Metabolomic analysis of spinach (Spinacia oleracea L.) grown under nutritional stress in hydroponic systems

Supplementary information

R script for Multivariate analysis - Magnesium stress condition in Spinach

Packages

library(mixOmics)
library(readxl)
library(textshape)
library(tidyverse)
library(ggpubr)
library(dplyr)
library(MVN)
library(vegan)
library(pairwiseAdonis)

Database “Magnesium Condition”

database.magnesium <- read.csv("C:/Users/cesar/Desktop/Tesis Maestria/TRATAMIENTOS/Magnesio/Magnesio Espinaca Anovas.csv")

database.magnesium

##    Sample  Condition Valine Alanine   GABA Glutamate Malate Succinate Citrate
## 1       1   Standard  252.2   408.3 1506.8    1329.9   88.8      61.4   157.1
## 2       2   Standard   48.9    88.1  145.9     401.0   36.0       8.1    47.1
## 3       3   Standard   58.7    87.8  237.2     589.7  143.9      28.6   211.7
## 4       4   Standard   93.5   158.8  371.1     531.5  106.0      17.2   171.2
## 5       5   Standard   84.8   146.3  271.8     491.6   42.9      14.5    57.6
## 6       6   Standard  125.6   188.4  538.6     772.2  197.3     106.4   243.1
## 7       7   Standard   71.0   103.0  305.0     448.1   47.2      17.1   110.4
## 8       8   Standard   56.5   106.5  194.9     510.4   34.5      17.9   141.5
## 9       9   Standard  129.6   240.5  607.0     637.6   62.2      37.4   115.6
## 10     10   Standard  129.3   241.4  607.5     724.3   74.2      37.0   114.2
## 11     11 Deficiency   98.1   219.7  417.2     639.7  102.1      28.3    98.2
## 12     12 Deficiency  112.5   143.4  417.5     360.2  189.8      15.5   211.3
## 13     13 Deficiency  435.2   511.2 1614.7    1505.2  404.8      20.8   678.9
## 14     14 Deficiency  196.8   210.6  586.1     397.3  410.5      25.7   551.3
## 15     15 Deficiency  186.1   207.3  692.0     511.4  268.3      13.1   249.0
## 16     16 Deficiency   74.3   112.6  193.9     282.7  634.5      29.3   333.7
## 17     17 Deficiency  167.1   165.0  497.2     447.5  247.0      18.3   252.2
## 18     18 Deficiency  259.3   298.8  860.0     641.8  187.1      20.1   370.5
## 19     19 Deficiency  178.2   193.7  587.6     492.8  354.7      29.1   378.5
## 20     20 Deficiency  302.7   336.2  962.3     856.9  732.6      36.0   792.1
## 21     21     Excess  378.2   493.4 1680.6    1269.4  720.0      64.9  1742.0
## 22     22     Excess  303.7   310.5  813.5     721.7  986.5      61.5  1036.8
## 23     23     Excess  262.7   292.7  700.1     678.4 1252.8      96.3  1374.7
## 24     24     Excess  846.7   910.6 2271.4    2347.3  899.9     150.7  1330.3
## 25     25     Excess  181.2   163.4  567.6     498.0  434.5      39.3   627.3
## 26     26     Excess  292.9   335.4  875.5     868.0  214.8      26.8   534.4
## 27     27     Excess  680.5   751.5 2210.4    2046.9 2362.9     185.5  1867.0
## 28     28     Excess  243.8   309.0 1004.8    1031.6  392.0      53.7   750.1
## 29     29     Excess  221.3   195.7  459.9     751.7  319.1      32.1   404.0
## 30     30     Excess  248.6   288.8  829.2     601.4 1400.2      36.9   642.4
##    Aspartate Betaine Glucose Fructose Sucrose Ascorbate Uridine Adenosine
## 1      897.7  1845.8   250.7    275.7    45.2     876.7   330.7     385.0
## 2      192.4   373.5    89.8     67.6    40.7      76.5    58.4      52.7
## 3      142.7   686.8   161.1    162.6    42.8     123.9    95.1      85.2
## 4      322.4   761.7   167.5    145.2    29.0      45.2   132.9      96.1
## 5      342.0   556.9   150.7    106.2    21.6     113.7   114.4      99.9
## 6      456.2  1288.1   269.3    166.4   120.7     277.9   148.3     120.4
## 7      149.2   664.6   145.0    144.5    17.2     116.9   118.8     113.0
## 8      136.2   611.0   129.5    111.3    26.6      80.6   104.7     101.4
## 9      492.3  1031.3   197.3    169.0    13.8     254.6   222.3     193.8
## 10     477.4  1023.2   155.8    165.8    13.7     261.9   214.6     186.9
## 11     382.1   942.5   113.4     96.9    13.0     222.9   113.0     123.3
## 12     169.9  2524.3   423.2    213.8    31.7      22.3   120.9     139.8
## 13     926.9 11692.7  5805.9   1433.1  2356.4     330.8   502.1     543.7
## 14     371.8  3977.2  3941.0   1180.6  1362.8      70.1   157.0     163.1
## 15     337.1  4320.1  2959.9   1227.5  1336.3     108.0   178.4     185.5
## 16     186.0   595.2   439.1    308.6     0.0       0.0    70.0      59.8
## 17     227.6  2965.2  1955.0    798.1  1048.1      31.0   161.3     176.4
## 18     306.8  4185.7  3242.9   1140.5  1624.4      76.9   250.5     221.8
## 19     413.4  2820.8  1707.8    741.9   482.4       0.0   158.1     166.5
## 20     540.0  4440.0  5337.7   1833.4  2993.5       0.0   245.5     234.1
## 21    1203.4 11791.9  3437.6   1894.8   816.4    1070.6   387.8     387.1
## 22     451.7  5417.0  6457.4   1849.2  5057.2     224.5   154.3     169.9
## 23     489.5  4357.1  3848.3    987.7  1418.2     121.5   121.1     129.6
## 24     994.9 13270.7  9306.4   3152.6  4943.5    1009.3   390.8     454.7
## 25     241.4  4168.5  4470.8   1182.8  1942.2     115.1   166.4     179.5
## 26     422.6  6427.6  3125.0    934.4   978.0     327.2   213.2     237.9
## 27    1069.0 17994.7 14409.8   4909.8  5555.4     906.9   627.1     604.8
## 28     503.8  9519.8  6236.6   1416.3   458.3     370.9   335.1     365.5
## 29     272.3  4499.4  4873.5   1053.6  2754.3     142.1   156.0     175.3
## 30     463.5  4616.9 10031.8   1911.9  6507.8     373.4   160.6     168.4
##    Fumarate Tyrosine Phenylalanine Guanosine Formate Choline Ferulate Glycerol
## 1      37.3    101.0         104.3     361.7   137.7   569.8     75.4    429.8
## 2      18.6     31.9          37.0      58.4    35.9    91.5     14.9     97.6
## 3      35.3     32.7          37.1      97.8    53.6   107.6     26.8    138.4
## 4      35.5     59.0          71.7     139.4    50.6   207.0     30.1    170.8
## 5      21.6     49.1          51.9     111.0    70.1   178.4     27.9    158.7
## 6      58.3     65.9          71.4     134.5    32.4   224.0     25.9    249.9
## 7      17.4     37.1          40.2     127.4    46.0   123.3     36.1    144.8
## 8      16.2     32.2          37.9     113.1    52.9   141.6     31.2    123.1
## 9      30.0     60.9          60.6     225.6    58.8   322.4     60.5    263.6
## 10     29.2     60.0          63.5     225.3    58.3   326.2     58.6    289.8
## 11     20.0     44.3          48.9     121.2    60.1   221.0     36.1    178.4
## 12     58.1     53.4          56.2     159.2    35.6   193.5     20.9    176.8
## 13    166.9    258.2         248.3     736.8    91.6  1474.7     68.8    684.7
## 14    129.8    118.5         105.0     209.7    56.3   346.9     31.2    364.4
## 15    135.4    116.3          95.1     246.5    69.8   383.5     31.0    312.7
## 16    126.3     43.9          56.8      80.6    40.7   144.7     13.5    170.8
## 17     69.3     95.9          79.0     238.1    36.1   344.6     28.8    290.5
## 18     63.6    173.5         153.3     317.1    44.8   483.5     35.4    365.2
## 19    158.3     95.1          91.8     210.0    46.2   386.6     27.4    322.9
## 20    239.4    223.2         181.8     323.7    56.5   646.8     40.8    558.5
## 21    362.2    183.0         175.2     501.0    82.1   716.0    110.9    852.5
## 22    256.8    193.7         135.6     194.1    34.1   482.8     41.7    383.5
## 23    396.6    120.6         115.6     179.9    28.6   288.8     31.2    310.0
## 24    177.2    464.6         386.0     493.1    56.4   657.0     76.4    753.6
## 25    138.5     98.2          77.3     220.0    22.2   303.5     34.1    202.0
## 26     96.3    157.1         128.1     301.6    35.6   390.9     57.1    341.6
## 27    680.6    415.3         323.9     811.6   131.5   718.4    176.2    957.9
## 28    140.7    139.9         133.3     470.3    40.4   533.4     52.9    587.2
## 29     72.3    152.9          99.8     199.2    44.5   252.6     34.2    243.1
## 30    284.0    168.3         149.6     185.2    47.9   370.8     34.8    290.9
##    Isoleucine Leucine p.Cumarate
## 1       154.5   279.5       64.0
## 2        31.1    74.8        5.5
## 3        43.4    89.1        9.2
## 4        55.8   134.7       12.0
## 5        49.5   103.0       19.5
## 6        82.1   151.4       20.2
## 7        49.5    79.0       19.0
## 8        39.0    69.7       15.7
## 9        73.3   127.0       37.8
## 10       73.0   121.5       31.0
## 11       54.1    87.0        8.5
## 12       64.3   116.8       46.1
## 13      277.7   523.4       11.8
## 14      123.9   251.2       18.6
## 15      124.5   232.0       13.9
## 16       44.3   110.0       11.8
## 17      107.3   210.8        9.7
## 18      158.4   326.4       16.1
## 19      114.7   209.3       11.5
## 20      211.3   403.1       23.9
## 21      214.8   386.8       46.6
## 22      194.0   366.9       17.9
## 23      155.8   305.3       18.2
## 24      544.7  1050.5       39.6
## 25      103.9   184.4       15.0
## 26      181.9   306.4       15.9
## 27      379.2   729.8       62.0
## 28      155.2   278.4       22.3
## 29      152.4   256.2       13.5
## 30      174.4   334.3       26.8

Multivariate Normality test “Mardia’s test and Doornik-Hansen’s test”

spinach.data.normality.test <- database.magnesium[1:30, 3:28]

mardia.result <- mardia(spinach.data.normality.test)
mardia.result

##              Test   Statistic    p.value     Method
## 1 Mardia Skewness 3107.930853 0.98234086 asymptotic
## 2 Mardia Kurtosis   -2.534384 0.01126452 asymptotic

doornik.result <- doornik_hansen(spinach.data.normality.test)
doornik.result

##             Test Statistic df      p.value     Method
## 1 Doornik-Hansen  310.2427 52 1.920849e-38 asymptotic

One -Way PERMANOVA Test

spinach.permanova <- database.magnesium[1:30, 3:28]

dist_matrix <- vegdist(spinach.permanova, method = "euclidean")

spinach.permanova <- database.magnesium[1:30, 2:28]

set.seed(42)
res.permanova <- adonis2(dist_matrix ~ Condition,
                         data = spinach.permanova,
                         permutations = 9999,
                         method = "euclidean")
print(res.permanova)

## Permutation test for adonis under reduced model
## Permutation: free
## Number of permutations: 9999
## 
## adonis2(formula = dist_matrix ~ Condition, data = spinach.permanova, permutations = 9999, method = "euclidean")
##          Df   SumOfSqs      R2      F Pr(>F)    
## Model     2  561099694 0.50564 13.808  2e-04 ***
## Residual 27  548588232 0.49436                  
## Total    29 1109687925 1.00000                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

POST - HOC Pairwise PERMANOVA Test

spinach.permanova <- database.magnesium[1:30, 3:28]

dist_matrix <- vegdist(spinach.permanova, method = "euclidean")

spinach.permanova <- database.magnesium[1:30, 2:28]

result_pairwise <- pairwise.adonis(dist_matrix,
                                   factors = spinach.permanova$Condition,
                                   sim.method = "euclidean",
                                   p.adjust.m = "bonferroni",
                                   perm = 9999)
result_pairwise

##                    pairs Df SumsOfSqs   F.Model        R2 p.value p.adjusted
## 1 Standard vs Deficiency  1  83555231 10.275032 0.3633959  0.0002     0.0006
## 2     Standard vs Excess  1 550717480 24.307225 0.5745408  0.0001     0.0003
## 3   Deficiency vs Excess  1 207376829  6.874558 0.2763690  0.0048     0.0144
##   sig
## 1  **
## 2  **
## 3   .

Multivariate Data For sPCA and sPLS-DA

database <- read.csv("C:/Users/cesar/Desktop/Tesis Maestria/TRATAMIENTOS/Magnesio/Matriz Datos Espinaca Magnesio.csv")

database <- textshape::column_to_rownames(database, loc = 1)

spinach <- as.data.frame(database)

spinach <- subset(spinach, select= -c(Class))

X <- spinach

Y <- database$Class

dim(X)

## [1] 30 26

“Sparse Principal Component Analysis” sPCA

explainedVariance <- tune.pca(X, ncomp = 10, center = TRUE, scale = TRUE)

plot(explainedVariance)

test.keepX <- c(seq(26))

tune.spca.res <- tune.spca(X, ncomp = 3,
                           nrepeat = 5,
                           folds = 10,
                           test.keepX = test.keepX)

plot(tune.spca.res)

spca <- spca(X, ncomp = 3,
             scale = TRUE,
             center = TRUE)

plotIndiv(spca, comp = c(1, 2), ind.names = TRUE,
          group = database$Class,
          ellipse = TRUE,
          cutoff = 0.5,
          size.title = 15,
          size.legend = 15,
          size.xlabel = 15,
          size.ylabel = 15,
          col = c("red", "green", "blue"),
          legend = TRUE, title = 'Magnesium stress in Spinach')

plotVar(spca, comp = c(1, 2), var.names = TRUE,
        cutoff = 0,
        rad.in = 1,
        title = 'Magnesium stress in spinach')

biplot(spca, cex = 1,
       group = database$Class,
       pch.size = 5,
       cutoff = 0.5,
       size.legend = 20,
       size.xlabel = 20,
       size.ylabel = 20,
       col = c("red", "green", "blue"),
       title = 'Magnesium stress Spinach')

plotLoadings(spca, comp = 1,
             size.title = 1,
             size.name = 1,
             size.axis = 1,
             ncomp = 26)

plotLoadings(spca, comp = 2,
             size.title = 1,
             size.name = 1,
             size.axis = 1,
             ncomp = 26)

“Sparse Partial Least Squares-Discriminant Analysis” sPLS-DA

splsda <- splsda(X, Y, ncomp = 10, scale = TRUE)

set.seed(30)

plotIndiv(splsda, comp = c(1, 2), ind.names = TRUE,
          group = database$Class,
          ellipse = TRUE,
          cutoff = 0.5,
          size.title = 15,
          size.legend = 15,
          size.xlabel = 15,
          size.ylabel = 15,
          col = c("red", "green", "blue"),
          legend = TRUE, title = 'Magnesium stress in Spinach')

perf.splsda <- perf(splsda, validation = "Mfold", 
                     folds = 5, nrepeat = 50,
                     progressBar = FALSE, auc = TRUE)

plot(perf.splsda, sd = TRUE, legend.position = "vertical")

perf.splsda$choice.ncomp

##         max.dist centroids.dist mahalanobis.dist
## overall        6              3                4
## BER            6              3                4

tune.splsda <- tune.splsda(X, Y, ncomp = 4, 
                           validation = 'Mfold',
                           folds = 5, nrepeat = 50, 
                           dist = 'max.dist',
                           test.keepX = c (5, 10, 15, 20, 26),
                           measure = "BER")
plot(tune.splsda)

final.splsda <- splsda(X, Y, ncomp = 3, keepX = c(5, 5) , scale = TRUE)

plotIndiv(final.splsda, comp = c(1, 2), ind.names = TRUE,
          group = database$Class,
          ellipse = TRUE,
          cutoff = 0.5,
          size.title = 15,
          size.legend = 15,
          size.xlabel = 15,
          size.ylabel = 15,
          col = c("red", "green", "blue"),
          legend = TRUE, title = 'Magnesium stress in Spinach')

plotVar(final.splsda, comp = c(1, 2), var.names = TRUE,
        cutoff = 0,
        rad.in = 1,
        title = 'Magnesium stress in spinach')

biplot(final.splsda, cex = 1,
       group = database$Class,
       pch.size = 5,
       cutoff = 0,
       size.legend = 20,
       size.xlabel = 20,
       size.ylabel = 20,
       col = c("red", "green", "blue"),
       title = 'Magnesium stress in Spinach')

plotLoadings(final.splsda, comp = 1,
             size.title = 1,
             size.name = 1)

plotLoadings(final.splsda, comp = 2,
             size.title = 1,
             size.name = 1)

sPLS-DA model evaluation

perf.res <- perf.assess(final.splsda, dist = "max.dist",
                        validation = "Mfold", 
                        folds = 5, 
                        nrepeat = 50)

perf.res$error.rate$overall[,'max.dist']

## [1] 0.2073333

perf.res$error.rate.class$max.dist

## Deficiency     Excess   Standard 
##      0.336      0.270      0.016

summary(Y)

##    Length  N.unique   N.blank Min.nchar Max.nchar 
##        30         3         0         6        10

perf.res$error.rate$BER[,'max.dist']

## [1] 0.2073333

auc.plsda <- auroc(final.splsda, roc.comp = 4, print = FALSE)

Analysis of Variance ANOVA for metabolites detected

ANOVATest.data <- read.csv("C:/Users/cesar/Desktop/Tesis Maestria/TRATAMIENTOS/Magnesio/Magnesio Espinaca Anovas.csv")

attach(ANOVATest.data)

str(ANOVATest.data)

## 'data.frame':    30 obs. of  28 variables:
##  $ Sample       : int  1 2 3 4 5 6 7 8 9 10 ...
##  $ Condition    : chr  "Standard" "Standard" "Standard" "Standard" ...
##  $ Valine       : num  252.2 48.9 58.7 93.5 84.8 ...
##  $ Alanine      : num  408.3 88.1 87.8 158.8 146.3 ...
##  $ GABA         : num  1507 146 237 371 272 ...
##  $ Glutamate    : num  1330 401 590 532 492 ...
##  $ Malate       : num  88.8 36 143.9 106 42.9 ...
##  $ Succinate    : num  61.4 8.1 28.6 17.2 14.5 ...
##  $ Citrate      : num  157.1 47.1 211.7 171.2 57.6 ...
##  $ Aspartate    : num  898 192 143 322 342 ...
##  $ Betaine      : num  1846 374 687 762 557 ...
##  $ Glucose      : num  250.7 89.8 161.1 167.5 150.7 ...
##  $ Fructose     : num  275.7 67.6 162.6 145.2 106.2 ...
##  $ Sucrose      : num  45.2 40.7 42.8 29 21.6 ...
##  $ Ascorbate    : num  876.7 76.5 123.9 45.2 113.7 ...
##  $ Uridine      : num  330.7 58.4 95.1 132.9 114.4 ...
##  $ Adenosine    : num  385 52.7 85.2 96.1 99.9 ...
##  $ Fumarate     : num  37.3 18.6 35.3 35.5 21.6 58.3 17.4 16.2 30 29.2 ...
##  $ Tyrosine     : num  101 31.9 32.7 59 49.1 65.9 37.1 32.2 60.9 60 ...
##  $ Phenylalanine: num  104.3 37 37.1 71.7 51.9 ...
##  $ Guanosine    : num  361.7 58.4 97.8 139.4 111 ...
##  $ Formate      : num  137.7 35.9 53.6 50.6 70.1 ...
##  $ Choline      : num  569.8 91.5 107.6 207 178.4 ...
##  $ Ferulate     : num  75.4 14.9 26.8 30.1 27.9 25.9 36.1 31.2 60.5 58.6 ...
##  $ Glycerol     : num  429.8 97.6 138.4 170.8 158.7 ...
##  $ Isoleucine   : num  154.5 31.1 43.4 55.8 49.5 ...
##  $ Leucine      : num  279.5 74.8 89.1 134.7 103 ...
##  $ p.Cumarate   : num  64 5.5 9.2 12 19.5 20.2 19 15.7 37.8 31 ...

Alanine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Alanine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Alanine[Condition == "Standard"]
## W = 0.84195, p-value = 0.04656

with(ANOVATest.data, shapiro.test(Alanine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Alanine[Condition == "Deficiency"]
## W = 0.8615, p-value = 0.07947

with(ANOVATest.data, shapiro.test(Alanine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Alanine[Condition == "Excess"]
## W = 0.81621, p-value = 0.0228

Hm_var <- bartlett.test(Alanine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Alanine by Condition
## Bartlett's K-squared = 8.3228, df = 2, p-value = 0.01559

#### ONE WAY - ANOVA

OneWay_test <- aov(Alanine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Condition    2 277799  138899   5.026 0.0139 *
## Residuals   27 746116   27634                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Alanine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency    165.25  -19.07575 349.57575 0.0853098
## Standard-Deficiency  -62.94 -247.26575 121.38575 0.6778003
## Standard-Excess     -228.19 -412.51575 -43.86425 0.0130078

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Alanine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Valine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Valine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Valine[Condition == "Standard"]
## W = 0.81302, p-value = 0.02086

with(ANOVATest.data, shapiro.test(Valine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Valine[Condition == "Deficiency"]
## W = 0.91423, p-value = 0.3114

with(ANOVATest.data, shapiro.test(Valine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Valine[Condition == "Excess"]
## W = 0.748, p-value = 0.003374

Hm_var <- bartlett.test(Valine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Valine by Condition
## Bartlett's K-squared = 13.183, df = 2, p-value = 0.001372

#### ONE WAY - ANOVA

OneWay_test <- aov(Valine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Condition    2 348389  174194   8.231 0.00162 **
## Residuals   27 571433   21164                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Valine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff         lwr       upr     p adj
## Excess-Deficiency    164.93    3.618443 326.24156 0.0443298
## Standard-Deficiency  -96.02 -257.331557  65.29156 0.3180392
## Standard-Excess     -260.95 -422.261557 -99.63844 0.0012124

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Valine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Leucine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Leucine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Leucine[Condition == "Standard"]
## W = 0.77811, p-value = 0.007851

with(ANOVATest.data, shapiro.test(Leucine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Leucine[Condition == "Deficiency"]
## W = 0.92304, p-value = 0.383

with(ANOVATest.data, shapiro.test(Leucine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Leucine[Condition == "Excess"]
## W = 0.74017, p-value = 0.002709

Hm_var <- bartlett.test(Leucine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Leucine by Condition
## Bartlett's K-squared = 15.229, df = 2, p-value = 0.0004932

#### ONE WAY - ANOVA

OneWay_test <- aov(Leucine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)   
## Condition    2 444818  222409    7.16 0.0032 **
## Residuals   27 838689   31063                  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Leucine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr        upr     p adj
## Excess-Deficiency    172.90  -22.52644  368.32644 0.0904462
## Standard-Deficiency -124.03 -319.45644   71.39644 0.2740697
## Standard-Excess     -296.93 -492.35644 -101.50356 0.0022811

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Leucine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Isoleucine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Isoleucine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Isoleucine[Condition == "Standard"]
## W = 0.7912, p-value = 0.01133

with(ANOVATest.data, shapiro.test(Isoleucine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Isoleucine[Condition == "Deficiency"]
## W = 0.9145, p-value = 0.3133

with(ANOVATest.data, shapiro.test(Isoleucine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Isoleucine[Condition == "Excess"]
## W = 0.74016, p-value = 0.002709

Hm_var <- bartlett.test(Isoleucine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Isoleucine by Condition
## Bartlett's K-squared = 13.01, df = 2, p-value = 0.001496

#### ONE WAY - ANOVA

OneWay_test <- aov(Isoleucine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Condition    2 130818   65409   8.035 0.00183 **
## Residuals   27 219786    8140                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Isoleucine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff         lwr       upr     p adj
## Excess-Deficiency     97.58   -2.462079 197.62208 0.0569563
## Standard-Deficiency  -62.93 -162.972079  37.11208 0.2800868
## Standard-Excess     -160.51 -260.552079 -60.46792 0.0013209

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Isoleucine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

GABA

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(GABA[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  GABA[Condition == "Standard"]
## W = 0.74473, p-value = 0.003078

with(ANOVATest.data, shapiro.test(GABA[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  GABA[Condition == "Deficiency"]
## W = 0.87848, p-value = 0.1253

with(ANOVATest.data, shapiro.test(GABA[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  GABA[Condition == "Excess"]
## W = 0.82517, p-value = 0.02926

Hm_var <- bartlett.test(GABA ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  GABA by Condition
## Bartlett's K-squared = 3.2936, df = 2, p-value = 0.1927

#### ONE WAY - ANOVA

OneWay_test <- aov(GABA ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value Pr(>F)  
## Condition    2 2303668 1151834   4.552 0.0198 *
## Residuals   27 6831841  253031                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = GABA ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff         lwr       upr     p adj
## Excess-Deficiency    458.45   -99.31556 1016.2156 0.1224463
## Standard-Deficiency -204.27  -762.03556  353.4956 0.6399837
## Standard-Excess     -662.72 -1220.48556 -104.9544 0.0174425

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = GABA, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Betaine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Betaine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Betaine[Condition == "Standard"]
## W = 0.8928, p-value = 0.1823

with(ANOVATest.data, shapiro.test(Betaine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Betaine[Condition == "Deficiency"]
## W = 0.77522, p-value = 0.00724

with(ANOVATest.data, shapiro.test(Betaine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Betaine[Condition == "Excess"]
## W = 0.83442, p-value = 0.03782

Hm_var <- bartlett.test(Betaine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Betaine by Condition
## Bartlett's K-squared = 29.582, df = 2, p-value = 3.77e-07

#### ONE WAY - ANOVA

OneWay_test <- aov(Betaine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df    Sum Sq   Mean Sq F value   Pr(>F)    
## Condition    2 271320466 135660233   12.58 0.000138 ***
## Residuals   27 291257977  10787332                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Betaine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                         diff         lwr        upr     p adj
## Excess-Deficiency    4359.99    718.1428  8001.8372 0.0165463
## Standard-Deficiency -2962.08  -6603.9272   679.7672 0.1274782
## Standard-Excess     -7322.07 -10963.9172 -3680.2228 0.0000916

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Betaine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Phenylalanine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Phenylalanine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Phenylalanine[Condition == "Standard"]
## W = 0.87191, p-value = 0.1052

with(ANOVATest.data, shapiro.test(Phenylalanine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Phenylalanine[Condition == "Deficiency"]
## W = 0.87001, p-value = 0.1

with(ANOVATest.data, shapiro.test(Phenylalanine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Phenylalanine[Condition == "Excess"]
## W = 0.77531, p-value = 0.007259

Hm_var <- bartlett.test(Phenylalanine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Phenylalanine by Condition
## Bartlett's K-squared = 15.518, df = 2, p-value = 0.0004269

#### ONE WAY - ANOVA

OneWay_test <- aov(Phenylalanine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Condition    2  66063   33032   6.716 0.00429 **
## Residuals   27 132801    4919                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Phenylalanine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency     60.82  -16.94494 138.58494 0.1472060
## Standard-Deficiency  -54.06 -131.82494  23.70494 0.2149225
## Standard-Excess     -114.88 -192.64494 -37.11506 0.0029817

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Phenylalanine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Tyrosine

#### PNORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Tyrosine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Tyrosine[Condition == "Standard"]
## W = 0.86164, p-value = 0.07978

with(ANOVATest.data, shapiro.test(Tyrosine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Tyrosine[Condition == "Deficiency"]
## W = 0.89713, p-value = 0.2037

with(ANOVATest.data, shapiro.test(Tyrosine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Tyrosine[Condition == "Excess"]
## W = 0.73831, p-value = 0.002571

Hm_var <- bartlett.test(Tyrosine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Tyrosine by Condition
## Bartlett's K-squared = 19.197, df = 2, p-value = 6.782e-05

#### ONE WAY - ANOVA

OneWay_test <- aov(Tyrosine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Condition    2 122806   61403   8.499 0.00137 **
## Residuals   27 195075    7225                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Tyrosine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff         lwr       upr     p adj
## Excess-Deficiency     87.13   -7.120481 181.38048 0.0741151
## Standard-Deficiency  -69.25 -163.500481  25.00048 0.1816555
## Standard-Excess     -156.38 -250.630481 -62.12952 0.0009259

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Tyrosine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Aspartate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Aspartate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Aspartate[Condition == "Standard"]
## W = 0.85705, p-value = 0.07042

with(ANOVATest.data, shapiro.test(Aspartate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Aspartate[Condition == "Deficiency"]
## W = 0.82581, p-value = 0.02979

with(ANOVATest.data, shapiro.test(Aspartate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Aspartate[Condition == "Excess"]
## W = 0.83438, p-value = 0.03778

Hm_var <- bartlett.test(Aspartate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Aspartate by Condition
## Bartlett's K-squared = 2.1035, df = 2, p-value = 0.3493

#### ONE WAY - ANOVA

OneWay_test <- aov(Aspartate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value Pr(>F)  
## Condition    2  379894  189947   2.555 0.0963 .
## Residuals   27 2007218   74341                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Aspartate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency    225.05  -77.27919 527.37919 0.1741778
## Standard-Deficiency  -25.31 -327.63919 277.01919 0.9765487
## Standard-Excess     -250.36 -552.68919  51.96919 0.1189389

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Aspartate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Glutamate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Glutamate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glutamate[Condition == "Standard"]
## W = 0.7728, p-value = 0.006765

with(ANOVATest.data, shapiro.test(Glutamate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glutamate[Condition == "Deficiency"]
## W = 0.78535, p-value = 0.009619

with(ANOVATest.data, shapiro.test(Glutamate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glutamate[Condition == "Excess"]
## W = 0.81076, p-value = 0.01959

Hm_var <- bartlett.test(Glutamate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Glutamate by Condition
## Bartlett's K-squared = 6.6875, df = 2, p-value = 0.0353

#### ONE WAY - ANOVA

OneWay_test <- aov(Glutamate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value Pr(>F)  
## Condition    2 1371678  685839   3.451 0.0463 *
## Residuals   27 5365535  198724                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Glutamate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency    467.89  -26.40854 962.18854 0.0661761
## Standard-Deficiency   30.08 -464.21854 524.37854 0.9875336
## Standard-Excess     -437.81 -932.10854  56.48854 0.0900055

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Glutamate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Adenosine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Adenosine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Adenosine[Condition == "Standard"]
## W = 0.75718, p-value = 0.004365

with(ANOVATest.data, shapiro.test(Adenosine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Adenosine[Condition == "Deficiency"]
## W = 0.73663, p-value = 0.002453

with(ANOVATest.data, shapiro.test(Adenosine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Adenosine[Condition == "Excess"]
## W = 0.85947, p-value = 0.07523

Hm_var <- bartlett.test(Adenosine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Adenosine by Condition
## Bartlett's K-squared = 2.0968, df = 2, p-value = 0.3505

#### ONE WAY - ANOVA

OneWay_test <- aov(Adenosine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Condition    2 104734   52367   3.086 0.0621 .
## Residuals   27 458224   16971                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Adenosine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr         upr     p adj
## Excess-Deficiency     85.87  -58.58144 230.3214387 0.3189633
## Standard-Deficiency  -57.96 -202.41144  86.4914387 0.5863696
## Standard-Excess     -143.83 -288.28144   0.6214387 0.0511586

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Adenosine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Guanosine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Guanosine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Guanosine[Condition == "Standard"]
## W = 0.84882, p-value = 0.05625

with(ANOVATest.data, shapiro.test(Guanosine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Guanosine[Condition == "Deficiency"]
## W = 0.77171, p-value = 0.006561

with(ANOVATest.data, shapiro.test(Guanosine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Guanosine[Condition == "Excess"]
## W = 0.81813, p-value = 0.02406

Hm_var <- bartlett.test(Guanosine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Guanosine by Condition
## Bartlett's K-squared = 5.9088, df = 2, p-value = 0.05211

#### ONE WAY - ANOVA

OneWay_test <- aov(Guanosine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Condition    2 192739   96370   3.402 0.0481 *
## Residuals   27 764844   28328                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Guanosine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr        upr     p adj
## Excess-Deficiency     91.31  -95.31472 277.934723 0.4558735
## Standard-Deficiency -104.87 -291.49472  81.754723 0.3584475
## Standard-Excess     -196.18 -382.80472  -9.555277 0.0379049

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Guanosine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Uridine

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Uridine[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Uridine[Condition == "Standard"]
## W = 0.88514, p-value = 0.1494

with(ANOVATest.data, shapiro.test(Uridine[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Uridine[Condition == "Deficiency"]
## W = 0.78845, p-value = 0.01049

with(ANOVATest.data, shapiro.test(Uridine[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Uridine[Condition == "Excess"]
## W = 0.829, p-value = 0.03254

Hm_var <- bartlett.test(Uridine ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Uridine by Condition
## Bartlett's K-squared = 3.9274, df = 2, p-value = 0.1403

#### ONE WAY - ANOVA

OneWay_test <- aov(Uridine ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Condition    2  70618   35309   2.245  0.125
## Residuals   27 424571   15725

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Uridine ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff       lwr      upr     p adj
## Excess-Deficiency     75.56  -63.4858 214.6058 0.3821209
## Standard-Deficiency  -41.66 -180.7058  97.3858 0.7404390
## Standard-Excess     -117.22 -256.2658  21.8258 0.1107869

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Uridine, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Glucose

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Glucose[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glucose[Condition == "Standard"]
## W = 0.92417, p-value = 0.3931

with(ANOVATest.data, shapiro.test(Glucose[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glucose[Condition == "Deficiency"]
## W = 0.93083, p-value = 0.4561

with(ANOVATest.data, shapiro.test(Glucose[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glucose[Condition == "Excess"]
## W = 0.87094, p-value = 0.1025

Hm_var <- bartlett.test(Glucose ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Glucose by Condition
## Bartlett's K-squared = 60.722, df = 2, p-value = 6.521e-14

#### ONE WAY - ANOVA

OneWay_test <- aov(Glucose ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df    Sum Sq   Mean Sq F value  Pr(>F)    
## Condition    2 212186595 106093297   18.56 8.5e-06 ***
## Residuals   27 154348876   5716625                    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Glucose ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                         diff       lwr        upr     p adj
## Excess-Deficiency    4027.13  1375.978  6678.2815 0.0022867
## Standard-Deficiency -2420.92 -5072.072   230.2315 0.0784773
## Standard-Excess     -6448.05 -9099.202 -3796.8985 0.0000057

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Glucose, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Fructose

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Fructose[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Fructose[Condition == "Standard"]
## W = 0.88925, p-value = 0.1663

with(ANOVATest.data, shapiro.test(Fructose[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Fructose[Condition == "Deficiency"]
## W = 0.95236, p-value = 0.6965

with(ANOVATest.data, shapiro.test(Fructose[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Fructose[Condition == "Excess"]
## W = 0.7775, p-value = 0.007718

Hm_var <- bartlett.test(Fructose ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Fructose by Condition
## Bartlett's K-squared = 43.572, df = 2, p-value = 3.455e-10

#### ONE WAY - ANOVA

OneWay_test <- aov(Fructose ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df   Sum Sq Mean Sq F value   Pr(>F)    
## Condition    2 15940480 7970240   12.83 0.000121 ***
## Residuals   27 16778720  621434                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Fructose ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                         diff        lwr       upr     p adj
## Excess-Deficiency    1031.87   157.7678 1905.9722 0.0182406
## Standard-Deficiency  -746.01 -1620.1122  128.0922 0.1053725
## Standard-Excess     -1777.88 -2651.9822 -903.7778 0.0000784

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Fructose, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Sucrose

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Sucrose[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Sucrose[Condition == "Standard"]
## W = 0.70463, p-value = 0.001002

with(ANOVATest.data, shapiro.test(Sucrose[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Sucrose[Condition == "Deficiency"]
## W = 0.91812, p-value = 0.3416

with(ANOVATest.data, shapiro.test(Sucrose[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Sucrose[Condition == "Excess"]
## W = 0.88536, p-value = 0.1502

Hm_var <- bartlett.test(Sucrose ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Sucrose by Condition
## Bartlett's K-squared = 63.292, df = 2, p-value = 1.804e-14

#### ONE WAY - ANOVA

OneWay_test <- aov(Sucrose ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df   Sum Sq  Mean Sq F value   Pr(>F)    
## Condition    2 46329841 23164921   11.31 0.000271 ***
## Residuals   27 55307184  2048414                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Sucrose ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                         diff        lwr        upr     p adj
## Excess-Deficiency    1918.27   331.2822  3505.2578 0.0154613
## Standard-Deficiency -1087.73 -2674.7178   499.2578 0.2237847
## Standard-Excess     -3006.00 -4592.9878 -1419.0122 0.0001978

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Sucrose, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Citrate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Citrate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Citrate[Condition == "Standard"]
## W = 0.96511, p-value = 0.8422

with(ANOVATest.data, shapiro.test(Citrate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Citrate[Condition == "Deficiency"]
## W = 0.93224, p-value = 0.4703

with(ANOVATest.data, shapiro.test(Citrate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Citrate[Condition == "Excess"]
## W = 0.91148, p-value = 0.2913

Hm_var <- bartlett.test(Citrate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Citrate by Condition
## Bartlett's K-squared = 27.647, df = 2, p-value = 9.919e-07

#### ONE WAY - ANOVA

OneWay_test <- aov(Citrate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value   Pr(>F)    
## Condition    2 4242403 2121201   19.68 5.34e-06 ***
## Residuals   27 2910066  107780                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Citrate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency    639.33   275.3025 1003.3575 0.0004909
## Standard-Deficiency -254.62  -618.6475  109.4075 0.2111204
## Standard-Excess     -893.95 -1257.9775 -529.9225 0.0000049

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Citrate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Malate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Malate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Malate[Condition == "Standard"]
## W = 0.86604, p-value = 0.08986

with(ANOVATest.data, shapiro.test(Malate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Malate[Condition == "Deficiency"]
## W = 0.91902, p-value = 0.3489

with(ANOVATest.data, shapiro.test(Malate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Malate[Condition == "Excess"]
## W = 0.88978, p-value = 0.1686

Hm_var <- bartlett.test(Malate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Malate by Condition
## Bartlett's K-squared = 37.472, df = 2, p-value = 7.297e-09

#### ONE WAY - ANOVA

OneWay_test <- aov(Malate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value   Pr(>F)    
## Condition    2 3447188 1723594   11.01 0.000319 ***
## Residuals   27 4226439  156535                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Malate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency    545.13   106.4275  983.8325 0.0126548
## Standard-Deficiency -269.84  -708.5425  168.8625 0.2953762
## Standard-Excess     -814.97 -1253.6725 -376.2675 0.0002517

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Malate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Succinate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Succinate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Succinate[Condition == "Standard"]
## W = 0.78901, p-value = 0.01066

with(ANOVATest.data, shapiro.test(Succinate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Succinate[Condition == "Deficiency"]
## W = 0.96197, p-value = 0.8081

with(ANOVATest.data, shapiro.test(Succinate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Succinate[Condition == "Excess"]
## W = 0.82201, p-value = 0.0268

Hm_var <- bartlett.test(Succinate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Succinate by Condition
## Bartlett's K-squared = 23.604, df = 2, p-value = 7.488e-06

#### ONE WAY - ANOVA

OneWay_test <- aov(Succinate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value  Pr(>F)   
## Condition    2  14510    7255   5.693 0.00865 **
## Residuals   27  34406    1274                   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Succinate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                       diff       lwr        upr     p adj
## Excess-Deficiency    51.15  11.56788 90.7321177 0.0093932
## Standard-Deficiency  10.94 -28.64212 50.5221177 0.7739923
## Standard-Excess     -40.21 -79.79212 -0.6278823 0.0459274

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Succinate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Fumarate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Fumarate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Fumarate[Condition == "Standard"]
## W = 0.88775, p-value = 0.16

with(ANOVATest.data, shapiro.test(Fumarate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Fumarate[Condition == "Deficiency"]
## W = 0.95799, p-value = 0.7627

with(ANOVATest.data, shapiro.test(Fumarate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Fumarate[Condition == "Excess"]
## W = 0.87624, p-value = 0.1181

Hm_var <- bartlett.test(Fumarate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Fumarate by Condition
## Bartlett's K-squared = 38.534, df = 2, p-value = 4.289e-09

#### ONE WAY - ANOVA

OneWay_test <- aov(Fumarate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value   Pr(>F)    
## Condition    2 271258  135629   10.65 0.000388 ***
## Residuals   27 343705   12730                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Fumarate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr        upr     p adj
## Excess-Deficiency    143.81   18.70464  268.91536 0.0218187
## Standard-Deficiency  -86.77 -211.87536   38.33536 0.2163533
## Standard-Excess     -230.58 -355.68536 -105.47464 0.0002772

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Fumarate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Formate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Formate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Formate[Condition == "Standard"]
## W = 0.72287, p-value = 0.001669

with(ANOVATest.data, shapiro.test(Formate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Formate[Condition == "Deficiency"]
## W = 0.8994, p-value = 0.2158

with(ANOVATest.data, shapiro.test(Formate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Formate[Condition == "Excess"]
## W = 0.79429, p-value = 0.01236

Hm_var <- bartlett.test(Formate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Formate by Condition
## Bartlett's K-squared = 3.384, df = 2, p-value = 0.1841

#### ONE WAY - ANOVA

OneWay_test <- aov(Formate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Condition    2    299   149.5   0.202  0.819
## Residuals   27  20031   741.9

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Formate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                      diff       lwr      upr     p adj
## Excess-Deficiency   -1.44 -31.64162 28.76162 0.9923270
## Standard-Deficiency  5.86 -24.34162 36.06162 0.8807923
## Standard-Excess      7.30 -22.90162 37.50162 0.8216674

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Formate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

p.Cumarate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(p.Cumarate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  p.Cumarate[Condition == "Standard"]
## W = 0.8493, p-value = 0.05699

with(ANOVATest.data, shapiro.test(p.Cumarate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  p.Cumarate[Condition == "Deficiency"]
## W = 0.72097, p-value = 0.001583

with(ANOVATest.data, shapiro.test(p.Cumarate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  p.Cumarate[Condition == "Excess"]
## W = 0.82944, p-value = 0.03294

Hm_var <- bartlett.test(p.Cumarate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  p.Cumarate by Condition
## Bartlett's K-squared = 1.74, df = 2, p-value = 0.4189

#### ONE WAY - ANOVA

OneWay_test <- aov(p.Cumarate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)
## Condition    2    566   283.1   1.237  0.306
## Residuals   27   6180   228.9

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = p.Cumarate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                      diff        lwr     upr     p adj
## Excess-Deficiency   10.59  -6.185797 27.3658 0.2776908
## Standard-Deficiency  6.20 -10.575797 22.9758 0.6348499
## Standard-Excess     -4.39 -21.165797 12.3858 0.7946027

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = p.Cumarate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Ferulate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Ferulate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Ferulate[Condition == "Standard"]
## W = 0.8708, p-value = 0.1021

with(ANOVATest.data, shapiro.test(Ferulate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Ferulate[Condition == "Deficiency"]
## W = 0.86499, p-value = 0.08735

with(ANOVATest.data, shapiro.test(Ferulate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Ferulate[Condition == "Excess"]
## W = 0.75421, p-value = 0.004016

Hm_var <- bartlett.test(Ferulate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Ferulate by Condition
## Bartlett's K-squared = 12.708, df = 2, p-value = 0.00174

#### ONE WAY - ANOVA

OneWay_test <- aov(Ferulate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df Sum Sq Mean Sq F value Pr(>F)  
## Condition    2   5705  2852.7   3.132 0.0598 .
## Residuals   27  24595   910.9                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Ferulate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                       diff        lwr       upr     p adj
## Excess-Deficiency    31.56  -1.905967 65.025967 0.0673896
## Standard-Deficiency   5.35 -28.115967 38.815967 0.9173085
## Standard-Excess     -26.21 -59.675967  7.255967 0.1464834

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Ferulate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Glycerol

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Glycerol[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glycerol[Condition == "Standard"]
## W = 0.87963, p-value = 0.1292

with(ANOVATest.data, shapiro.test(Glycerol[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glycerol[Condition == "Deficiency"]
## W = 0.87424, p-value = 0.112

with(ANOVATest.data, shapiro.test(Glycerol[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Glycerol[Condition == "Excess"]
## W = 0.87163, p-value = 0.1044

Hm_var <- bartlett.test(Glycerol ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Glycerol by Condition
## Bartlett's K-squared = 7.8601, df = 2, p-value = 0.01964

#### ONE WAY - ANOVA

OneWay_test <- aov(Glycerol ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value Pr(>F)  
## Condition    2  408102  204051   5.381 0.0108 *
## Residuals   27 1023887   37922                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Glycerol ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency    149.74  -66.18795 365.66795 0.2164462
## Standard-Deficiency -135.84 -351.76795  80.08795 0.2800185
## Standard-Excess     -285.58 -501.50795 -69.65205 0.0078123

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Glycerol, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Ascorbate

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Ascorbate[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Ascorbate[Condition == "Standard"]
## W = 0.66705, p-value = 0.0003521

with(ANOVATest.data, shapiro.test(Ascorbate[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Ascorbate[Condition == "Deficiency"]
## W = 0.79764, p-value = 0.01357

with(ANOVATest.data, shapiro.test(Ascorbate[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Ascorbate[Condition == "Excess"]
## W = 0.80878, p-value = 0.01853

Hm_var <- bartlett.test(Ascorbate ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Ascorbate by Condition
## Bartlett's K-squared = 10.945, df = 2, p-value = 0.004201

#### ONE WAY - ANOVA

OneWay_test <- aov(Ascorbate ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value Pr(>F)  
## Condition    2  740810  370405   5.142 0.0128 *
## Residuals   27 1945022   72038                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Ascorbate ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff        lwr       upr     p adj
## Excess-Deficiency    379.95   82.34165 677.55835 0.0103189
## Standard-Deficiency  136.59 -161.01835 434.19835 0.4996558
## Standard-Excess     -243.36 -540.96835  54.24835 0.1248970

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Ascorbate, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()

Choline

#### NORMALITY's TEST AND HOMOGENEITY OF VARIANCE

with(ANOVATest.data, shapiro.test(Choline[Condition == "Standard"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Choline[Condition == "Standard"]
## W = 0.84392, p-value = 0.04915

with(ANOVATest.data, shapiro.test(Choline[Condition == "Deficiency"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Choline[Condition == "Deficiency"]
## W = 0.71489, p-value = 0.001335

with(ANOVATest.data, shapiro.test(Choline[Condition == "Excess"]))

## 
##  Shapiro-Wilk normality test
## 
## data:  Choline[Condition == "Excess"]
## W = 0.90177, p-value = 0.2291

Hm_var <- bartlett.test(Choline ~ Condition, data =ANOVATest.data)
Hm_var

## 
##  Bartlett test of homogeneity of variances
## 
## data:  Choline by Condition
## Bartlett's K-squared = 9.4912, df = 2, p-value = 0.00869

#### ONE WAY - ANOVA

OneWay_test <- aov(Choline ~ Condition, data =ANOVATest.data)
summary(OneWay_test)

##             Df  Sum Sq Mean Sq F value Pr(>F)  
## Condition    2  377446  188723   2.823  0.077 .
## Residuals   27 1805009   66852                 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

#### POST-HOC TUKEY's Test

TukeyHSD(OneWay_test)

##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = Choline ~ Condition, data = ANOVATest.data)
## 
## $Condition
##                        diff       lwr       upr     p adj
## Excess-Deficiency      8.84 -277.8566 295.53658 0.9967833
## Standard-Deficiency -233.40 -520.0966  53.29658 0.1270292
## Standard-Excess     -242.24 -528.9366  44.45658 0.1097815

#### BOXPLOT

ggplot(ANOVATest.data, aes(x = Condition, y = Choline, fill = Condition)) +
  geom_boxplot() +
  geom_jitter (shape = 15,
               color = "steelblue",
               position = position_jitter(0.21)) +
  theme_classic()