Nested Anova
# Load the workspace with the imported and prepared data
# data have been summarised previously, checked for normality, and if needed transformed
load("~/AgFace/Plant_Production/Environment_comparison/CO2_TOS_Irrigation_Cultivar_nested/Nested_design.RData")Setting up a split-split-plot design for each of the physical experimental designs in 2007 and 2008/2009 * Rings are split for TOS in 2007 * Rings are split for irrigation in 2008/2009
# ++++++++++++++++++++++++++++++++++++++++++++++++++===
# Nested AOV model
# 2007 aov(trans_value ~ CO2 * Irrigation * TOS * Cultivar +
# Error(RingID / TOS)
# 2008/9 aov(trans_value ~ CO2 * Irrigation * TOS * Cultivar +
# Error(RingID / Irrigation)
# ++++++++++++++++++++++++++++++++++++++++++++++++++===
# The dataframe "yj.homogeneous" has the homogeneous data for yitpi and janz
# The vector "trans_value" holds the measured data, or in case the measured dta mere not normally distributed, it holds the transformed data. (Box-Cox transformation not shown)# Create a small test data frame
# only yield data, for the year 2009
small.testdf <- yj.homogeneous[yj.homogeneous$Year == 2009 &
yj.homogeneous$TrialID == "Horsham" &
yj.homogeneous$Stage == "DC90" &
yj.homogeneous$variable == "Yield..g.m2.", ]
# show the data
small.testdf## TrialID Year RingID CO2 Irrigation TOS Cultivar Stage variable
## 45519 Horsham 2009 1 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45534 Horsham 2009 1 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45567 Horsham 2009 1 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45591 Horsham 2009 1 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45630 Horsham 2009 2 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45663 Horsham 2009 2 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45693 Horsham 2009 2 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45708 Horsham 2009 2 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45735 Horsham 2009 3 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45750 Horsham 2009 3 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45801 Horsham 2009 3 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45807 Horsham 2009 3 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45846 Horsham 2009 4 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45855 Horsham 2009 4 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45912 Horsham 2009 4 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45924 Horsham 2009 4 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45939 Horsham 2009 5 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45942 Horsham 2009 5 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45945 Horsham 2009 5 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45948 Horsham 2009 5 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45951 Horsham 2009 6 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45954 Horsham 2009 6 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45957 Horsham 2009 6 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45960 Horsham 2009 6 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45963 Horsham 2009 7 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45966 Horsham 2009 7 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45969 Horsham 2009 7 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45972 Horsham 2009 7 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45975 Horsham 2009 8 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45978 Horsham 2009 8 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45981 Horsham 2009 8 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45984 Horsham 2009 8 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45987 Horsham 2009 9 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45990 Horsham 2009 9 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45993 Horsham 2009 9 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45996 Horsham 2009 9 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45999 Horsham 2009 10 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 46002 Horsham 2009 10 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 46005 Horsham 2009 10 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 46008 Horsham 2009 10 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 46011 Horsham 2009 11 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 46014 Horsham 2009 11 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 46017 Horsham 2009 11 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 46020 Horsham 2009 11 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 46023 Horsham 2009 12 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 46026 Horsham 2009 12 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 46029 Horsham 2009 12 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 46032 Horsham 2009 12 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 46035 Horsham 2009 13 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 46038 Horsham 2009 13 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 46041 Horsham 2009 13 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 46044 Horsham 2009 13 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 46047 Horsham 2009 14 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 46050 Horsham 2009 14 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 46053 Horsham 2009 14 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 46056 Horsham 2009 14 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 46059 Horsham 2009 15 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 46062 Horsham 2009 15 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 46065 Horsham 2009 15 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 46068 Horsham 2009 15 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 46071 Horsham 2009 16 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 46074 Horsham 2009 16 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 46077 Horsham 2009 16 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 46080 Horsham 2009 16 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## value trans_value
## 45519 140.90 140.90
## 45534 185.04 185.04
## 45567 114.72 114.72
## 45591 173.01 173.01
## 45630 222.41 222.41
## 45663 247.95 247.95
## 45693 378.00 378.00
## 45708 363.94 363.94
## 45735 283.65 283.65
## 45750 398.44 398.44
## 45801 200.90 200.90
## 45807 233.26 233.26
## 45846 264.00 264.00
## 45855 299.54 299.54
## 45912 278.81 278.81
## 45924 330.06 330.06
## 45939 102.05 102.05
## 45942 281.23 281.23
## 45945 92.51 92.51
## 45948 153.00 153.00
## 45951 326.10 326.10
## 45954 261.86 261.86
## 45957 542.45 542.45
## 45960 398.23 398.23
## 45963 328.36 328.36
## 45966 219.32 219.32
## 45969 317.44 317.44
## 45972 340.86 340.86
## 45975 75.88 75.88
## 45978 110.05 110.05
## 45981 114.72 114.72
## 45984 164.65 164.65
## 45987 213.04 213.04
## 45990 301.60 301.60
## 45993 444.21 444.21
## 45996 360.42 360.42
## 45999 137.63 137.63
## 46002 88.64 88.64
## 46005 305.29 305.29
## 46008 257.05 257.05
## 46011 124.97 124.97
## 46014 118.38 118.38
## 46017 181.05 181.05
## 46020 194.87 194.87
## 46023 209.28 209.28
## 46026 202.54 202.54
## 46029 258.59 258.59
## 46032 205.15 205.15
## 46035 226.36 226.36
## 46038 180.59 180.59
## 46041 178.59 178.59
## 46044 205.78 205.78
## 46047 271.36 271.36
## 46050 277.76 277.76
## 46053 277.92 277.92
## 46056 204.15 204.15
## 46059 377.44 377.44
## 46062 436.55 436.55
## 46065 381.60 381.60
## 46068 283.54 283.54
## 46071 137.59 137.59
## 46074 101.91 101.91
## 46077 145.96 145.96
## 46080 183.04 183.04# set up the anova
nested.aov.2009 <- aov(trans_value ~ CO2 * TOS * Irrigation * Cultivar +
Error(RingID / Irrigation),
data = small.testdf,
na.action = na.omit)
summary(nested.aov.2009)##
## Error: RingID
## Df Sum Sq Mean Sq F value Pr(>F)
## CO2 1 83551 83551 10.7 0.0067 **
## TOS 1 255105 255105 32.7 9.6e-05 ***
## CO2:TOS 1 0 0 0.0 0.9957
## Residuals 12 93634 7803
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: RingID:Irrigation
## Df Sum Sq Mean Sq F value Pr(>F)
## Irrigation 1 30884 30884 4.56 0.054 .
## CO2:Irrigation 1 23154 23154 3.42 0.089 .
## TOS:Irrigation 1 3592 3592 0.53 0.480
## CO2:TOS:Irrigation 1 15 15 0.00 0.964
## Residuals 12 81248 6771
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: Within
## Df Sum Sq Mean Sq F value Pr(>F)
## Cultivar 1 18476 18476 8.59 0.0073 **
## CO2:Cultivar 1 382 382 0.18 0.6771
## TOS:Cultivar 1 168 168 0.08 0.7822
## Irrigation:Cultivar 1 1147 1147 0.53 0.4723
## CO2:TOS:Cultivar 1 110 110 0.05 0.8226
## CO2:Irrigation:Cultivar 1 72 72 0.03 0.8566
## TOS:Irrigation:Cultivar 1 345 345 0.16 0.6922
## CO2:TOS:Irrigation:Cultivar 1 1621 1621 0.75 0.3940
## Residuals 24 51627 2151
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1# For 2007:
small.testdf <- yj.homogeneous[yj.homogeneous$Year == 2007 &
yj.homogeneous$TrialID == "Horsham" &
yj.homogeneous$Stage == "DC90" &
yj.homogeneous$variable == "Yield..g.m2.", ]
# show the data
small.testdf## TrialID Year RingID CO2 Irrigation TOS Cultivar Stage variable
## 45507 Horsham 2007 1 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45513 Horsham 2007 1 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45525 Horsham 2007 1 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45531 Horsham 2007 1 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45540 Horsham 2007 2 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45546 Horsham 2007 2 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45549 Horsham 2007 2 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45555 Horsham 2007 2 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45564 Horsham 2007 3 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45573 Horsham 2007 3 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45579 Horsham 2007 3 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45582 Horsham 2007 3 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45594 Horsham 2007 4 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45597 Horsham 2007 4 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45606 Horsham 2007 4 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45612 Horsham 2007 4 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45615 Horsham 2007 5 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45621 Horsham 2007 5 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45627 Horsham 2007 5 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45636 Horsham 2007 5 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45642 Horsham 2007 6 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45648 Horsham 2007 6 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45657 Horsham 2007 6 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45666 Horsham 2007 6 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45669 Horsham 2007 7 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45675 Horsham 2007 7 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45684 Horsham 2007 7 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45687 Horsham 2007 7 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45696 Horsham 2007 8 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45702 Horsham 2007 8 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45711 Horsham 2007 8 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45717 Horsham 2007 8 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45726 Horsham 2007 9 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45732 Horsham 2007 9 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45738 Horsham 2007 9 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45744 Horsham 2007 9 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45756 Horsham 2007 10 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45759 Horsham 2007 10 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45768 Horsham 2007 10 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45774 Horsham 2007 10 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45780 Horsham 2007 11 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45786 Horsham 2007 11 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45792 Horsham 2007 11 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45798 Horsham 2007 11 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45810 Horsham 2007 12 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45816 Horsham 2007 12 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45819 Horsham 2007 12 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45828 Horsham 2007 12 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45834 Horsham 2007 13 aCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45840 Horsham 2007 13 aCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45843 Horsham 2007 13 aCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45849 Horsham 2007 13 aCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45864 Horsham 2007 14 aCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45870 Horsham 2007 14 aCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## 45873 Horsham 2007 14 aCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45879 Horsham 2007 14 aCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45885 Horsham 2007 15 eCO2 Rain TOS1 Janz DC90 Yield..g.m2.
## 45891 Horsham 2007 15 eCO2 Rain TOS1 Yitpi DC90 Yield..g.m2.
## 45900 Horsham 2007 15 eCO2 Rain TOS2 Yitpi DC90 Yield..g.m2.
## 45903 Horsham 2007 15 eCO2 Rain TOS2 Janz DC90 Yield..g.m2.
## 45915 Horsham 2007 16 eCO2 Sup TOS1 Janz DC90 Yield..g.m2.
## 45921 Horsham 2007 16 eCO2 Sup TOS1 Yitpi DC90 Yield..g.m2.
## 45927 Horsham 2007 16 eCO2 Sup TOS2 Yitpi DC90 Yield..g.m2.
## 45933 Horsham 2007 16 eCO2 Sup TOS2 Janz DC90 Yield..g.m2.
## value trans_value
## 45507 327.88 327.88
## 45513 299.07 299.07
## 45525 256.90 256.90
## 45531 235.09 235.09
## 45540 245.02 245.02
## 45546 315.51 315.51
## 45549 359.81 359.81
## 45555 279.60 279.60
## 45564 303.22 303.22
## 45573 396.94 396.94
## 45579 471.18 471.18
## 45582 406.54 406.54
## 45594 303.74 303.74
## 45597 329.44 329.44
## 45606 238.89 238.89
## 45612 341.86 341.86
## 45615 173.78 173.78
## 45621 217.73 217.73
## 45627 253.12 253.12
## 45636 300.62 300.62
## 45642 499.22 499.22
## 45648 381.62 381.62
## 45657 271.63 271.63
## 45666 269.46 269.46
## 45669 280.78 280.78
## 45675 257.15 257.15
## 45684 398.75 398.75
## 45687 397.98 397.98
## 45696 309.19 309.19
## 45702 302.18 302.18
## 45711 264.11 264.11
## 45717 212.48 212.48
## 45726 336.29 336.29
## 45732 267.69 267.69
## 45738 323.21 323.21
## 45744 527.26 527.26
## 45756 258.40 258.40
## 45759 119.14 119.14
## 45768 338.79 338.79
## 45774 228.97 228.97
## 45780 NA NA
## 45786 310.75 310.75
## 45792 97.76 97.76
## 45798 127.13 127.13
## 45810 342.68 342.68
## 45816 344.24 344.24
## 45819 90.16 90.16
## 45828 180.35 180.35
## 45834 197.68 197.68
## 45840 156.13 156.13
## 45843 154.98 154.98
## 45849 233.64 233.64
## 45864 225.55 225.55
## 45870 295.27 295.27
## 45873 353.58 353.58
## 45879 360.59 360.59
## 45885 292.83 292.83
## 45891 306.85 306.85
## 45900 120.33 120.33
## 45903 227.56 227.56
## 45915 445.48 445.48
## 45921 306.07 306.07
## 45927 294.09 294.09
## 45933 324.00 324.00# set up teh anova for the different nesting in 2007
nested.aov.2007 <- aov(trans_value ~ CO2 * TOS * Irrigation * Cultivar +
Error(RingID / TOS),
data = small.testdf,
na.action = na.omit)
summary(nested.aov.2007)##
## Error: RingID
## Df Sum Sq Mean Sq F value Pr(>F)
## CO2 1 30100 30100 4.91 0.049 *
## TOS 1 24769 24769 4.04 0.070 .
## Irrigation 1 88311 88311 14.40 0.003 **
## CO2:Irrigation 1 19618 19618 3.20 0.101
## Residuals 11 67472 6134
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: RingID:TOS
## Df Sum Sq Mean Sq F value Pr(>F)
## TOS 1 150430 150430 70.17 4.2e-06 ***
## Cultivar 1 7007 7007 3.27 0.098 .
## CO2:TOS 1 221 221 0.10 0.754
## TOS:Irrigation 1 11227 11227 5.24 0.043 *
## CO2:TOS:Irrigation 1 2687 2687 1.25 0.287
## Residuals 11 23583 2144
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: Within
## Df Sum Sq Mean Sq F value Pr(>F)
## Cultivar 1 1928 1928 0.53 0.48
## CO2:Cultivar 1 878 878 0.24 0.63
## TOS:Cultivar 1 172 172 0.05 0.83
## Irrigation:Cultivar 1 4308 4308 1.17 0.29
## CO2:TOS:Cultivar 1 303 303 0.08 0.78
## CO2:Irrigation:Cultivar 1 1305 1305 0.36 0.56
## TOS:Irrigation:Cultivar 1 1480 1480 0.40 0.53
## CO2:TOS:Irrigation:Cultivar 1 114 114 0.03 0.86
## Residuals 23 84451 3672# the resulting tables don't have the same structure as for 2009.
# TOS shows up in the "Error RingID" table.
# this is caused by an imbalance in the data.
# there is one missing value in the yield data
# if this gap is filled, the structure of the results table follows the same logic as in 2009
# however, gap-filling is not a good idea for a such a small data set
# replacing the missing value with the value of "300" - just for this example
small.testdf$trans_value[is.na(small.testdf$trans_value)] <- 300
nested.aov.2007 <- aov(trans_value ~ CO2 * TOS * Irrigation * Cultivar +
Error(RingID / TOS),
data = small.testdf,
na.action = na.omit)
summary(nested.aov.2007)##
## Error: RingID
## Df Sum Sq Mean Sq F value Pr(>F)
## CO2 1 29070 29070 4.77 0.0496 *
## Irrigation 1 101751 101751 16.69 0.0015 **
## CO2:Irrigation 1 15370 15370 2.52 0.1384
## Residuals 12 73180 6098
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: RingID:TOS
## Df Sum Sq Mean Sq F value Pr(>F)
## TOS 1 159180 159180 46.82 1.8e-05 ***
## CO2:TOS 1 110 110 0.03 0.86
## TOS:Irrigation 1 5810 5810 1.71 0.22
## CO2:TOS:Irrigation 1 258 258 0.08 0.79
## Residuals 12 40800 3400
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Error: Within
## Df Sum Sq Mean Sq F value Pr(>F)
## Cultivar 1 1753 1753 0.49 0.49
## CO2:Cultivar 1 697 697 0.19 0.66
## TOS:Cultivar 1 84 84 0.02 0.88
## Irrigation:Cultivar 1 3641 3641 1.02 0.32
## CO2:TOS:Cultivar 1 113 113 0.03 0.86
## CO2:Irrigation:Cultivar 1 1809 1809 0.51 0.48
## TOS:Irrigation:Cultivar 1 1023 1023 0.29 0.60
## CO2:TOS:Irrigation:Cultivar 1 11 11 0.00 0.96
## Residuals 24 85863 3578