Multiple comparisons for algae cover

Data from Kneitel and Lessin (2010)

Obs treat richness total algae y
1 Control 8 78 1 0.10017
2 Control 5 84 7 0.26776
3 Control 10 115 45 0.73531
4 Control 7 200 100 1.57080
5 Control 6 72 20 0.46365
6 Low 8 73 15 0.39770
7 Low 7 124 70 0.99116
8 Low 8 116 50 0.78540
9 Low 8 92 5 0.22551
10 Low 7 138 60 0.88608
11 Medium 7 124 85 1.17310
12 Medium 8 116 80 1.10715
13 Medium 8 145 60 0.88608
14 Medium 6 154 100 1.57080
15 Medium 7 129 90 1.24905
16 High 6 134 95 1.34528
17 High 7 138 95 1.34528
18 High 8 103 70 0.99116
19 High 8 119 75 1.04720
20 High 6 132 80 1.10715
21 VeryHigh 6 148 95 1.34528
22 VeryHigh 5 134 95 1.34528
23 VeryHigh 5 119 100 1.57080
24 VeryHigh 5 117 90 1.24905
25 VeryHigh 5 129 80 1.10715
Multiple comparisons for algae cover; Data from Kneitel and Lessin 2010; Plot of y by treat y 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 treat Control High Low Medium VeryHigh Multiple comparisons for algae cover Data from Kneitel and Lessin (2010)

Multiple comparisons for algae cover

Data from Kneitel and Lessin (2010)

The GLM Procedure

Class Level Information
Class Levels Values
treat 5 Control High Low Medium VeryHigh
Number of Observations Read 25
Number of Observations Used 25

Multiple comparisons for algae cover

Data from Kneitel and Lessin (2010)

The GLM Procedure

 

Dependent Variable: y

Source DF Sum of Squares Mean Square F Value Pr > F
Model 4 2.13816313 0.53454078 4.76 0.0073
Error 20 2.24444069 0.11222203    
Corrected Total 24 4.38260382      
R-Square Coeff Var Root MSE y Mean
0.487875 33.68371 0.334996 0.994533
Source DF Type I SS Mean Square F Value Pr > F
treat 4 2.13816313 0.53454078 4.76 0.0073
Source DF Type III SS Mean Square F Value Pr > F
treat 4 2.13816313 0.53454078 4.76 0.0073
Multiple comparisons for algae cover; Data from Kneitel and Lessin 2010; Panel of Fit Diagnostics for y Fit Diagnostics for y 0.3855 Adj R-Square 0.4879 R-Square 0.1122 MSE 20 Error DF 5 Parameters 25 Observations Proportion Less 0 1 Residual 0 1 Fit–Mean -0.5 0.0 0.5 1.0 -0.9 0 0.9 Residual 0 10 20 30 40 Percent 0 10 20 Observation 0.0 0.2 0.4 Cook's D 0.0 0.5 1.0 1.5 Predicted Value 0.0 0.5 1.0 1.5 y -2 -1 0 1 2 Quantile -0.5 0.0 0.5 1.0 Residual 0.2 0.3 0.4 Leverage -2 0 2 4 RStudent 0.6 0.8 1.0 1.2 Predicted Value -2 0 2 4 RStudent 0.6 1.2 Predicted Value -0.5 0.0 0.5 1.0 Residual
Multiple comparisons for algae cover; Data from Kneitel and Lessin 2010; Fit Plot for y by treat 0.0 0.5 1.0 1.5 y Control High Low Medium VeryHigh treat Distribution of y 0.0 0.5 1.0 1.5 y Control High Low Medium VeryHigh treat 0.0073 Prob > F 4.76 F Distribution of y

Multiple comparisons for algae cover

Data from Kneitel and Lessin (2010)

The GLM Procedure

Multiple comparisons for algae cover; Data from Kneitel and Lessin 2010; Distribution of y by treat 0.0 0.5 1.0 1.5 y Control High Low Medium VeryHigh treat Distribution of y

Multiple comparisons for algae cover

Data from Kneitel and Lessin (2010)

The GLM Procedure

 

Tukey's Studentized Range (HSD) Test for y

Note:This test controls the Type I experimentwise error rate.

Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 0.112222
Critical Value of Studentized Range 4.23186
Minimum Significant Difference 0.634
Comparisons significant at the 0.05 level are indicated by ***.
treat
Comparison		 Difference
Between
Means		 Simultaneous 95% Confidence Limits  
VeryHigh - Medium 0.1263 -0.5077 0.7603  
VeryHigh - High 0.1563 -0.4777 0.7903  
VeryHigh - Low 0.6663 0.0323 1.3003 ***
VeryHigh - Control 0.6960 0.0620 1.3300 ***
Medium - VeryHigh -0.1263 -0.7603 0.5077  
Medium - High 0.0300 -0.6040 0.6640  
Medium - Low 0.5401 -0.0939 1.1741  
Medium - Control 0.5697 -0.0643 1.2037  
High - VeryHigh -0.1563 -0.7903 0.4777  
High - Medium -0.0300 -0.6640 0.6040  
High - Low 0.5100 -0.1239 1.1440  
High - Control 0.5397 -0.0943 1.1737  
Low - VeryHigh -0.6663 -1.3003 -0.0323 ***
Low - Medium -0.5401 -1.1741 0.0939  
Low - High -0.5100 -1.1440 0.1239  
Low - Control 0.0296 -0.6044 0.6636  
Control - VeryHigh -0.6960 -1.3300 -0.0620 ***
Control - Medium -0.5697 -1.2037 0.0643  
Control - High -0.5397 -1.1737 0.0943  
Control - Low -0.0296 -0.6636 0.6044  

Multiple comparisons for algae cover

Data from Kneitel and Lessin (2010)

The GLM Procedure

 

Tukey's Studentized Range (HSD) Test for y

Note:This test controls the Type I experimentwise error rate, but it generally has a higher Type II error rate than REGWQ.

Alpha 0.05
Error Degrees of Freedom 20
Error Mean Square 0.112222
Critical Value of Studentized Range 4.23186
Minimum Significant Difference 0.634
Multiple comparisons for algae cover; Data from Kneitel and Lessin 2010; VeryHigh Medium High Low Control 1.3235 1.1972 1.1672 0.6572 0.6275 treat Estimate y Tukey Grouping for Means of treat (Alpha = 0.05) Means covered by the same bar are not significantly different.