Three-way ANOVA for biomass

Data from Maestre and Reynolds (2007)

Obs nitrohet nitrogen water biomass y
1 N 40 125 4.372 0.64068
2 N 40 125 4.482 0.65147
3 N 40 125 4.221 0.62542
4 N 40 125 3.977 0.59956
5 N 40 250 7.400 0.86923
6 N 40 250 8.027 0.90455
7 N 40 250 7.883 0.89669
8 N 40 250 7.769 0.89037
9 N 40 375 7.226 0.85890
10 N 40 375 8.126 0.90988
11 N 40 375 6.840 0.83506
12 N 40 375 7.901 0.89768
13 N 80 125 5.140 0.71096
14 N 80 125 3.913 0.59251
15 N 80 125 4.669 0.66922
16 N 80 125 4.306 0.63407
17 N 80 250 9.099 0.95899
18 N 80 250 9.711 0.98726
19 N 80 250 9.123 0.96014
20 N 80 250 9.709 0.98717
21 N 80 375 10.701 1.02942
22 N 80 375 11.552 1.06266
23 N 80 375 11.356 1.05523
24 N 80 375 9.759 0.98941
25 N 120 125 5.021 0.70079
26 N 120 125 4.970 0.69636
27 N 120 125 5.055 0.70372
28 N 120 125 4.862 0.68681
29 N 120 250 9.029 0.95564
30 N 120 250 10.791 1.03306
31 N 120 250 9.115 0.95976
32 N 120 250 10.319 1.01364
33 N 120 375 12.189 1.08597
34 N 120 375 14.381 1.15779
35 N 120 375 13.153 1.11902
36 N 120 375 14.066 1.14817
37 Y 40 125 5.458 0.73703
38 Y 40 125 5.017 0.70044
39 Y 40 125 5.479 0.73870
40 Y 40 125 5.714 0.75694
41 Y 40 250 8.972 0.95289
42 Y 40 250 9.234 0.96539
43 Y 40 250 8.032 0.90482
44 Y 40 250 8.372 0.92283
45 Y 40 375 9.464 0.97607
46 Y 40 375 9.563 0.98059
47 Y 40 375 9.385 0.97243
48 Y 40 375 8.226 0.91519
49 Y 80 125 6.616 0.82060
50 Y 80 125 6.909 0.83942
51 Y 80 125 6.851 0.83575
52 Y 80 125 6.098 0.78519
53 Y 80 250 10.792 1.03310
54 Y 80 250 10.164 1.00706
55 Y 80 250 10.947 1.03930
56 Y 80 250 9.582 0.98146
57 Y 80 375 14.936 1.17423
58 Y 80 375 13.607 1.13376
59 Y 80 375 14.231 1.15324
60 Y 80 375 12.038 1.08055
61 Y 120 125 7.389 0.86859
62 Y 120 125 6.683 0.82497
63 Y 120 125 7.759 0.88981
64 Y 120 125 6.752 0.82943
65 Y 120 250 10.731 1.03064
66 Y 120 250 12.640 1.10175
67 Y 120 250 10.350 1.01494
68 Y 120 250 11.550 1.06258
69 Y 120 375 14.697 1.16723
70 Y 120 375 17.826 1.25105
71 Y 120 375 14.711 1.16764
72 Y 120 375 13.614 1.13399
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y by nitrohet identified by nitrogen y 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 nitrohet N Y Three-way ANOVA for biomass Data from Maestre and Reynolds (2007) nitrogen 40 80 120
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y by nitrogen identified by water y 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 nitrogen 40 50 60 70 80 90 100 110 120 Three-way ANOVA for biomass Data from Maestre and Reynolds (2007) water 125 250 375
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y by nitrohet identified by water y 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 nitrohet N Y Three-way ANOVA for biomass Data from Maestre and Reynolds (2007) water 125 250 375
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y by nitrogen identified by water y 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 nitrogen 40 50 60 70 80 90 100 110 120 Three-way ANOVA for biomass Data from Maestre and Reynolds (2007) nitrohet=N water 125 250 375
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y by nitrogen identified by water y 0.7 0.8 0.9 1.0 1.1 1.2 1.3 nitrogen 40 50 60 70 80 90 100 110 120 Three-way ANOVA for biomass Data from Maestre and Reynolds (2007) nitrohet=Y water 125 250 375

Three-way ANOVA for biomass

Data from Maestre and Reynolds (2007)

The GLM Procedure

Class Level Information
Class Levels Values
nitrohet 2 N Y
nitrogen 3 40 80 120
water 3 125 250 375
Number of Observations Read 72
Number of Observations Used 72

Three-way ANOVA for biomass

Data from Maestre and Reynolds (2007)

The GLM Procedure

 

Dependent Variable: y

Source DF Sum of Squares Mean Square F Value Pr > F
Model 17 1.86010971 0.10941822 106.05 <.0001
Error 54 0.05571723 0.00103180    
Corrected Total 71 1.91582694      
R-Square Coeff Var Root MSE y Mean
0.970917 3.492176 0.032122 0.919818
Source DF Type I SS Mean Square F Value Pr > F
nitrohet 1 0.14872636 0.14872636 144.14 <.0001
nitrogen 2 0.26766625 0.13383312 129.71 <.0001
nitrohet*nitrogen 2 0.00191433 0.00095717 0.93 0.4017
water 2 1.35577897 0.67788949 657.00 <.0001
nitrohet*water 2 0.02702407 0.01351204 13.10 <.0001
nitrogen*water 4 0.05325694 0.01331423 12.90 <.0001
nitroh*nitroge*water 4 0.00574279 0.00143570 1.39 0.2492
Source DF Type III SS Mean Square F Value Pr > F
nitrohet 1 0.14872636 0.14872636 144.14 <.0001
nitrogen 2 0.26766625 0.13383312 129.71 <.0001
nitrohet*nitrogen 2 0.00191433 0.00095717 0.93 0.4017
water 2 1.35577897 0.67788949 657.00 <.0001
nitrohet*water 2 0.02702407 0.01351204 13.10 <.0001
nitrogen*water 4 0.05325694 0.01331423 12.90 <.0001
nitroh*nitroge*water 4 0.00574279 0.00143570 1.39 0.2492
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Panel of Fit Diagnostics for y Fit Diagnostics for y 0.9618 Adj R-Square 0.9709 R-Square 0.001 MSE 54 Error DF 18 Parameters 72 Observations Proportion Less 0 1 Residual 0 1 Fit–Mean -0.3 -0.1 0.1 -0.09 0.09 Residual 0 10 20 30 Percent 0 60 Observation 0.00 0.05 0.10 Cook's D 0.6 1.2 Predicted Value 0.6 0.8 1.0 1.2 y -2 0 2 Quantile -0.05 0.00 0.05 Residual 0.25 0.50 Leverage -2 0 2 RStudent 0.6 0.8 1.0 1.2 Predicted Value -2 0 2 RStudent 0.6 0.9 1.2 Predicted -0.05 0.00 0.05 Residual

Three-way ANOVA for biomass

Data from Maestre and Reynolds (2007)

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Tukey

nitrohet y LSMEAN H0:LSMean1=LSMean2
Pr > |t|
N 0.87436837 <.0001
Y 0.96526708  
nitrohet y LSMEAN 95% Confidence Limits
N 0.874368 0.863635 0.885102
Y 0.965267 0.954534 0.976000
Least Squares Means for Effect nitrohet
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 -0.090899 -0.106077 -0.075720
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y least-squares means for nitrohet. 0.88 0.90 0.92 0.94 0.96 y LS-Mean N Y nitrohet LS-Means for nitrohet
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of all pairwise y least-squares means differences for nitrohet with Tukey adjustment at significance level 0.05. y Comparisons for nitrohet N Y N Y 0.88 0.90 0.92 0.94 0.96 0.88 0.90 0.92 0.94 0.96
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Y N 0.9653 0.8744 nitrohet Estimate y Tukey Grouping for LS- Means of nitrohet (Alpha = 0.05) LS-means covered by the same bar are not significantly different.

Three-way ANOVA for biomass

Data from Maestre and Reynolds (2007)

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Tukey

nitrogen y LSMEAN LSMEAN Number
40 0.83761753 1
80 0.93836289 2
120 0.98347277 3
Least Squares Means for effect nitrogen
Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: y
i/j 1 2 3
1   <.0001 <.0001
2 <.0001   <.0001
3 <.0001 <.0001  
nitrogen y LSMEAN 95% Confidence Limits
40 0.837618 0.824472 0.850763
80 0.938363 0.925217 0.951508
120 0.983473 0.970327 0.996618
Least Squares Means for Effect nitrogen
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 -0.100745 -0.123092 -0.078399
1 3 -0.145855 -0.168202 -0.123509
2 3 -0.045110 -0.067457 -0.022763
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y least-squares means for nitrogen. 0.85 0.90 0.95 y LS-Mean 40 80 120 nitrogen LS-Means for nitrogen
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of all pairwise y least-squares means differences for nitrogen with Tukey adjustment at significance level 0.05. y Comparisons for nitrogen 40 80 120 40 80 120 0.85 0.90 0.95 1.00 0.85 0.90 0.95 1.00
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; 120 80 40 0.9835 0.9384 0.8376 nitrogen Estimate y Tukey Grouping for LS- Means of nitrogen (Alpha = 0.05) LS-means covered by the same bar are not significantly different.

Three-way ANOVA for biomass

Data from Maestre and Reynolds (2007)

The GLM Procedure

Least Squares Means

Adjustment for Multiple Comparisons: Tukey

water y LSMEAN LSMEAN Number
125 0.73076846 1
250 0.97638611 2
375 1.05229861 3
Least Squares Means for effect water
Pr > |t| for H0: LSMean(i)=LSMean(j)

Dependent Variable: y
i/j 1 2 3
1   <.0001 <.0001
2 <.0001   <.0001
3 <.0001 <.0001  
water y LSMEAN 95% Confidence Limits
125 0.730768 0.717623 0.743914
250 0.976386 0.963241 0.989532
375 1.052299 1.039153 1.065444
Least Squares Means for Effect water
i j Difference Between Means Simultaneous 95% Confidence Limits for LSMean(i)-LSMean(j)
1 2 -0.245618 -0.267964 -0.223271
1 3 -0.321530 -0.343877 -0.299183
2 3 -0.075913 -0.098259 -0.053566
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of y least-squares means for water. 0.8 0.9 1.0 y LS-Mean 125 250 375 water LS-Means for water
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; Plot of all pairwise y least-squares means differences for water with Tukey adjustment at significance level 0.05. y Comparisons for water 125 250 375 125 250 375 0.7 0.8 0.9 1.0 0.7 0.8 0.9 1.0
Three-way ANOVA for biomass; Data from Maestre and Reynolds 2007; 375 250 125 1.0523 0.9764 0.7308 water Estimate y Tukey Grouping for LS- Means of water (Alpha = 0.05) LS-means covered by the same bar are not significantly different.