rep(c("5"),times=50),rep(c("6"),times=50),rep(c("7"),times=50))) Softness <- c(4,7,9,9,7,4,8,8,6,7,9,8,8,7,4,6,8,8,6,8,3,6,7,8,6,8,8,3,7,8,9,7,9,6,7,7,6,6,7,8,6,6,7,6,7,7,6,7,7,8,4,7,8,8,7,4,8,5,7,3,8,8,8,8,7,7,7,7,8,7,7,8,8,7,6,8,8,7,7,6,9,5,8,7,7,8,6,7,8,8,6,6,6,7,7,7,7,7,8,6,5,7,8,8,7,4,5,7,7,8,8,8,7,8,6,6,8,8,7,7,2,4,8,8,7,8,8,4,7,6,8,8,8,5,7,8,7,8,6,8,6,7,7,9,7,6,7,8,6,7,4,5,7,8,7,3,7,6,7,6,9,8,8,7,6,7,7,7,6,7,4,7,8,7,7,6,8,6,5,8,8,7,9,5,7,7,7,7,6,8,8,6,7,6,6,8,7,6,8,7,4,6,8,7,7,8,4,7,8,4,8,8,8,7,7,4,7,6,4,6,2,9,7,7,5,7,8,4,8,6,8,1,5,6,7,7,7,6,6,8,6,6,7,9,7,7,8,8,7,7,6,8,7,8,7,8,5,9,6,8,9,8,9,9,5,4,9,8,4,7,6,8,8,8,6,7,8,3,8,8,7,6,6,6,7,7,6,7,7,6,8,7,6,8,8,8,5,6,7,8,7,7,9,9,8,6,6,5,8,8,9,8,9,7,6,4,7,7,4,7,6,8,8,8,5,8,8,4,7,8,7,7,7,6,7,8,6,6,7,6,7,6,7,7,6,9,5,8,8,7,6,8,9,9,7,8,5,8,8,4,9,6,8,8,6,6,9,7,7,6,7,8,8,8,7,7,8,3,7,8,6,4,8,5,6,8,5,7,7,8,6,5,8,9,8,8,7,9,9,8) dfc <- data.frame(Samples,Assessors,Softness) tukey.add.test(dfc$Softness,dfc$Samples,dfc$Assessors) Tukey's one df test for additivity data: dfc$Samples and dfc$Assessors on dfc$Softness F = 1.4263, num.df = 1, denom.df = 342, p-value = 0.2332 dfc.aov <- aov(Softness~Samples + Assessors,dfc) summary(dfc.aov) Df Sum Sq Mean Sq F value Pr(>F) Samples 7 12.96 1.8514 1.5845 0.1388 Assessors 49 356.49 7.2753 6.2263 <2e-16 ***** **Residuals 343 400.79 1.1685** **---** **Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > oldpar <- par(oma=c(0,0,3,0), mfrow=c(2,2)) plot(dfc.aov) par(oldpar) sample.A <- c(6,8,9,8,7,5,4,5,6,7,8,8,8,8,4,3,7,8,8,8,5,4,7,8,7,6,8,6,7,5,7,8,7,5,7,8,5,5,6,6,6,6,7,5,7,8,7,8,6,8) sample.B <- c(6,7,8,8,7,7,6,4,7,5,7,7,8,5,7,3,7,7,8,4,8,7,7,7,5,7,8,7,7,8,8,4,6,5,8,8,7,7,6,6,6,5,6,7,8,7,7,8,8,7) sample.C <- c(6,7,9,8,7,3,5,4,7,4,8,8,7,8,6,4,7,9,7,7,2,2,8,8,4,7,8,3,6,4,8,6,7,5,6,7,8,7,6,8,7,6,7,9,6,8,7,8,6,8) sample.D <- c(3,6,6,8,5,4,5,5,7,8,9,8,8,8,3,5,3,8,8,4,4,7,6,7,7,7,8,6,5,4,8,6,9,6,7,7,6,5,6,7,7,6,7,6,7,6,7,8,8,7) sample.E <- c(7,6,9,7,7,8,6,7,7,8,8,8,6,8,7,2,7,7,4,4,1,9,8,7,4,8,8,4,8,5,7,1,6,4,6,8,6,7,6,8,6,6,7,9,7,8,8,7,7,7) sample.F <- c(7,7,6,8,7,8,5,8,7,8,9,8,8,7,5,3,8,7,4,7,6,8,7,8,7,7,8,5,7,4,8,6,8,7,6,8,6,7,6,7,8,6,6,7,7,6,5,8,8,7) sample.G <- c(7,6,9,9,7,4,6,6,8,8,9,8,9,8,3,2,8,6,5,7,2,9,8,8,7,8,8,5,8,7,6,6,8,6,6,8,7,7,8,7,6,6,7,8,6,8,5,8,8,8) sample.H <- c(3,7,9,9,7,4,6,7,8,6,8,6,7,7,6,3,8,7,8,6,5,4,6,8,7,6,8,5,7,5,6,5,8,6,6,8,5,7,6,8,6,6,8,9,8,7,7,7,8,8) > mean (sample.A) [1] 6.6 > mean (sample.B) [1] 6.66 > mean (sample.C) [1] 6.46 > mean (sample.D) [1] 6.36 > mean (sample.E) [1] 6.52 > mean (sample.F) [1] 6.82 > mean (sample.G) [1] 6.88 > mean (sample.H) [1] 6.64 Assessors <- factor(rep(c(1:50),times=8)) Samples <- factor(c(rep(c("0"),times=50),rep(c("1"),times=50),rep(c("2"),times=50),rep(c("3"),times=50),rep(c("4"),times=50),rep(c("5"),times=50),rep(c("6"),times=50),rep(c("7"),times=50))) Iciness <- c(6,8,9,8,7,5,4,5,6,7,8,8,8,8,4,3,7,8,8,8,5,4,7,8,7,6,8,6,7,5,7,8,7,5,7,8,5,5,6,6,6,6,7,5,7,8,7,8,6,8,6,7,8,8,7,7,6,4,7,5,7,7,8,5,7,3,7,7,8,4,8,7,7,7,5,7,8,7,7,8,8,4,6,5,8,8,7,7,6,6,6,5,6,7,8,7,7,8,8,7,6,7,9,8,7,3,5,4,7,4,8,8,7,8,6,4,7,9,7,7,2,2,8,8,4,7,8,3,6,4,8,6,7,5,6,7,8,7,6,8,7,6,7,9,6,8,7,8,6,8,3,6,6,8,5,4,5,5,7,8,9,8,8,8,3,5,3,8,8,4,4,7,6,7,7,7,8,6,5,4,8,6,9,6,7,7,6,5,6,7,7,6,7,6,7,6,7,8,8,7,7,6,9,7,7,8,6,7,7,8,8,8,6,8,7,2,7,7,4,4,1,9,8,7,4,8,8,4,8,5,7,1,6,4,6,8,6,7,6,8,6,6,7,9,7,8,8,7,7,7,7,7,6,8,7,8,5,8,7,8,9,8,8,7,5,3,8,7,4,7,6,8,7,8,7,7,8,5,7,4,8,6,8,7,6,8,6,7,6,7,8,6,6,7,7,6,5,8,8,7,7,6,9,9,7,4,6,6,8,8,9,8,9,8,3,2,8,6,5,7,2,9,8,8,7,8,8,5,8,7,6,6,8,6,6,8,7,7,8,7,6,6,7,8,6,8,5,8,8,8,3,7,9,9,7,4,6,7,8,6,8,6,7,7,6,3,8,7,8,6,5,4,6,8,7,6,8,5,7,5,6,5,8,6,6,8,5,7,6,8,6,6,8,9,8,7,7,7,8,8) dfc <- data.frame(Samples,Assessors,Iciness) tukey.add.test(dfc$Iciness,dfc$Samples,dfc$Assessors)
 * 1) softness
 * 1) Iciness

Tukey's one df test for additivity data: dfc$Samples and dfc$Assessors on dfc$Iciness F = 0.501, num.df = 1, denom.df = 342, p-value = 0.4795 dfc.aov <- aov(Iciness~Samples + Assessors,dfc) summary(dfc.aov) Df Sum Sq Mean Sq F value Pr(>F) Samples 7 10.66 1.5225 1.0763 0.3781 Assessors 49 442.60 9.0327 6.3852 <2e-16 ***** **Residuals 343 485.22 1.4146** **---** **Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 x11 oldpar <- par(oma=c(0,0,3,0), mfrow=c(2,2)) plot(dfc.aov) par(oldpar) sample.A <- c(5,7,9,9,8,8,6,8,6,6,8,9,7,8,4,6,7,8,6,8,3,5,7,7,6,7,8,4,6,6,9,9,8,8,5,7,8,7,6,7,9,6,6,6,6,8,9,6,8,6,8) sample.B <- c(6,7,9,8,8,8,7,6,7,7,8,8,8,7,6,5,7,7,7,6,7,7,8,8,5,8,8,7,7,5,9,9,5,8,8,7,9,7,6,9,6,6,6,7,7,7,7,7,9,8,7) sample.C <- c(6,7,9,8,8,8,4,4,7,7,8,8,7,8,4,4,8,8,6,6,2,3,9,8,5,8,8,5,7,6,9,8,8,6,6,6,8,8,7,7,8,6,6,7,8,6,8,7,9,6,8) sample.D <- c(7,6,6,8,7,8,5,4,8,7,9,9,8,8,5,7,6,8,7,6,3,7,6,8,7,7,8,6,5,7,8,8,7,9,6,7,9,6,6,7,8,8,6,8,6,7,8,7,7,8,7) sample.E <- c(5,6,8,8,8,9,5,7,9,7,8,8,7,7,7,4,8,6,4,5,2,8,8,8,5,7,8,5,8,6,9,8,2,5,5,6,9,5,8,6,9,6,6,7,9,7,8,8,9,7,7) sample.F <- c(7,8,6,8,8,9,5,9,7,8,9,8,8,8,6,3,8,7,6,7,5,8,8,8,6,7,8,4,7,7,9,8,8,7,5,6,9,5,7,7,8,8,7,6,7,7,9,6,8,7,7) sample.G <- c(7,6,9,9,8,7,8,5,8,8,9,8,8,7,5,3,8,6,7,8,4,9,8,8,6,8,8,5,8,8,9,7,7,7,6,6,9,6,6,7,7,6,6,7,8,6,9,5,9,8,8) sample.H <- c(6,7,9,9,8,7,6,7,8,6,9,6,8,8,6,5,8,7,7,6,6,6,7,8,7,7,8,4,7,7,9,6,5,8,5,6,9,5,7,7,8,6,6,8,9,8,8,7,8,8,8) > mean (sample.A) [1] 6.941176 > mean (sample.B) [1] 7.17647 > mean (sample.C) [1] 6.82353 > mean (sample.D) [1] 6.980392 > mean (sample.E) [1] 6.803922 > mean (sample.F) [1] 7.137255 > mean (sample.G) [1] 7.156863 > mean (sample.H) [1] 7.078431
 * 1) overall preference

Assessors <- factor(rep(c(1:51),times=8)) Samples <- factor(c(rep(c("0"),times=51),rep(c("1"),times=51),rep(c("2"),times=51),rep(c("3"),times=51),rep(c("4"),times=51),rep(c("5"),times=51),rep(c("6"),times=51),rep(c("7"),times=51))) overall <- c(5,7,9,9,8,8,6,8,6,6,8,9,7,8,4,6,7,8,6,8,3,5,7,7,6,7,8,4,6,6,9,9,8,8,5,7,8,7,6,7,9,6,6,6,6,8,9,6,8,6,8,6,7,9,8,8,8,7,6,7,7,8,8,8,7,6,5,7,7,7,6,7,7,8,8,5,8,8,7,7,5,9,9,5,8,8,7,9,7,6,9,6,6,6,7,7,7,7,7,9,8,7,6,7,9,8,8,8,4,4,7,7,8,8,7,8,4,4,8,8,6,6,2,3,9,8,5,8,8,5,7,6,9,8,8,6,6,6,8,8,7,7,8,6,6,7,8,6,8,7,9,6,8,7,6,6,8,7,8,5,4,8,7,9,9,8,8,5,7,6,8,7,6,3,7,6,8,7,7,8,6,5,7,8,8,7,9,6,7,9,6,6,7,8,8,6,8,6,7,8,7,7,8,7,5,6,8,8,8,9,5,7,9,7,8,8,7,7,7,4,8,6,4,5,2,8,8,8,5,7,8,5,8,6,9,8,2,5,5,6,9,5,8,6,9,6,6,7,9,7,8,8,9,7,7,7,8,6,8,8,9,5,9,7,8,9,8,8,8,6,3,8,7,6,7,5,8,8,8,6,7,8,4,7,7,9,8,8,7,5,6,9,5,7,7,8,8,7,6,7,7,9,6,8,7,7,7,6,9,9,8,7,8,5,8,8,9,8,8,7,5,3,8,6,7,8,4,9,8,8,6,8,8,5,8,8,9,7,7,7,6,6,9,6,6,7,7,6,6,7,8,6,9,5,9,8,8,6,7,9,9,8,7,6,7,8,6,9,6,8,8,6,5,8,7,7,6,6,6,7,8,7,7,8,4,7,7,9,6,5,8,5,6,9,5,7,7,8,6,6,8,9,8,8,7,8,8,8) dfc <- data.frame(Samples,Assessors,overall) dfc <- data.frame(Samples,Assessors,overall) tukey.add.test(dfc$overall,dfc$Samples,dfc$Assessors)

Tukey's one df test for additivity data: dfc$Samples and dfc$Assessors on dfc$overall F = 10.3079, num.df = 1, denom.df = 349, p-value = 0.001448 overall <-matrix(c(5,7,9,9,8,8,6,8,6,6,8,9,7,8,4,6,7,8,6,8,3,5,7,7,6,7,8,4,6,6,9,9,8,8,5,7,8,7,6,7,9,6,6,6,6,8,9,6,8,6,8,6,7,9,8,8,8,7,6,7,7,8,8,8,7,6,5,7,7,7,6,7,7,8,8,5,8,8,7,7,5,9,9,5,8,8,7,9,7,6,9,6,6,6,7,7,7,7,7,9,8,7,6,7,9,8,8,8,4,4,7,7,8,8,7,8,4,4,8,8,6,6,2,3,9,8,5,8,8,5,7,6,9,8,8,6,6,6,8,8,7,7,8,6,6,7,8,6,8,7,9,6,8,7,6,6,8,7,8,5,4,8,7,9,9,8,8,5,7,6,8,7,6,3,7,6,8,7,7,8,6,5,7,8,8,7,9,6,7,9,6,6,7,8,8,6,8,6,7,8,7,7,8,7,5,6,8,8,8,9,5,7,9,7,8,8,7,7,7,4,8,6,4,5,2,8,8,8,5,7,8,5,8,6,9,8,2,5,5,6,9,5,8,6,9,6,6,7,9,7,8,8,9,7,7,7,8,6,8,8,9,5,9,7,8,9,8,8,8,6,3,8,7,6,7,5,8,8,8,6,7,8,4,7,7,9,8,8,7,5,6,9,5,7,7,8,8,7,6,7,7,9,6,8,7,7,7,6,9,9,8,7,8,5,8,8,9,8,8,7,5,3,8,6,7,8,4,9,8,8,6,8,8,5,8,8,9,7,7,7,6,6,9,6,6,7,7,6,6,7,8,6,9,5,9,8,8,6,7,9,9,8,7,6,7,8,6,9,6,8,8,6,5,8,7,7,6,6,6,7,8,7,7,8,4,7,7,9,6,5,8,5,6,9,5,7,7,8,6,6,8,9,8,8,7,8,8,8),nrow=51,byrow=FALSE, dimnames=list(1:51,c("A","B","C","D","E","F","G","H"))) result <- friedman.test(overall) result

Friedman rank sum test

data: overall Friedman chi-squared = 7.2282, df = 7, p-value = 0.4055

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