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)
## ── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
## ✔ ggplot2 3.3.6     ✔ purrr   0.3.4
## ✔ tibble  3.1.7     ✔ dplyr   1.0.9
## ✔ tidyr   1.2.0     ✔ stringr 1.4.0
## ✔ readr   2.1.2     ✔ forcats 0.5.1
## ── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
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## ✖ dplyr::lag()    masks stats::lag()
library(dplyr)
library(reshape2)
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library(knitr)
library(afex)
## Loading required package: lme4
## Loading required package: Matrix
## 
## Attaching package: 'Matrix'
## 
## The following objects are masked from 'package:tidyr':
## 
##     expand, pack, unpack
## 
## ************
## 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")
## ************
## 
## Attaching package: 'afex'
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library(emmeans)
library(ggplot2)
library(psych)
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##     %+%, alpha
library(car)
## Loading required package: carData
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## Attaching package: '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