Exercise 2
Winelyn Pelias
2022-09-26
Two-way Anova
Data
library(readxl)
Data1 <- read_excel("D:/Winelyn/Data1.xlsx")
View(Data1)
TT1<-Data1
TT1# A tibble: 27 × 5
PhaseInterval Temperature `Adlay with wash` `Adlay with mi…` `Adlay with mi…`
<chr> <chr> <dbl> <dbl> <dbl>
1 3- day 25°C 759 220 819
2 3- day 25°C 736 812 763
3 3- day 25°C 891 316 457
4 3- day 30°C 573 96 356
5 3- day 30°C 584 137 247
6 3- day 30°C 482 147 298
7 3- day 35°C 384 79 346
8 3- day 35°C 264 934 823
9 3- day 35°C 208 556 536
10 5-day 25°C 888 267 879
# … with 17 more rows#Start by loading the following R packages:
library(tidyverse)# data manipulation and visualizationWarning: package 'tidyverse' was built under R version 4.2.1── Attaching packages ─────────────────────────────────────── tidyverse 1.3.2 ──
✔ ggplot2 3.3.6 ✔ purrr 0.3.4
✔ tibble 3.1.7 ✔ dplyr 1.0.10
✔ tidyr 1.2.1 ✔ stringr 1.4.0
✔ readr 2.1.2 ✔ forcats 0.5.2 Warning: package 'ggplot2' was built under R version 4.2.1Warning: package 'tidyr' was built under R version 4.2.1Warning: package 'readr' was built under R version 4.2.1Warning: package 'dplyr' was built under R version 4.2.1Warning: package 'forcats' was built under R version 4.2.1── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag() masks stats::lag()library(ggpubr)#creating easily publication ready plotsWarning: package 'ggpubr' was built under R version 4.2.1library(rstatix)#pipe-friendly R functions for easy statistical analysesWarning: package 'rstatix' was built under R version 4.2.1
Attaching package: 'rstatix'
The following object is masked from 'package:stats':
filterlibrary(readxl)TT<-TT1%>%
gather(key = "Phase", value = CFUcount, `Adlay with wash`, `Adlay with milk`, `Adlay with milk and molasses`) %>%
convert_as_factor(PhaseInterval, Temperature)
TT# A tibble: 81 × 4
PhaseInterval Temperature Phase CFUcount
<fct> <fct> <chr> <dbl>
1 3- day 25°C Adlay with wash 759
2 3- day 25°C Adlay with wash 736
3 3- day 25°C Adlay with wash 891
4 3- day 30°C Adlay with wash 573
5 3- day 30°C Adlay with wash 584
6 3- day 30°C Adlay with wash 482
7 3- day 35°C Adlay with wash 384
8 3- day 35°C Adlay with wash 264
9 3- day 35°C Adlay with wash 208
10 5-day 25°C Adlay with wash 888
# … with 71 more rowsplot.design(CFUcount ~ ., data = TT)
Summary Statistics
CFU Count by Phase Interval
TT %>%
group_by(PhaseInterval) %>%
get_summary_stats(CFUcount, type = "mean_sd")# A tibble: 3 × 5
PhaseInterval variable n mean sd
<fct> <chr> <dbl> <dbl> <dbl>
1 3- day CFUcount 27 475. 267.
2 5-day CFUcount 27 284. 269.
3 7-day CFUcount 27 182. 271.CFU Count by Temperature
TT %>%
group_by(Temperature) %>%
get_summary_stats(CFUcount, type = "mean_sd")# A tibble: 3 × 5
Temperature variable n mean sd
<fct> <chr> <dbl> <dbl> <dbl>
1 25°C CFUcount 27 480. 353.
2 30°C CFUcount 27 231. 191.
3 35°C CFUcount 27 229. 243.CFU Count by Phase
TT %>%
group_by(Phase) %>%
get_summary_stats(CFUcount, type = "mean_sd")# A tibble: 3 × 5
Phase variable n mean sd
<chr> <chr> <dbl> <dbl> <dbl>
1 Adlay with milk CFUcount 27 188. 227.
2 Adlay with milk and molasses CFUcount 27 293. 261.
3 Adlay with wash CFUcount 27 459. 323.CFU Count by Temperature and Phase Interval
TT %>%
group_by(PhaseInterval, Temperature) %>%
get_summary_stats(CFUcount, type = "mean_sd")# A tibble: 9 × 6
PhaseInterval Temperature variable n mean sd
<fct> <fct> <chr> <dbl> <dbl> <dbl>
1 3- day 25°C CFUcount 9 641. 244.
2 3- day 30°C CFUcount 9 324. 187.
3 3- day 35°C CFUcount 9 459. 282.
4 5-day 25°C CFUcount 9 460. 346.
5 5-day 30°C CFUcount 9 250. 218.
6 5-day 35°C CFUcount 9 142. 98.7
7 7-day 25°C CFUcount 9 340. 416.
8 7-day 30°C CFUcount 9 120. 108.
9 7-day 35°C CFUcount 9 85.4 104. CFU Count by Temperature and Phase
TT %>%
group_by(Temperature, Phase) %>%
get_summary_stats(CFUcount, type = "mean_sd")# A tibble: 9 × 6
Temperature Phase variable n mean sd
<fct> <chr> <chr> <dbl> <dbl> <dbl>
1 25°C Adlay with milk CFUcount 9 243. 230.
2 25°C Adlay with milk and molasses CFUcount 9 416. 330.
3 25°C Adlay with wash CFUcount 9 783. 267.
4 30°C Adlay with milk CFUcount 9 91 57.9
5 30°C Adlay with milk and molasses CFUcount 9 193. 98.9
6 30°C Adlay with wash CFUcount 9 410. 213.
7 35°C Adlay with milk CFUcount 9 232. 309.
8 35°C Adlay with milk and molasses CFUcount 9 269. 271.
9 35°C Adlay with wash CFUcount 9 186. 135. CFU Count by PhaseInterval and Phase
TT %>%
group_by(PhaseInterval, Phase) %>%
get_summary_stats(CFUcount, type = "mean_sd")# A tibble: 9 × 6
PhaseInterval Phase variable n mean sd
<fct> <chr> <chr> <dbl> <dbl> <dbl>
1 3- day Adlay with milk CFUcount 9 366. 323.
2 3- day Adlay with milk and molasses CFUcount 9 516. 231.
3 3- day Adlay with wash CFUcount 9 542. 231.
4 5-day Adlay with milk CFUcount 9 145. 60.0
5 5-day Adlay with milk and molasses CFUcount 9 201. 260.
6 5-day Adlay with wash CFUcount 9 507. 281.
7 7-day Adlay with milk CFUcount 9 54.2 41.1
8 7-day Adlay with milk and molasses CFUcount 9 162. 125.
9 7-day Adlay with wash CFUcount 9 329. 422. CFU Count by Temperature, PhaseInterval and Phase
TT %>%
group_by(Temperature, PhaseInterval, Phase) %>%
get_summary_stats(CFUcount, type = "mean_sd")# A tibble: 27 × 7
PhaseInterval Temperature Phase variable n mean sd
<fct> <fct> <chr> <chr> <dbl> <dbl> <dbl>
1 3- day 25°C Adlay with milk CFUcount 3 449. 318.
2 3- day 25°C Adlay with milk and mol… CFUcount 3 680. 195.
3 3- day 25°C Adlay with wash CFUcount 3 795. 83.6
4 5-day 25°C Adlay with milk CFUcount 3 194 64.9
5 5-day 25°C Adlay with milk and mol… CFUcount 3 412. 406.
6 5-day 25°C Adlay with wash CFUcount 3 775. 228.
7 7-day 25°C Adlay with milk CFUcount 3 84.3 28.4
8 7-day 25°C Adlay with milk and mol… CFUcount 3 157. 169.
9 7-day 25°C Adlay with wash CFUcount 3 778. 476.
10 3- day 30°C Adlay with milk CFUcount 3 127. 27.0
# … with 17 more rowsPlots of two-way interaction effects of factors on CFUcount response variable
op <- par(mfrow = c(3, 1))
with(TT, {
interaction.plot(PhaseInterval, Temperature, CFUcount)
interaction.plot(PhaseInterval, Phase, CFUcount)
interaction.plot(Temperature, Phase, CFUcount)
}
)
Visualization
library(ggplot2)
ggplot(TT) +
aes(x = PhaseInterval, y = "CFUcount", color=PhaseInterval) +
geom_jitter() +
theme(legend.position = "none")
library(ggplot2)
ggplot(TT) +
aes(x = Temperature, y = "CFUcount", color=Temperature) +
geom_jitter() +
theme(legend.position = "none")
library(ggplot2)
ggplot(TT) +
aes(x = Phase, y = "CFUcount", color=Phase) +
geom_jitter() +
theme(legend.position = "none")
boxplot <- ggboxplot(TT,x ="PhaseInterval", y = "CFUcount", color = "PhaseInterval",palette = "jco")
boxplot
boxplot <- ggboxplot(TT,x ="Temperature", y = "CFUcount", color = "Temperature",palette = "jco")
boxplot
boxplot <- ggboxplot(TT,x ="Phase", y = "CFUcount", color = "Phase",palette = "jco")
boxplot
Inference and models of 3-way Anova
fm <- aov(CFUcount ~ Temperature * PhaseInterval * Phase, data = TT)
summary(fm) Df Sum Sq Mean Sq F value Pr(>F)
Temperature 2 1127928 563964 15.461 4.91e-06 ***
PhaseInterval 2 1196565 598283 16.402 2.72e-06 ***
Phase 2 1009439 504719 13.837 1.41e-05 ***
Temperature:PhaseInterval 4 141273 35318 0.968 0.432511
Temperature:Phase 4 868286 217071 5.951 0.000483 ***
PhaseInterval:Phase 4 183377 45844 1.257 0.298296
Temperature:PhaseInterval:Phase 8 344446 43056 1.180 0.327947
Residuals 54 1969686 36476
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1The main effects Temperature, Phase Interval and, Phase as well as the interactions between Temperature and Phase significantly influence the mean CFU count. Since the three-way interaction is not significant, it is now drop in the model in order to find the most provident model which better explains the variability in the data.
Without the three-way interaction in the model
fm <- update(fm, . ~ . -PhaseInterval:Temperature:Phase)
summary(fm) Df Sum Sq Mean Sq F value Pr(>F)
Temperature 2 1127928 563964 15.110 4.52e-06 ***
PhaseInterval 2 1196565 598283 16.029 2.45e-06 ***
Phase 2 1009439 504719 13.522 1.34e-05 ***
Temperature:PhaseInterval 4 141273 35318 0.946 0.443427
Temperature:Phase 4 868286 217071 5.816 0.000486 ***
PhaseInterval:Phase 4 183377 45844 1.228 0.308089
Residuals 62 2314132 37325
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1It provides the same results.
Multiple COmparison Test
TukeyHSD(fm) Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = CFUcount ~ Temperature + PhaseInterval + Phase + Temperature:PhaseInterval + Temperature:Phase + PhaseInterval:Phase, data = TT)
$Temperature
diff lwr upr p adj
30°C-25°C -249.00000 -375.2612 -122.7388 0.0000387
35°C-25°C -251.62963 -377.8909 -125.3684 0.0000323
35°C-30°C -2.62963 -128.8909 123.6316 0.9986221
$PhaseInterval
diff lwr upr p adj
5-day-3- day -190.7407 -317.0020 -64.47949 0.0016593
7-day-3- day -293.3333 -419.5946 -167.07209 0.0000017
7-day-5-day -102.5926 -228.8538 23.66866 0.1331498
$Phase
diff lwr upr
Adlay with milk and molasses-Adlay with milk 104.4074 -21.85384 230.6687
Adlay with wash-Adlay with milk 271.0741 144.81283 397.3353
Adlay with wash-Adlay with milk and molasses 166.6667 40.40542 292.9279
p adj
Adlay with milk and molasses-Adlay with milk 0.1242572
Adlay with wash-Adlay with milk 0.0000083
Adlay with wash-Adlay with milk and molasses 0.0066122
$`Temperature:PhaseInterval`
diff lwr upr p adj
30°C:3- day-25°C:3- day -317.000000 -609.69463 -24.305368 0.0241515
35°C:3- day-25°C:3- day -182.555556 -475.25019 110.139076 0.5462603
25°C:5-day-25°C:3- day -181.111111 -473.80574 111.583521 0.5569014
30°C:5-day-25°C:3- day -391.333333 -684.02797 -98.638702 0.0019196
35°C:5-day-25°C:3- day -499.333333 -792.02797 -206.638702 0.0000278
25°C:7-day-25°C:3- day -301.888889 -594.58352 -9.194257 0.0382290
30°C:7-day-25°C:3- day -521.666667 -814.36130 -228.972035 0.0000110
35°C:7-day-25°C:3- day -556.000000 -848.69463 -263.305368 0.0000026
35°C:3- day-30°C:3- day 134.444444 -158.25019 427.139076 0.8620933
25°C:5-day-30°C:3- day 135.888889 -156.80574 428.583521 0.8549406
30°C:5-day-30°C:3- day -74.333333 -367.02797 218.361298 0.9959589
35°C:5-day-30°C:3- day -182.333333 -475.02797 110.361298 0.5478965
25°C:7-day-30°C:3- day 15.111111 -277.58352 307.805743 1.0000000
30°C:7-day-30°C:3- day -204.666667 -497.36130 88.027965 0.3894424
35°C:7-day-30°C:3- day -239.000000 -531.69463 53.694632 0.1978946
25°C:5-day-35°C:3- day 1.444444 -291.25019 294.139076 1.0000000
30°C:5-day-35°C:3- day -208.777778 -501.47241 83.916854 0.3625212
35°C:5-day-35°C:3- day -316.777778 -609.47241 -24.083146 0.0243190
25°C:7-day-35°C:3- day -119.333333 -412.02797 173.361298 0.9244983
30°C:7-day-35°C:3- day -339.111111 -631.80574 -46.416479 0.0118841
35°C:7-day-35°C:3- day -373.444444 -666.13908 -80.749813 0.0036605
30°C:5-day-25°C:5-day -210.222222 -502.91685 82.472409 0.3532879
35°C:5-day-25°C:5-day -318.222222 -610.91685 -25.527591 0.0232491
25°C:7-day-25°C:5-day -120.777778 -413.47241 171.916854 0.9195219
30°C:7-day-25°C:5-day -340.555556 -633.25019 -47.860924 0.0113300
35°C:7-day-25°C:5-day -374.888889 -667.58352 -82.194257 0.0034773
35°C:5-day-30°C:5-day -108.000000 -400.69463 184.694632 0.9565848
25°C:7-day-30°C:5-day 89.444444 -203.25019 382.139076 0.9862098
30°C:7-day-30°C:5-day -130.333333 -423.02797 162.361298 0.8813333
35°C:7-day-30°C:5-day -164.666667 -457.36130 128.027965 0.6767451
25°C:7-day-35°C:5-day 197.444444 -95.25019 490.139076 0.4387931
30°C:7-day-35°C:5-day -22.333333 -315.02797 270.361298 0.9999995
35°C:7-day-35°C:5-day -56.666667 -349.36130 236.027965 0.9994120
30°C:7-day-25°C:7-day -219.777778 -512.47241 72.916854 0.2954456
35°C:7-day-25°C:7-day -254.111111 -546.80574 38.583521 0.1392936
35°C:7-day-30°C:7-day -34.333333 -327.02797 258.361298 0.9999867
$`Temperature:Phase`
diff
30°C:Adlay with milk-25°C:Adlay with milk -151.555556
35°C:Adlay with milk-25°C:Adlay with milk -10.888889
25°C:Adlay with milk and molasses-25°C:Adlay with milk 173.666667
30°C:Adlay with milk and molasses-25°C:Adlay with milk -49.444444
35°C:Adlay with milk and molasses-25°C:Adlay with milk 26.555556
25°C:Adlay with wash-25°C:Adlay with milk 540.000000
30°C:Adlay with wash-25°C:Adlay with milk 167.666667
35°C:Adlay with wash-25°C:Adlay with milk -56.888889
35°C:Adlay with milk-30°C:Adlay with milk 140.666667
25°C:Adlay with milk and molasses-30°C:Adlay with milk 325.222222
30°C:Adlay with milk and molasses-30°C:Adlay with milk 102.111111
35°C:Adlay with milk and molasses-30°C:Adlay with milk 178.111111
25°C:Adlay with wash-30°C:Adlay with milk 691.555556
30°C:Adlay with wash-30°C:Adlay with milk 319.222222
35°C:Adlay with wash-30°C:Adlay with milk 94.666667
25°C:Adlay with milk and molasses-35°C:Adlay with milk 184.555556
30°C:Adlay with milk and molasses-35°C:Adlay with milk -38.555556
35°C:Adlay with milk and molasses-35°C:Adlay with milk 37.444444
25°C:Adlay with wash-35°C:Adlay with milk 550.888889
30°C:Adlay with wash-35°C:Adlay with milk 178.555556
35°C:Adlay with wash-35°C:Adlay with milk -46.000000
30°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses -223.111111
35°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses -147.111111
25°C:Adlay with wash-25°C:Adlay with milk and molasses 366.333333
30°C:Adlay with wash-25°C:Adlay with milk and molasses -6.000000
35°C:Adlay with wash-25°C:Adlay with milk and molasses -230.555556
35°C:Adlay with milk and molasses-30°C:Adlay with milk and molasses 76.000000
25°C:Adlay with wash-30°C:Adlay with milk and molasses 589.444444
30°C:Adlay with wash-30°C:Adlay with milk and molasses 217.111111
35°C:Adlay with wash-30°C:Adlay with milk and molasses -7.444444
25°C:Adlay with wash-35°C:Adlay with milk and molasses 513.444444
30°C:Adlay with wash-35°C:Adlay with milk and molasses 141.111111
35°C:Adlay with wash-35°C:Adlay with milk and molasses -83.444444
30°C:Adlay with wash-25°C:Adlay with wash -372.333333
35°C:Adlay with wash-25°C:Adlay with wash -596.888889
35°C:Adlay with wash-30°C:Adlay with wash -224.555556
lwr
30°C:Adlay with milk-25°C:Adlay with milk -444.25019
35°C:Adlay with milk-25°C:Adlay with milk -303.58352
25°C:Adlay with milk and molasses-25°C:Adlay with milk -119.02797
30°C:Adlay with milk and molasses-25°C:Adlay with milk -342.13908
35°C:Adlay with milk and molasses-25°C:Adlay with milk -266.13908
25°C:Adlay with wash-25°C:Adlay with milk 247.30537
30°C:Adlay with wash-25°C:Adlay with milk -125.02797
35°C:Adlay with wash-25°C:Adlay with milk -349.58352
35°C:Adlay with milk-30°C:Adlay with milk -152.02797
25°C:Adlay with milk and molasses-30°C:Adlay with milk 32.52759
30°C:Adlay with milk and molasses-30°C:Adlay with milk -190.58352
35°C:Adlay with milk and molasses-30°C:Adlay with milk -114.58352
25°C:Adlay with wash-30°C:Adlay with milk 398.86092
30°C:Adlay with wash-30°C:Adlay with milk 26.52759
35°C:Adlay with wash-30°C:Adlay with milk -198.02797
25°C:Adlay with milk and molasses-35°C:Adlay with milk -108.13908
30°C:Adlay with milk and molasses-35°C:Adlay with milk -331.25019
35°C:Adlay with milk and molasses-35°C:Adlay with milk -255.25019
25°C:Adlay with wash-35°C:Adlay with milk 258.19426
30°C:Adlay with wash-35°C:Adlay with milk -114.13908
35°C:Adlay with wash-35°C:Adlay with milk -338.69463
30°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses -515.80574
35°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses -439.80574
25°C:Adlay with wash-25°C:Adlay with milk and molasses 73.63870
30°C:Adlay with wash-25°C:Adlay with milk and molasses -298.69463
35°C:Adlay with wash-25°C:Adlay with milk and molasses -523.25019
35°C:Adlay with milk and molasses-30°C:Adlay with milk and molasses -216.69463
25°C:Adlay with wash-30°C:Adlay with milk and molasses 296.74981
30°C:Adlay with wash-30°C:Adlay with milk and molasses -75.58352
35°C:Adlay with wash-30°C:Adlay with milk and molasses -300.13908
25°C:Adlay with wash-35°C:Adlay with milk and molasses 220.74981
30°C:Adlay with wash-35°C:Adlay with milk and molasses -151.58352
35°C:Adlay with wash-35°C:Adlay with milk and molasses -376.13908
30°C:Adlay with wash-25°C:Adlay with wash -665.02797
35°C:Adlay with wash-25°C:Adlay with wash -889.58352
35°C:Adlay with wash-30°C:Adlay with wash -517.25019
upr
30°C:Adlay with milk-25°C:Adlay with milk 141.13908
35°C:Adlay with milk-25°C:Adlay with milk 281.80574
25°C:Adlay with milk and molasses-25°C:Adlay with milk 466.36130
30°C:Adlay with milk and molasses-25°C:Adlay with milk 243.25019
35°C:Adlay with milk and molasses-25°C:Adlay with milk 319.25019
25°C:Adlay with wash-25°C:Adlay with milk 832.69463
30°C:Adlay with wash-25°C:Adlay with milk 460.36130
35°C:Adlay with wash-25°C:Adlay with milk 235.80574
35°C:Adlay with milk-30°C:Adlay with milk 433.36130
25°C:Adlay with milk and molasses-30°C:Adlay with milk 617.91685
30°C:Adlay with milk and molasses-30°C:Adlay with milk 394.80574
35°C:Adlay with milk and molasses-30°C:Adlay with milk 470.80574
25°C:Adlay with wash-30°C:Adlay with milk 984.25019
30°C:Adlay with wash-30°C:Adlay with milk 611.91685
35°C:Adlay with wash-30°C:Adlay with milk 387.36130
25°C:Adlay with milk and molasses-35°C:Adlay with milk 477.25019
30°C:Adlay with milk and molasses-35°C:Adlay with milk 254.13908
35°C:Adlay with milk and molasses-35°C:Adlay with milk 330.13908
25°C:Adlay with wash-35°C:Adlay with milk 843.58352
30°C:Adlay with wash-35°C:Adlay with milk 471.25019
35°C:Adlay with wash-35°C:Adlay with milk 246.69463
30°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses 69.58352
35°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses 145.58352
25°C:Adlay with wash-25°C:Adlay with milk and molasses 659.02797
30°C:Adlay with wash-25°C:Adlay with milk and molasses 286.69463
35°C:Adlay with wash-25°C:Adlay with milk and molasses 62.13908
35°C:Adlay with milk and molasses-30°C:Adlay with milk and molasses 368.69463
25°C:Adlay with wash-30°C:Adlay with milk and molasses 882.13908
30°C:Adlay with wash-30°C:Adlay with milk and molasses 509.80574
35°C:Adlay with wash-30°C:Adlay with milk and molasses 285.25019
25°C:Adlay with wash-35°C:Adlay with milk and molasses 806.13908
30°C:Adlay with wash-35°C:Adlay with milk and molasses 433.80574
35°C:Adlay with wash-35°C:Adlay with milk and molasses 209.25019
30°C:Adlay with wash-25°C:Adlay with wash -79.63870
35°C:Adlay with wash-25°C:Adlay with wash -304.19426
35°C:Adlay with wash-30°C:Adlay with wash 68.13908
p adj
30°C:Adlay with milk-25°C:Adlay with milk 0.7653129
35°C:Adlay with milk-25°C:Adlay with milk 1.0000000
25°C:Adlay with milk and molasses-25°C:Adlay with milk 0.6117119
30°C:Adlay with milk and molasses-25°C:Adlay with milk 0.9997855
35°C:Adlay with milk and molasses-25°C:Adlay with milk 0.9999982
25°C:Adlay with wash-25°C:Adlay with milk 0.0000051
30°C:Adlay with wash-25°C:Adlay with milk 0.6553245
35°C:Adlay with wash-25°C:Adlay with milk 0.9993949
35°C:Adlay with milk-30°C:Adlay with milk 0.8298726
25°C:Adlay with milk and molasses-30°C:Adlay with milk 0.0186450
30°C:Adlay with milk and molasses-30°C:Adlay with milk 0.9687340
35°C:Adlay with milk and molasses-30°C:Adlay with milk 0.5790210
25°C:Adlay with wash-30°C:Adlay with milk 0.0000000
30°C:Adlay with wash-30°C:Adlay with milk 0.0225336
35°C:Adlay with wash-30°C:Adlay with milk 0.9802806
25°C:Adlay with milk and molasses-35°C:Adlay with milk 0.5315548
30°C:Adlay with milk and molasses-35°C:Adlay with milk 0.9999675
35°C:Adlay with milk and molasses-35°C:Adlay with milk 0.9999740
25°C:Adlay with wash-35°C:Adlay with milk 0.0000032
30°C:Adlay with wash-35°C:Adlay with milk 0.5757444
35°C:Adlay with wash-35°C:Adlay with milk 0.9998753
30°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses 0.2766775
35°C:Adlay with milk and molasses-25°C:Adlay with milk and molasses 0.7928248
25°C:Adlay with wash-25°C:Adlay with milk and molasses 0.0047042
30°C:Adlay with wash-25°C:Adlay with milk and molasses 1.0000000
35°C:Adlay with wash-25°C:Adlay with milk and molasses 0.2375438
35°C:Adlay with milk and molasses-30°C:Adlay with milk and molasses 0.9952982
25°C:Adlay with wash-30°C:Adlay with milk and molasses 0.0000006
30°C:Adlay with wash-30°C:Adlay with milk and molasses 0.3109981
35°C:Adlay with wash-30°C:Adlay with milk and molasses 1.0000000
25°C:Adlay with wash-35°C:Adlay with milk and molasses 0.0000155
30°C:Adlay with wash-35°C:Adlay with milk and molasses 0.8274336
35°C:Adlay with wash-35°C:Adlay with milk and molasses 0.9912100
30°C:Adlay with wash-25°C:Adlay with wash 0.0038077
35°C:Adlay with wash-25°C:Adlay with wash 0.0000004
35°C:Adlay with wash-30°C:Adlay with wash 0.2687814
$`PhaseInterval:Phase`
diff
5-day:Adlay with milk-3- day:Adlay with milk -221.666667
7-day:Adlay with milk-3- day:Adlay with milk -312.111111
3- day:Adlay with milk and molasses-3- day:Adlay with milk 149.777778
5-day:Adlay with milk and molasses-3- day:Adlay with milk -165.666667
7-day:Adlay with milk and molasses-3- day:Adlay with milk -204.666667
3- day:Adlay with wash-3- day:Adlay with milk 176.000000
5-day:Adlay with wash-3- day:Adlay with milk 140.888889
7-day:Adlay with wash-3- day:Adlay with milk -37.444444
7-day:Adlay with milk-5-day:Adlay with milk -90.444444
3- day:Adlay with milk and molasses-5-day:Adlay with milk 371.444444
5-day:Adlay with milk and molasses-5-day:Adlay with milk 56.000000
7-day:Adlay with milk and molasses-5-day:Adlay with milk 17.000000
3- day:Adlay with wash-5-day:Adlay with milk 397.666667
5-day:Adlay with wash-5-day:Adlay with milk 362.555556
7-day:Adlay with wash-5-day:Adlay with milk 184.222222
3- day:Adlay with milk and molasses-7-day:Adlay with milk 461.888889
5-day:Adlay with milk and molasses-7-day:Adlay with milk 146.444444
7-day:Adlay with milk and molasses-7-day:Adlay with milk 107.444444
3- day:Adlay with wash-7-day:Adlay with milk 488.111111
5-day:Adlay with wash-7-day:Adlay with milk 453.000000
7-day:Adlay with wash-7-day:Adlay with milk 274.666667
5-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses -315.444444
7-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses -354.444444
3- day:Adlay with wash-3- day:Adlay with milk and molasses 26.222222
5-day:Adlay with wash-3- day:Adlay with milk and molasses -8.888889
7-day:Adlay with wash-3- day:Adlay with milk and molasses -187.222222
7-day:Adlay with milk and molasses-5-day:Adlay with milk and molasses -39.000000
3- day:Adlay with wash-5-day:Adlay with milk and molasses 341.666667
5-day:Adlay with wash-5-day:Adlay with milk and molasses 306.555556
7-day:Adlay with wash-5-day:Adlay with milk and molasses 128.222222
3- day:Adlay with wash-7-day:Adlay with milk and molasses 380.666667
5-day:Adlay with wash-7-day:Adlay with milk and molasses 345.555556
7-day:Adlay with wash-7-day:Adlay with milk and molasses 167.222222
5-day:Adlay with wash-3- day:Adlay with wash -35.111111
7-day:Adlay with wash-3- day:Adlay with wash -213.444444
7-day:Adlay with wash-5-day:Adlay with wash -178.333333
lwr
5-day:Adlay with milk-3- day:Adlay with milk -514.36130
7-day:Adlay with milk-3- day:Adlay with milk -604.80574
3- day:Adlay with milk and molasses-3- day:Adlay with milk -142.91685
5-day:Adlay with milk and molasses-3- day:Adlay with milk -458.36130
7-day:Adlay with milk and molasses-3- day:Adlay with milk -497.36130
3- day:Adlay with wash-3- day:Adlay with milk -116.69463
5-day:Adlay with wash-3- day:Adlay with milk -151.80574
7-day:Adlay with wash-3- day:Adlay with milk -330.13908
7-day:Adlay with milk-5-day:Adlay with milk -383.13908
3- day:Adlay with milk and molasses-5-day:Adlay with milk 78.74981
5-day:Adlay with milk and molasses-5-day:Adlay with milk -236.69463
7-day:Adlay with milk and molasses-5-day:Adlay with milk -275.69463
3- day:Adlay with wash-5-day:Adlay with milk 104.97203
5-day:Adlay with wash-5-day:Adlay with milk 69.86092
7-day:Adlay with wash-5-day:Adlay with milk -108.47241
3- day:Adlay with milk and molasses-7-day:Adlay with milk 169.19426
5-day:Adlay with milk and molasses-7-day:Adlay with milk -146.25019
7-day:Adlay with milk and molasses-7-day:Adlay with milk -185.25019
3- day:Adlay with wash-7-day:Adlay with milk 195.41648
5-day:Adlay with wash-7-day:Adlay with milk 160.30537
7-day:Adlay with wash-7-day:Adlay with milk -18.02797
5-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses -608.13908
7-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses -647.13908
3- day:Adlay with wash-3- day:Adlay with milk and molasses -266.47241
5-day:Adlay with wash-3- day:Adlay with milk and molasses -301.58352
7-day:Adlay with wash-3- day:Adlay with milk and molasses -479.91685
7-day:Adlay with milk and molasses-5-day:Adlay with milk and molasses -331.69463
3- day:Adlay with wash-5-day:Adlay with milk and molasses 48.97203
5-day:Adlay with wash-5-day:Adlay with milk and molasses 13.86092
7-day:Adlay with wash-5-day:Adlay with milk and molasses -164.47241
3- day:Adlay with wash-7-day:Adlay with milk and molasses 87.97203
5-day:Adlay with wash-7-day:Adlay with milk and molasses 52.86092
7-day:Adlay with wash-7-day:Adlay with milk and molasses -125.47241
5-day:Adlay with wash-3- day:Adlay with wash -327.80574
7-day:Adlay with wash-3- day:Adlay with wash -506.13908
7-day:Adlay with wash-5-day:Adlay with wash -471.02797
upr
5-day:Adlay with milk-3- day:Adlay with milk 71.02797
7-day:Adlay with milk-3- day:Adlay with milk -19.41648
3- day:Adlay with milk and molasses-3- day:Adlay with milk 442.47241
5-day:Adlay with milk and molasses-3- day:Adlay with milk 127.02797
7-day:Adlay with milk and molasses-3- day:Adlay with milk 88.02797
3- day:Adlay with wash-3- day:Adlay with milk 468.69463
5-day:Adlay with wash-3- day:Adlay with milk 433.58352
7-day:Adlay with wash-3- day:Adlay with milk 255.25019
7-day:Adlay with milk-5-day:Adlay with milk 202.25019
3- day:Adlay with milk and molasses-5-day:Adlay with milk 664.13908
5-day:Adlay with milk and molasses-5-day:Adlay with milk 348.69463
7-day:Adlay with milk and molasses-5-day:Adlay with milk 309.69463
3- day:Adlay with wash-5-day:Adlay with milk 690.36130
5-day:Adlay with wash-5-day:Adlay with milk 655.25019
7-day:Adlay with wash-5-day:Adlay with milk 476.91685
3- day:Adlay with milk and molasses-7-day:Adlay with milk 754.58352
5-day:Adlay with milk and molasses-7-day:Adlay with milk 439.13908
7-day:Adlay with milk and molasses-7-day:Adlay with milk 400.13908
3- day:Adlay with wash-7-day:Adlay with milk 780.80574
5-day:Adlay with wash-7-day:Adlay with milk 745.69463
7-day:Adlay with wash-7-day:Adlay with milk 567.36130
5-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses -22.74981
7-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses -61.74981
3- day:Adlay with wash-3- day:Adlay with milk and molasses 318.91685
5-day:Adlay with wash-3- day:Adlay with milk and molasses 283.80574
7-day:Adlay with wash-3- day:Adlay with milk and molasses 105.47241
7-day:Adlay with milk and molasses-5-day:Adlay with milk and molasses 253.69463
3- day:Adlay with wash-5-day:Adlay with milk and molasses 634.36130
5-day:Adlay with wash-5-day:Adlay with milk and molasses 599.25019
7-day:Adlay with wash-5-day:Adlay with milk and molasses 420.91685
3- day:Adlay with wash-7-day:Adlay with milk and molasses 673.36130
5-day:Adlay with wash-7-day:Adlay with milk and molasses 638.25019
7-day:Adlay with wash-7-day:Adlay with milk and molasses 459.91685
5-day:Adlay with wash-3- day:Adlay with wash 257.58352
7-day:Adlay with wash-3- day:Adlay with wash 79.25019
7-day:Adlay with wash-5-day:Adlay with wash 114.36130
p adj
5-day:Adlay with milk-3- day:Adlay with milk 0.2847174
7-day:Adlay with milk-3- day:Adlay with milk 0.0280868
3- day:Adlay with milk and molasses-3- day:Adlay with milk 0.7764964
5-day:Adlay with milk and molasses-3- day:Adlay with milk 0.6696406
7-day:Adlay with milk and molasses-3- day:Adlay with milk 0.3894424
3- day:Adlay with wash-3- day:Adlay with milk 0.5945719
5-day:Adlay with wash-3- day:Adlay with milk 0.8286553
7-day:Adlay with wash-3- day:Adlay with milk 0.9999740
7-day:Adlay with milk-5-day:Adlay with milk 0.9851974
3- day:Adlay with milk and molasses-5-day:Adlay with milk 0.0039295
5-day:Adlay with milk and molasses-5-day:Adlay with milk 0.9994608
7-day:Adlay with milk and molasses-5-day:Adlay with milk 0.9999999
3- day:Adlay with wash-5-day:Adlay with milk 0.0015204
5-day:Adlay with wash-5-day:Adlay with milk 0.0053672
7-day:Adlay with wash-5-day:Adlay with milk 0.5340028
3- day:Adlay with milk and molasses-7-day:Adlay with milk 0.0001273
5-day:Adlay with milk and molasses-7-day:Adlay with milk 0.7968194
7-day:Adlay with milk and molasses-7-day:Adlay with milk 0.9578552
3- day:Adlay with wash-7-day:Adlay with milk 0.0000440
5-day:Adlay with wash-7-day:Adlay with milk 0.0001814
7-day:Adlay with wash-7-day:Adlay with milk 0.0824539
5-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses 0.0253459
7-day:Adlay with milk and molasses-3- day:Adlay with milk and molasses 0.0070991
3- day:Adlay with wash-3- day:Adlay with milk and molasses 0.9999984
5-day:Adlay with wash-3- day:Adlay with milk and molasses 1.0000000
7-day:Adlay with wash-3- day:Adlay with milk and molasses 0.5120295
7-day:Adlay with milk and molasses-5-day:Adlay with milk and molasses 0.9999645
3- day:Adlay with wash-5-day:Adlay with milk and molasses 0.0109201
5-day:Adlay with wash-5-day:Adlay with milk and molasses 0.0332517
7-day:Adlay with wash-5-day:Adlay with milk and molasses 0.8905604
3- day:Adlay with wash-7-day:Adlay with milk and molasses 0.0028276
5-day:Adlay with wash-7-day:Adlay with milk and molasses 0.0095914
7-day:Adlay with wash-7-day:Adlay with milk and molasses 0.6585174
5-day:Adlay with wash-3- day:Adlay with wash 0.9999842
7-day:Adlay with wash-3- day:Adlay with wash 0.3331386
7-day:Adlay with wash-5-day:Adlay with wash 0.5773828