local({r <- getOption("repos")
r["CRAN"] <- "http://cran.r-project.org"
options(repos = r)
})
install.packages("knitr")
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install.packages("afex")
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install.packages("emmeans")
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install.packages("contribution")
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install.packages("ggplot2")
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install.packages("mosaic")
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install.packages("multcompView")
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library(tools)
library(tidyverse)
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library(dplyr)
library(reshape2)
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library(knitr)
library(afex)
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## ************
## Welcome to afex. For support visit: http://afex.singmann.science/
## - Functions for ANOVAs: aov_car(), aov_ez(), and aov_4()
## - Methods for calculating p-values with mixed(): 'S', 'KR', 'LRT', and 'PB'
## - 'afex_aov' and 'mixed' objects can be passed to emmeans() for follow-up tests
## - NEWS: emmeans() for ANOVA models now uses model = 'multivariate' as default.
## - Get and set global package options with: afex_options()
## - Set orthogonal sum-to-zero contrasts globally: set_sum_contrasts()
## - For example analyses see: browseVignettes("afex")
## ************
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library(emmeans)
library(ggplot2)
library(psych)
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library(car)
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library(ggplot2)
library(ggthemes)
library(multcompView)
mydata <- read.csv("~/Desktop/R Studio_Thesis/R Studio_Thesis_Polylactose/Data/SCFA_June.csv")
mydata
## Group Acetic Propionic Isobutyric Butyric Isovaleric Valeric
## 1 1 2.48 1.48 1.39 1.32 1.30 0.00
## 2 1 2.57 1.48 1.41 1.33 1.34 0.00
## 3 1 2.47 1.48 1.37 1.31 1.26 1.09
## 4 2 2.11 1.59 1.63 1.47 1.65 1.09
## 5 2 1.96 1.53 1.43 1.33 1.35 0.00
## 6 2 2.30 1.47 1.32 1.26 1.19 0.00
## 7 3 2.25 1.47 1.33 1.28 1.23 0.00
## 8 3 1.96 1.52 1.42 1.35 1.33 0.00
## 9 3 2.15 0.00 1.31 1.27 1.17 0.00
## 10 4 1.89 0.00 0.00 0.00 0.00 0.00
## 11 4 1.90 0.00 0.00 1.24 0.00 0.00
## 12 4 1.95 0.00 0.00 1.23 0.00 0.00
## 13 5 2.11 0.00 0.00 0.00 0.00 0.00
## 14 5 2.13 0.00 0.00 0.00 0.00 0.00
## 15 5 0.00 0.00 0.00 0.00 0.00 0.00
## 16 6 0.00 0.00 0.00 0.00 0.00 0.00
## 17 6 0.00 0.00 0.00 0.00 0.00 0.00
## 18 6 1.81 0.00 0.00 0.00 0.00 0.00
## 19 7 1.77 0.00 0.00 0.00 0.00 0.00
## 20 7 1.83 0.00 0.00 0.00 0.00 0.00
## 21 7 1.85 0.00 0.00 0.00 0.00 0.00
## 22 8 2.28 1.45 1.23 1.23 1.06 1.06
## 23 8 1.85 1.45 1.23 1.23 1.06 1.06
## 24 8 2.38 1.45 1.23 1.23 1.06 1.06
## 25 9 1.96 1.52 1.35 1.33 1.14 1.07
## 26 9 3.12 1.52 1.71 1.45 1.66 1.08
## 27 9 4.35 1.54 1.69 0.00 0.00 0.00
## 28 10 2.20 1.59 1.65 1.91 1.65 1.09
## 29 10 2.24 1.59 1.60 1.85 1.56 1.08
## 30 10 2.62 1.85 2.22 2.03 2.38 1.19
## 31 11 3.32 1.51 1.54 1.34 1.42 1.11
## 32 11 2.69 1.50 1.56 1.39 1.53 1.07
## 33 11 2.70 1.49 1.49 1.36 1.38 1.11
## 34 12 2.06 0.00 0.00 1.24 0.00 0.00
## 35 12 1.87 0.00 0.00 0.00 0.00 0.00
## 36 12 2.04 0.00 0.00 0.00 0.00 0.00
## 37 13 2.11 0.00 0.00 0.00 0.00 0.00
## 38 13 2.13 0.00 0.00 0.00 0.00 0.00
## 39 13 0.00 0.00 0.00 0.00 0.00 0.00
## 40 14 1.81 0.00 0.00 0.00 0.00 0.00
## 41 14 1.81 0.00 0.00 0.00 0.00 0.00
## 42 14 1.82 0.00 0.00 0.00 0.00 0.00
## 43 15 1.97 0.00 0.00 0.00 0.00 0.00
## 44 15 1.81 0.00 0.00 0.00 0.00 0.00
## 45 15 1.95 0.00 0.00 0.00 0.00 0.00
## 46 16 3.35 0.00 0.00 0.00 1.14 1.08
## 47 16 1.97 0.00 1.30 1.26 1.15 0.00
## 48 16 2.08 0.00 1.28 0.00 1.27 0.00
str(mydata)
## 'data.frame': 48 obs. of 7 variables:
## $ Group : int 1 1 1 2 2 2 3 3 3 4 ...
## $ Acetic : num 2.48 2.57 2.47 2.11 1.96 2.3 2.25 1.96 2.15 1.89 ...
## $ Propionic : num 1.48 1.48 1.48 1.59 1.53 1.47 1.47 1.52 0 0 ...
## $ Isobutyric: num 1.39 1.41 1.37 1.63 1.43 1.32 1.33 1.42 1.31 0 ...
## $ Butyric : num 1.32 1.33 1.31 1.47 1.33 1.26 1.28 1.35 1.27 0 ...
## $ Isovaleric: num 1.3 1.34 1.26 1.65 1.35 1.19 1.23 1.33 1.17 0 ...
## $ Valeric : num 0 0 1.09 1.09 0 0 0 0 0 0 ...
mydata$group <- as.factor(mydata$Group)
str(mydata)
## 'data.frame': 48 obs. of 8 variables:
## $ Group : int 1 1 1 2 2 2 3 3 3 4 ...
## $ Acetic : num 2.48 2.57 2.47 2.11 1.96 2.3 2.25 1.96 2.15 1.89 ...
## $ Propionic : num 1.48 1.48 1.48 1.59 1.53 1.47 1.47 1.52 0 0 ...
## $ Isobutyric: num 1.39 1.41 1.37 1.63 1.43 1.32 1.33 1.42 1.31 0 ...
## $ Butyric : num 1.32 1.33 1.31 1.47 1.33 1.26 1.28 1.35 1.27 0 ...
## $ Isovaleric: num 1.3 1.34 1.26 1.65 1.35 1.19 1.23 1.33 1.17 0 ...
## $ Valeric : num 0 0 1.09 1.09 0 0 0 0 0 0 ...
## $ group : Factor w/ 16 levels "1","2","3","4",..: 1 1 1 2 2 2 3 3 3 4 ...
Prop.aov <- aov(Propionic ~ group, data = mydata)
Prop.aov
## Call:
## aov(formula = Propionic ~ group, data = mydata)
##
## Terms:
## group Residuals
## Sum of Squares 25.7024 1.5440
## Deg. of Freedom 15 32
##
## Residual standard error: 0.2196588
## Estimated effects may be unbalanced
summary(Prop.aov)
## Df Sum Sq Mean Sq F value Pr(>F)
## group 15 25.702 1.7135 35.51 1.08e-15 ***
## Residuals 32 1.544 0.0483
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Acetic.aov <- aov(Acetic ~ group, data = mydata)
Acetic.aov
## Call:
## aov(formula = Acetic ~ group, data = mydata)
##
## Terms:
## group Residuals
## Sum of Squares 16.43113 12.88700
## Deg. of Freedom 15 32
##
## Residual standard error: 0.6346013
## Estimated effects may be unbalanced
summary(Acetic.aov)
## Df Sum Sq Mean Sq F value Pr(>F)
## group 15 16.43 1.0954 2.72 0.00856 **
## Residuals 32 12.89 0.4027
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Butyric.aov <- aov <- aov(Butyric ~ group, data = mydata)
Butyric.aov
## Call:
## aov(formula = Butyric ~ group, data = mydata)
##
## Terms:
## group Residuals
## Sum of Squares 19.713967 4.440533
## Deg. of Freedom 15 32
##
## Residual standard error: 0.372514
## Estimated effects may be unbalanced
summary(Butyric.aov)
## Df Sum Sq Mean Sq F value Pr(>F)
## group 15 19.714 1.3143 9.471 6.8e-08 ***
## Residuals 32 4.441 0.1388
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
tukey.test_prop <- TukeyHSD(Prop.aov)
tukey.test_prop
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Propionic ~ group, data = mydata)
##
## $group
## diff lwr upr p adj
## 2-1 5.000000e-02 -0.61504758 0.7150476 1.0000000
## 3-1 -4.833333e-01 -1.14838091 0.1817142 0.3757066
## 4-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 5-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 6-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 7-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 8-1 -3.000000e-02 -0.69504758 0.6350476 1.0000000
## 9-1 4.666667e-02 -0.61838091 0.7117142 1.0000000
## 10-1 1.966667e-01 -0.46838091 0.8617142 0.9987935
## 11-1 2.000000e-02 -0.64504758 0.6850476 1.0000000
## 12-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 13-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 14-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 15-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 16-1 -1.480000e+00 -2.14504758 -0.8149524 0.0000002
## 3-2 -5.333333e-01 -1.19838091 0.1317142 0.2353873
## 4-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 5-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 6-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 7-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 8-2 -8.000000e-02 -0.74504758 0.5850476 1.0000000
## 9-2 -3.333333e-03 -0.66838091 0.6617142 1.0000000
## 10-2 1.466667e-01 -0.51838091 0.8117142 0.9999621
## 11-2 -3.000000e-02 -0.69504758 0.6350476 1.0000000
## 12-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 13-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 14-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 15-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 16-2 -1.530000e+00 -2.19504758 -0.8649524 0.0000001
## 4-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 5-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 6-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 7-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 8-3 4.533333e-01 -0.21171425 1.1183809 0.4774783
## 9-3 5.300000e-01 -0.13504758 1.1950476 0.2434317
## 10-3 6.800000e-01 0.01495242 1.3450476 0.0410207
## 11-3 5.033333e-01 -0.16171425 1.1683809 0.3146472
## 12-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 13-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 14-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 15-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 16-3 -9.966667e-01 -1.66171425 -0.3316191 0.0003704
## 5-4 5.551115e-16 -0.66504758 0.6650476 1.0000000
## 6-4 -2.220446e-16 -0.66504758 0.6650476 1.0000000
## 7-4 2.960595e-16 -0.66504758 0.6650476 1.0000000
## 8-4 1.450000e+00 0.78495242 2.1150476 0.0000003
## 9-4 1.526667e+00 0.86161909 2.1917142 0.0000001
## 10-4 1.676667e+00 1.01161909 2.3417142 0.0000000
## 11-4 1.500000e+00 0.83495242 2.1650476 0.0000002
## 12-4 -9.251859e-16 -0.66504758 0.6650476 1.0000000
## 13-4 -2.590520e-16 -0.66504758 0.6650476 1.0000000
## 14-4 -5.921189e-16 -0.66504758 0.6650476 1.0000000
## 15-4 -9.251859e-16 -0.66504758 0.6650476 1.0000000
## 16-4 -1.036208e-15 -0.66504758 0.6650476 1.0000000
## 6-5 -7.771561e-16 -0.66504758 0.6650476 1.0000000
## 7-5 -2.590520e-16 -0.66504758 0.6650476 1.0000000
## 8-5 1.450000e+00 0.78495242 2.1150476 0.0000003
## 9-5 1.526667e+00 0.86161909 2.1917142 0.0000001
## 10-5 1.676667e+00 1.01161909 2.3417142 0.0000000
## 11-5 1.500000e+00 0.83495242 2.1650476 0.0000002
## 12-5 -1.480297e-15 -0.66504758 0.6650476 1.0000000
## 13-5 -8.141636e-16 -0.66504758 0.6650476 1.0000000
## 14-5 -1.147230e-15 -0.66504758 0.6650476 1.0000000
## 15-5 -1.480297e-15 -0.66504758 0.6650476 1.0000000
## 16-5 -1.591320e-15 -0.66504758 0.6650476 1.0000000
## 7-6 5.181041e-16 -0.66504758 0.6650476 1.0000000
## 8-6 1.450000e+00 0.78495242 2.1150476 0.0000003
## 9-6 1.526667e+00 0.86161909 2.1917142 0.0000001
## 10-6 1.676667e+00 1.01161909 2.3417142 0.0000000
## 11-6 1.500000e+00 0.83495242 2.1650476 0.0000002
## 12-6 -7.031412e-16 -0.66504758 0.6650476 1.0000000
## 13-6 -3.700743e-17 -0.66504758 0.6650476 1.0000000
## 14-6 -3.700743e-16 -0.66504758 0.6650476 1.0000000
## 15-6 -7.031412e-16 -0.66504758 0.6650476 1.0000000
## 16-6 -8.141636e-16 -0.66504758 0.6650476 1.0000000
## 8-7 1.450000e+00 0.78495242 2.1150476 0.0000003
## 9-7 1.526667e+00 0.86161909 2.1917142 0.0000001
## 10-7 1.676667e+00 1.01161909 2.3417142 0.0000000
## 11-7 1.500000e+00 0.83495242 2.1650476 0.0000002
## 12-7 -1.221245e-15 -0.66504758 0.6650476 1.0000000
## 13-7 -5.551115e-16 -0.66504758 0.6650476 1.0000000
## 14-7 -8.881784e-16 -0.66504758 0.6650476 1.0000000
## 15-7 -1.221245e-15 -0.66504758 0.6650476 1.0000000
## 16-7 -1.332268e-15 -0.66504758 0.6650476 1.0000000
## 9-8 7.666667e-02 -0.58838091 0.7417142 1.0000000
## 10-8 2.266667e-01 -0.43838091 0.8917142 0.9946955
## 11-8 5.000000e-02 -0.61504758 0.7150476 1.0000000
## 12-8 -1.450000e+00 -2.11504758 -0.7849524 0.0000003
## 13-8 -1.450000e+00 -2.11504758 -0.7849524 0.0000003
## 14-8 -1.450000e+00 -2.11504758 -0.7849524 0.0000003
## 15-8 -1.450000e+00 -2.11504758 -0.7849524 0.0000003
## 16-8 -1.450000e+00 -2.11504758 -0.7849524 0.0000003
## 10-9 1.500000e-01 -0.51504758 0.8150476 0.9999498
## 11-9 -2.666667e-02 -0.69171425 0.6383809 1.0000000
## 12-9 -1.526667e+00 -2.19171425 -0.8616191 0.0000001
## 13-9 -1.526667e+00 -2.19171425 -0.8616191 0.0000001
## 14-9 -1.526667e+00 -2.19171425 -0.8616191 0.0000001
## 15-9 -1.526667e+00 -2.19171425 -0.8616191 0.0000001
## 16-9 -1.526667e+00 -2.19171425 -0.8616191 0.0000001
## 11-10 -1.766667e-01 -0.84171425 0.4883809 0.9996399
## 12-10 -1.676667e+00 -2.34171425 -1.0116191 0.0000000
## 13-10 -1.676667e+00 -2.34171425 -1.0116191 0.0000000
## 14-10 -1.676667e+00 -2.34171425 -1.0116191 0.0000000
## 15-10 -1.676667e+00 -2.34171425 -1.0116191 0.0000000
## 16-10 -1.676667e+00 -2.34171425 -1.0116191 0.0000000
## 12-11 -1.500000e+00 -2.16504758 -0.8349524 0.0000002
## 13-11 -1.500000e+00 -2.16504758 -0.8349524 0.0000002
## 14-11 -1.500000e+00 -2.16504758 -0.8349524 0.0000002
## 15-11 -1.500000e+00 -2.16504758 -0.8349524 0.0000002
## 16-11 -1.500000e+00 -2.16504758 -0.8349524 0.0000002
## 13-12 6.661338e-16 -0.66504758 0.6650476 1.0000000
## 14-12 3.330669e-16 -0.66504758 0.6650476 1.0000000
## 15-12 0.000000e+00 -0.66504758 0.6650476 1.0000000
## 16-12 -1.110223e-16 -0.66504758 0.6650476 1.0000000
## 14-13 -3.330669e-16 -0.66504758 0.6650476 1.0000000
## 15-13 -6.661338e-16 -0.66504758 0.6650476 1.0000000
## 16-13 -7.771561e-16 -0.66504758 0.6650476 1.0000000
## 15-14 -3.330669e-16 -0.66504758 0.6650476 1.0000000
## 16-14 -4.440892e-16 -0.66504758 0.6650476 1.0000000
## 16-15 -1.110223e-16 -0.66504758 0.6650476 1.0000000
tukey.test_acetic <- TukeyHSD(Acetic.aov)
tukey.test_acetic
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Acetic ~ group, data = mydata)
##
## $group
## diff lwr upr p adj
## 2-1 -3.833333e-01 -2.30467670 1.53801003 0.9999894
## 3-1 -3.866667e-01 -2.30801003 1.53467670 0.9999882
## 4-1 -5.933333e-01 -2.51467670 1.32801003 0.9980749
## 5-1 -1.093333e+00 -3.01467670 0.82801003 0.7461644
## 6-1 -1.903333e+00 -3.82467670 0.01801003 0.0542423
## 7-1 -6.900000e-01 -2.61134336 1.23134336 0.9911959
## 8-1 -3.366667e-01 -2.25801003 1.58467670 0.9999981
## 9-1 6.366667e-01 -1.28467670 2.55801003 0.9959983
## 10-1 -1.533333e-01 -2.07467670 1.76801003 1.0000000
## 11-1 3.966667e-01 -1.52467670 2.31801003 0.9999836
## 12-1 -5.166667e-01 -2.43801003 1.40467670 0.9995853
## 13-1 -1.093333e+00 -3.01467670 0.82801003 0.7461644
## 14-1 -6.933333e-01 -2.61467670 1.22801003 0.9907854
## 15-1 -5.966667e-01 -2.51801003 1.32467670 0.9979569
## 16-1 -4.000000e-02 -1.96134336 1.88134336 1.0000000
## 3-2 -3.333333e-03 -1.92467670 1.91801003 1.0000000
## 4-2 -2.100000e-01 -2.13134336 1.71134336 1.0000000
## 5-2 -7.100000e-01 -2.63134336 1.21134336 0.9884979
## 6-2 -1.520000e+00 -3.44134336 0.40134336 0.2530172
## 7-2 -3.066667e-01 -2.22801003 1.61467670 0.9999995
## 8-2 4.666667e-02 -1.87467670 1.96801003 1.0000000
## 9-2 1.020000e+00 -0.90134336 2.94134336 0.8244694
## 10-2 2.300000e-01 -1.69134336 2.15134336 1.0000000
## 11-2 7.800000e-01 -1.14134336 2.70134336 0.9736415
## 12-2 -1.333333e-01 -2.05467670 1.78801003 1.0000000
## 13-2 -7.100000e-01 -2.63134336 1.21134336 0.9884979
## 14-2 -3.100000e-01 -2.23134336 1.61134336 0.9999994
## 15-2 -2.133333e-01 -2.13467670 1.70801003 1.0000000
## 16-2 3.433333e-01 -1.57801003 2.26467670 0.9999975
## 4-3 -2.066667e-01 -2.12801003 1.71467670 1.0000000
## 5-3 -7.066667e-01 -2.62801003 1.21467670 0.9889880
## 6-3 -1.516667e+00 -3.43801003 0.40467670 0.2559235
## 7-3 -3.033333e-01 -2.22467670 1.61801003 0.9999995
## 8-3 5.000000e-02 -1.87134336 1.97134336 1.0000000
## 9-3 1.023333e+00 -0.89801003 2.94467670 0.8211948
## 10-3 2.333333e-01 -1.68801003 2.15467670 1.0000000
## 11-3 7.833333e-01 -1.13801003 2.70467670 0.9726834
## 12-3 -1.300000e-01 -2.05134336 1.79134336 1.0000000
## 13-3 -7.066667e-01 -2.62801003 1.21467670 0.9889880
## 14-3 -3.066667e-01 -2.22801003 1.61467670 0.9999995
## 15-3 -2.100000e-01 -2.13134336 1.71134336 1.0000000
## 16-3 3.466667e-01 -1.57467670 2.26801003 0.9999972
## 5-4 -5.000000e-01 -2.42134336 1.42134336 0.9997167
## 6-4 -1.310000e+00 -3.23134336 0.61134336 0.4771025
## 7-4 -9.666667e-02 -2.01801003 1.82467670 1.0000000
## 8-4 2.566667e-01 -1.66467670 2.17801003 1.0000000
## 9-4 1.230000e+00 -0.69134336 3.15134336 0.5777081
## 10-4 4.400000e-01 -1.48134336 2.36134336 0.9999393
## 11-4 9.900000e-01 -0.93134336 2.91134336 0.8525573
## 12-4 7.666667e-02 -1.84467670 1.99801003 1.0000000
## 13-4 -5.000000e-01 -2.42134336 1.42134336 0.9997167
## 14-4 -1.000000e-01 -2.02134336 1.82134336 1.0000000
## 15-4 -3.333333e-03 -1.92467670 1.91801003 1.0000000
## 16-4 5.533333e-01 -1.36801003 2.47467670 0.9990988
## 6-5 -8.100000e-01 -2.73134336 1.11134336 0.9640605
## 7-5 4.033333e-01 -1.51801003 2.32467670 0.9999797
## 8-5 7.566667e-01 -1.16467670 2.67801003 0.9796591
## 9-5 1.730000e+00 -0.19134336 3.65134336 0.1144360
## 10-5 9.400000e-01 -0.98134336 2.86134336 0.8934729
## 11-5 1.490000e+00 -0.43134336 3.41134336 0.2799984
## 12-5 5.766667e-01 -1.34467670 2.49801003 0.9985822
## 13-5 -2.220446e-16 -1.92134336 1.92134336 1.0000000
## 14-5 4.000000e-01 -1.52134336 2.32134336 0.9999817
## 15-5 4.966667e-01 -1.42467670 2.41801003 0.9997381
## 16-5 1.053333e+00 -0.86801003 2.97467670 0.7904318
## 7-6 1.213333e+00 -0.70801003 3.13467670 0.5989242
## 8-6 1.566667e+00 -0.35467670 3.48801003 0.2147405
## 9-6 2.540000e+00 0.61865664 4.46134336 0.0022871
## 10-6 1.750000e+00 -0.17134336 3.67134336 0.1053865
## 11-6 2.300000e+00 0.37865664 4.22134336 0.0079695
## 12-6 1.386667e+00 -0.53467670 3.30801003 0.3865410
## 13-6 8.100000e-01 -1.11134336 2.73134336 0.9640605
## 14-6 1.210000e+00 -0.71134336 3.13134336 0.6031634
## 15-6 1.306667e+00 -0.61467670 3.22801003 0.4812050
## 16-6 1.863333e+00 -0.05801003 3.78467670 0.0648392
## 8-7 3.533333e-01 -1.56801003 2.27467670 0.9999964
## 9-7 1.326667e+00 -0.59467670 3.24801003 0.4567656
## 10-7 5.366667e-01 -1.38467670 2.45801003 0.9993602
## 11-7 1.086667e+00 -0.83467670 3.00801003 0.7537729
## 12-7 1.733333e-01 -1.74801003 2.09467670 1.0000000
## 13-7 -4.033333e-01 -2.32467670 1.51801003 0.9999797
## 14-7 -3.333333e-03 -1.92467670 1.91801003 1.0000000
## 15-7 9.333333e-02 -1.82801003 2.01467670 1.0000000
## 16-7 6.500000e-01 -1.27134336 2.57134336 0.9950727
## 9-8 9.733333e-01 -0.94801003 2.89467670 0.8670382
## 10-8 1.833333e-01 -1.73801003 2.10467670 1.0000000
## 11-8 7.333333e-01 -1.18801003 2.65467670 0.9845657
## 12-8 -1.800000e-01 -2.10134336 1.74134336 1.0000000
## 13-8 -7.566667e-01 -2.67801003 1.16467670 0.9796591
## 14-8 -3.566667e-01 -2.27801003 1.56467670 0.9999959
## 15-8 -2.600000e-01 -2.18134336 1.66134336 0.9999999
## 16-8 2.966667e-01 -1.62467670 2.21801003 0.9999997
## 10-9 -7.900000e-01 -2.71134336 1.13134336 0.9706895
## 11-9 -2.400000e-01 -2.16134336 1.68134336 1.0000000
## 12-9 -1.153333e+00 -3.07467670 0.76801003 0.6744149
## 13-9 -1.730000e+00 -3.65134336 0.19134336 0.1144360
## 14-9 -1.330000e+00 -3.25134336 0.59134336 0.4527360
## 15-9 -1.233333e+00 -3.15467670 0.68801003 0.5734645
## 16-9 -6.766667e-01 -2.59801003 1.24467670 0.9926936
## 11-10 5.500000e-01 -1.37134336 2.47134336 0.9991574
## 12-10 -3.633333e-01 -2.28467670 1.55801003 0.9999947
## 13-10 -9.400000e-01 -2.86134336 0.98134336 0.8934729
## 14-10 -5.400000e-01 -2.46134336 1.38134336 0.9993140
## 15-10 -4.433333e-01 -2.36467670 1.47801003 0.9999334
## 16-10 1.133333e-01 -1.80801003 2.03467670 1.0000000
## 12-11 -9.133333e-01 -2.83467670 1.00801003 0.9121349
## 13-11 -1.490000e+00 -3.41134336 0.43134336 0.2799984
## 14-11 -1.090000e+00 -3.01134336 0.83134336 0.7499793
## 15-11 -9.933333e-01 -2.91467670 0.92801003 0.8495629
## 16-11 -4.366667e-01 -2.35801003 1.48467670 0.9999448
## 13-12 -5.766667e-01 -2.49801003 1.34467670 0.9985822
## 14-12 -1.766667e-01 -2.09801003 1.74467670 1.0000000
## 15-12 -8.000000e-02 -2.00134336 1.84134336 1.0000000
## 16-12 4.766667e-01 -1.44467670 2.39801003 0.9998392
## 14-13 4.000000e-01 -1.52134336 2.32134336 0.9999817
## 15-13 4.966667e-01 -1.42467670 2.41801003 0.9997381
## 16-13 1.053333e+00 -0.86801003 2.97467670 0.7904318
## 15-14 9.666667e-02 -1.82467670 2.01801003 1.0000000
## 16-14 6.533333e-01 -1.26801003 2.57467670 0.9948158
## 16-15 5.566667e-01 -1.36467670 2.47801003 0.9990367
tukey.test_butyric <- TukeyHSD(Butyric.aov)
tukey.test_butyric
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Butyric ~ group, data = mydata)
##
## $group
## diff lwr upr p adj
## 2-1 3.333333e-02 -1.09450444 1.1611711 1.0000000
## 3-1 -2.000000e-02 -1.14783778 1.1078378 1.0000000
## 4-1 -4.966667e-01 -1.62450444 0.6311711 0.9494447
## 5-1 -1.320000e+00 -2.44783778 -0.1921622 0.0103368
## 6-1 -1.320000e+00 -2.44783778 -0.1921622 0.0103368
## 7-1 -1.320000e+00 -2.44783778 -0.1921622 0.0103368
## 8-1 -9.000000e-02 -1.21783778 1.0378378 1.0000000
## 9-1 -3.933333e-01 -1.52117111 0.7345044 0.9933546
## 10-1 6.100000e-01 -0.51783778 1.7378378 0.8052340
## 11-1 4.333333e-02 -1.08450444 1.1711711 1.0000000
## 12-1 -9.066667e-01 -2.03450444 0.2211711 0.2323087
## 13-1 -1.320000e+00 -2.44783778 -0.1921622 0.0103368
## 14-1 -1.320000e+00 -2.44783778 -0.1921622 0.0103368
## 15-1 -1.320000e+00 -2.44783778 -0.1921622 0.0103368
## 16-1 -9.000000e-01 -2.02783778 0.2278378 0.2417279
## 3-2 -5.333333e-02 -1.18117111 1.0745044 1.0000000
## 4-2 -5.300000e-01 -1.65783778 0.5978378 0.9188384
## 5-2 -1.353333e+00 -2.48117111 -0.2254956 0.0077494
## 6-2 -1.353333e+00 -2.48117111 -0.2254956 0.0077494
## 7-2 -1.353333e+00 -2.48117111 -0.2254956 0.0077494
## 8-2 -1.233333e-01 -1.25117111 1.0045044 1.0000000
## 9-2 -4.266667e-01 -1.55450444 0.7011711 0.9857495
## 10-2 5.766667e-01 -0.55117111 1.7045044 0.8592731
## 11-2 1.000000e-02 -1.11783778 1.1378378 1.0000000
## 12-2 -9.400000e-01 -2.06783778 0.1878378 0.1891815
## 13-2 -1.353333e+00 -2.48117111 -0.2254956 0.0077494
## 14-2 -1.353333e+00 -2.48117111 -0.2254956 0.0077494
## 15-2 -1.353333e+00 -2.48117111 -0.2254956 0.0077494
## 16-2 -9.333333e-01 -2.06117111 0.1945044 0.1972834
## 4-3 -4.766667e-01 -1.60450444 0.6511711 0.9633307
## 5-3 -1.300000e+00 -2.42783778 -0.1721622 0.0122662
## 6-3 -1.300000e+00 -2.42783778 -0.1721622 0.0122662
## 7-3 -1.300000e+00 -2.42783778 -0.1721622 0.0122662
## 8-3 -7.000000e-02 -1.19783778 1.0578378 1.0000000
## 9-3 -3.733333e-01 -1.50117111 0.7545044 0.9960407
## 10-3 6.300000e-01 -0.49783778 1.7578378 0.7688219
## 11-3 6.333333e-02 -1.06450444 1.1911711 1.0000000
## 12-3 -8.866667e-01 -2.01450444 0.2411711 0.2613668
## 13-3 -1.300000e+00 -2.42783778 -0.1721622 0.0122662
## 14-3 -1.300000e+00 -2.42783778 -0.1721622 0.0122662
## 15-3 -1.300000e+00 -2.42783778 -0.1721622 0.0122662
## 16-3 -8.800000e-01 -2.00783778 0.2478378 0.2715858
## 5-4 -8.233333e-01 -1.95117111 0.3045044 0.3688253
## 6-4 -8.233333e-01 -1.95117111 0.3045044 0.3688253
## 7-4 -8.233333e-01 -1.95117111 0.3045044 0.3688253
## 8-4 4.066667e-01 -0.72117111 1.5345044 0.9908543
## 9-4 1.033333e-01 -1.02450444 1.2311711 1.0000000
## 10-4 1.106667e+00 -0.02117111 2.2345044 0.0588173
## 11-4 5.400000e-01 -0.58783778 1.6678378 0.9077294
## 12-4 -4.100000e-01 -1.53783778 0.7178378 0.9901243
## 13-4 -8.233333e-01 -1.95117111 0.3045044 0.3688253
## 14-4 -8.233333e-01 -1.95117111 0.3045044 0.3688253
## 15-4 -8.233333e-01 -1.95117111 0.3045044 0.3688253
## 16-4 -4.033333e-01 -1.53117111 0.7245044 0.9915405
## 6-5 -1.110223e-16 -1.12783778 1.1278378 1.0000000
## 7-5 -5.551115e-16 -1.12783778 1.1278378 1.0000000
## 8-5 1.230000e+00 0.10216222 2.3578378 0.0220705
## 9-5 9.266667e-01 -0.20117111 2.0545044 0.2056449
## 10-5 1.930000e+00 0.80216222 3.0578378 0.0000403
## 11-5 1.363333e+00 0.23549556 2.4911711 0.0071032
## 12-5 4.133333e-01 -0.71450444 1.5411711 0.9893485
## 13-5 -1.776357e-15 -1.12783778 1.1278378 1.0000000
## 14-5 -1.776357e-15 -1.12783778 1.1278378 1.0000000
## 15-5 -1.776357e-15 -1.12783778 1.1278378 1.0000000
## 16-5 4.200000e-01 -0.70783778 1.5478378 0.9876521
## 7-6 -4.440892e-16 -1.12783778 1.1278378 1.0000000
## 8-6 1.230000e+00 0.10216222 2.3578378 0.0220705
## 9-6 9.266667e-01 -0.20117111 2.0545044 0.2056449
## 10-6 1.930000e+00 0.80216222 3.0578378 0.0000403
## 11-6 1.363333e+00 0.23549556 2.4911711 0.0071032
## 12-6 4.133333e-01 -0.71450444 1.5411711 0.9893485
## 13-6 -1.665335e-15 -1.12783778 1.1278378 1.0000000
## 14-6 -1.665335e-15 -1.12783778 1.1278378 1.0000000
## 15-6 -1.665335e-15 -1.12783778 1.1278378 1.0000000
## 16-6 4.200000e-01 -0.70783778 1.5478378 0.9876521
## 8-7 1.230000e+00 0.10216222 2.3578378 0.0220705
## 9-7 9.266667e-01 -0.20117111 2.0545044 0.2056449
## 10-7 1.930000e+00 0.80216222 3.0578378 0.0000403
## 11-7 1.363333e+00 0.23549556 2.4911711 0.0071032
## 12-7 4.133333e-01 -0.71450444 1.5411711 0.9893485
## 13-7 -1.221245e-15 -1.12783778 1.1278378 1.0000000
## 14-7 -1.221245e-15 -1.12783778 1.1278378 1.0000000
## 15-7 -1.221245e-15 -1.12783778 1.1278378 1.0000000
## 16-7 4.200000e-01 -0.70783778 1.5478378 0.9876521
## 9-8 -3.033333e-01 -1.43117111 0.8245044 0.9995845
## 10-8 7.000000e-01 -0.42783778 1.8278378 0.6253730
## 11-8 1.333333e-01 -0.99450444 1.2611711 1.0000000
## 12-8 -8.166667e-01 -1.94450444 0.3111711 0.3814083
## 13-8 -1.230000e+00 -2.35783778 -0.1021622 0.0220705
## 14-8 -1.230000e+00 -2.35783778 -0.1021622 0.0220705
## 15-8 -1.230000e+00 -2.35783778 -0.1021622 0.0220705
## 16-8 -8.100000e-01 -1.93783778 0.3178378 0.3942077
## 10-9 1.003333e+00 -0.12450444 2.1311711 0.1245089
## 11-9 4.366667e-01 -0.69117111 1.5645044 0.9824749
## 12-9 -5.133333e-01 -1.64117111 0.6145044 0.9353556
## 13-9 -9.266667e-01 -2.05450444 0.2011711 0.2056449
## 14-9 -9.266667e-01 -2.05450444 0.2011711 0.2056449
## 15-9 -9.266667e-01 -2.05450444 0.2011711 0.2056449
## 16-9 -5.066667e-01 -1.63450444 0.6211711 0.9412765
## 11-10 -5.666667e-01 -1.69450444 0.5611711 0.8736775
## 12-10 -1.516667e+00 -2.64450444 -0.3888289 0.0018138
## 13-10 -1.930000e+00 -3.05783778 -0.8021622 0.0000403
## 14-10 -1.930000e+00 -3.05783778 -0.8021622 0.0000403
## 15-10 -1.930000e+00 -3.05783778 -0.8021622 0.0000403
## 16-10 -1.510000e+00 -2.63783778 -0.3821622 0.0019266
## 12-11 -9.500000e-01 -2.07783778 0.1778378 0.1775094
## 13-11 -1.363333e+00 -2.49117111 -0.2354956 0.0071032
## 14-11 -1.363333e+00 -2.49117111 -0.2354956 0.0071032
## 15-11 -1.363333e+00 -2.49117111 -0.2354956 0.0071032
## 16-11 -9.433333e-01 -2.07117111 0.1845044 0.1852271
## 13-12 -4.133333e-01 -1.54117111 0.7145044 0.9893485
## 14-12 -4.133333e-01 -1.54117111 0.7145044 0.9893485
## 15-12 -4.133333e-01 -1.54117111 0.7145044 0.9893485
## 16-12 6.666667e-03 -1.12117111 1.1345044 1.0000000
## 14-13 0.000000e+00 -1.12783778 1.1278378 1.0000000
## 15-13 0.000000e+00 -1.12783778 1.1278378 1.0000000
## 16-13 4.200000e-01 -0.70783778 1.5478378 0.9876521
## 15-14 0.000000e+00 -1.12783778 1.1278378 1.0000000
## 16-14 4.200000e-01 -0.70783778 1.5478378 0.9876521
## 16-15 4.200000e-01 -0.70783778 1.5478378 0.9876521
cld <- multcompLetters4(Acetic.aov, tukey.test_acetic)
dt_Acetic <- group_by(mydata, mydata$Group) %>%
summarise(m = mean(Acetic), sd = sd(Acetic)) %>%
arrange(desc(m))
cld <- as.data.frame.list(cld$group)
dt_Acetic$cld <- cld$Letters
print(dt_Acetic)
## # A tibble: 16 × 4
## `mydata$Group` m sd cld
## <int> <dbl> <dbl> <chr>
## 1 9 3.14 1.20 a
## 2 11 2.90 0.361 a
## 3 1 2.51 0.0551 ab
## 4 16 2.47 0.767 ab
## 5 10 2.35 0.232 ab
## 6 8 2.17 0.282 ab
## 7 2 2.12 0.170 ab
## 8 3 2.12 0.147 ab
## 9 12 1.99 0.104 ab
## 10 4 1.91 0.0321 ab
## 11 15 1.91 0.0872 ab
## 12 7 1.82 0.0416 ab
## 13 14 1.81 0.00577 ab
## 14 5 1.41 1.22 ab
## 15 13 1.41 1.22 ab
## 16 6 0.603 1.05 b
cld <- multcompLetters4(Prop.aov, tukey.test_prop)
dt_propionic <- group_by(mydata, mydata$Group) %>%
summarise(m = mean(Propionic), sd = sd(Propionic)) %>%
arrange(desc(m))
cld <- as.data.frame.list(cld$group)
dt_propionic$cld <- cld$Letters
print(dt_propionic)
## # A tibble: 16 × 4
## `mydata$Group` m sd cld
## <int> <dbl> <dbl> <chr>
## 1 10 1.68 0.150 a
## 2 2 1.53 0.0600 ab
## 3 9 1.53 0.0115 ab
## 4 11 1.5 0.0100 ab
## 5 1 1.48 0 ab
## 6 8 1.45 0 ab
## 7 3 0.997 0.864 b
## 8 4 0 0 c
## 9 5 0 0 c
## 10 6 0 0 c
## 11 7 0 0 c
## 12 12 0 0 c
## 13 13 0 0 c
## 14 14 0 0 c
## 15 15 0 0 c
## 16 16 0 0 c
cld <- multcompLetters4(Butyric.aov, tukey.test_butyric)
dt_butyric <- group_by(mydata, mydata$Group) %>%
summarise(m = mean(Butyric), sd = sd(Butyric)) %>%
arrange(desc(m))
cld <- as.data.frame.list(cld$group)
dt_butyric$cld <- cld$Letters
print(dt_butyric)
## # A tibble: 16 × 4
## `mydata$Group` m sd cld
## <int> <dbl> <dbl> <chr>
## 1 10 1.93 0.0917 a
## 2 11 1.36 0.0252 ab
## 3 2 1.35 0.107 ab
## 4 1 1.32 0.0100 ab
## 5 3 1.3 0.0436 ab
## 6 8 1.23 0 ab
## 7 9 0.927 0.805 abc
## 8 4 0.823 0.713 abc
## 9 16 0.42 0.727 bc
## 10 12 0.413 0.716 bc
## 11 5 0 0 c
## 12 6 0 0 c
## 13 7 0 0 c
## 14 13 0 0 c
## 15 14 0 0 c
## 16 15 0 0 c