Results: mvtubes.sas

Multivariate tests on Little Fungus Tube data

Check dummy variable creation

The FREQ Procedure

The Freq Procedure

Table mcg198 * mcg

Cross-Tabular Freq Table

Frequency
Table of mcg198 by mcg
mcg198 mcg
198 205 213 221 223 225 Total
0
0
4
4
4
4
4
20
1
4
0
0
0
0
0
4
Total
4
4
4
4
4
4
24

Table mcg205 * mcg

Cross-Tabular Freq Table

Frequency
Table of mcg205 by mcg
mcg205 mcg
198 205 213 221 223 225 Total
0
4
0
4
4
4
4
20
1
0
4
0
0
0
0
4
Total
4
4
4
4
4
4
24

Table mcg213 * mcg

Cross-Tabular Freq Table

Frequency
Table of mcg213 by mcg
mcg213 mcg
198 205 213 221 223 225 Total
0
4
4
0
4
4
4
20
1
0
0
4
0
0
0
4
Total
4
4
4
4
4
4
24

Table mcg221 * mcg

Cross-Tabular Freq Table

Frequency
Table of mcg221 by mcg
mcg221 mcg
198 205 213 221 223 225 Total
0
4
4
4
0
4
4
20
1
0
0
0
4
0
0
4
Total
4
4
4
4
4
4
24

Table mcg223 * mcg

Cross-Tabular Freq Table

Frequency
Table of mcg223 by mcg
mcg223 mcg
198 205 213 221 223 225 Total
0
4
4
4
4
0
4
20
1
0
0
0
0
4
0
4
Total
4
4
4
4
4
4
24

Table mcg225 * mcg

Cross-Tabular Freq Table

Frequency
Table of mcg225 by mcg
mcg225 mcg
198 205 213 221 223 225 Total
0
4
4
4
4
4
0
20
1
0
0
0
0
0
4
4
Total
4
4
4
4
4
4
24

Table fungus1 * mcg

Cross-Tabular Freq Table

Frequency
Table of fungus1 by mcg
fungus1 mcg
198 205 213 221 223 225 Total
-1
0
0
0
0
0
4
4
0
0
4
4
4
4
0
16
1
4
0
0
0
0
0
4
Total
4
4
4
4
4
4
24

Table fungus2 * mcg

Cross-Tabular Freq Table

Frequency
Table of fungus2 by mcg
fungus2 mcg
198 205 213 221 223 225 Total
-1
0
0
0
0
0
4
4
0
4
0
4
4
4
0
16
1
0
4
0
0
0
0
4
Total
4
4
4
4
4
4
24

Table fungus3 * mcg

Cross-Tabular Freq Table

Frequency
Table of fungus3 by mcg
fungus3 mcg
198 205 213 221 223 225 Total
-1
0
0
0
0
0
4
4
0
4
4
0
4
4
0
16
1
0
0
4
0
0
0
4
Total
4
4
4
4
4
4
24

Table fungus4 * mcg

Cross-Tabular Freq Table

Frequency
Table of fungus4 by mcg
fungus4 mcg
198 205 213 221 223 225 Total
-1
0
0
0
0
0
4
4
0
4
4
4
0
4
0
16
1
0
0
0
4
0
0
4
Total
4
4
4
4
4
4
24

Table fungus5 * mcg

Cross-Tabular Freq Table

Frequency
Table of fungus5 by mcg
fungus5 mcg
198 205 213 221 223 225 Total
-1
0
0
0
0
0
4
4
0
4
4
4
4
0
0
16
1
0
0
0
0
4
0
4
Total
4
4
4
4
4
4
24

Multivariate tests on Little Fungus Tube data

Manova with proc glm

The GLM Procedure

The GLM Procedure

Data

Class Levels

Class Level Information
Class Levels Values
mcg 6 198 205 213 221 223 225

Number of Observations

Number of Observations Read 24
Number of Observations Used 24

Multivariate tests on Little Fungus Tube data

Manova with proc glm

The GLM Procedure

 

Dependent Variable: length10

Analysis of Variance

length10

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 52.49177083 10.49835417 28.81 <.0001
Error 18 6.55812500 0.36434028    
Corrected Total 23 59.04989583      

Fit Statistics

R-Square Coeff Var Root MSE length10 Mean
0.888939 2.420273 0.603606 24.93958

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
mcg 5 52.49177083 10.49835417 28.81 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
mcg 5 52.49177083 10.49835417 28.81 <.0001

Contrasts

Contrast DF Contrast SS Mean Square F Value Pr > F
AllBut198 4 13.90175000 3.47543750 9.54 0.0003

Box Plot

Fit Plot for length10 by mcg

Multivariate tests on Little Fungus Tube data

Manova with proc glm

The GLM Procedure

 

Dependent Variable: weight

weight

Overall ANOVA

Source DF Sum of Squares Mean Square F Value Pr > F
Model 5 872.458333 174.491667 13.72 <.0001
Error 18 229.000000 12.722222    
Corrected Total 23 1101.458333      

Fit Statistics

R-Square Coeff Var Root MSE weight Mean
0.792094 12.75764 3.566822 27.95833

Type I Model ANOVA

Source DF Type I SS Mean Square F Value Pr > F
mcg 5 872.4583333 174.4916667 13.72 <.0001

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
mcg 5 872.4583333 174.4916667 13.72 <.0001

Contrasts

Contrast DF Contrast SS Mean Square F Value Pr > F
AllBut198 4 860.4250000 215.1062500 16.91 <.0001

Box Plot

Fit Plot for weight by mcg

Multivariate tests on Little Fungus Tube data

Manova with proc glm

The GLM Procedure

Multivariate Analysis of Variance

Multivariate Analysis of Variance

Model MANOVA

mcg

Characteristic Structure

Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SSCP Matrix for mcg
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
length10 weight
9.75729573 76.88 0.36961364 -0.03396039
2.93440536 23.12 0.14180790 0.05774913

Multivariate Tests

MANOVA Test Criteria and F Approximations for the Hypothesis of No Overall mcg Effect
H = Type III SSCP Matrix for mcg
E = Error SSCP Matrix

S=2 M=1 N=7.5
Statistic Value F Value Num DF Den DF Pr > F
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
Wilks' Lambda 0.02362750 18.72 10 34 <.0001
Pillai's Trace 1.65287182 17.14 10 36 <.0001
Hotelling-Lawley Trace 12.69170110 20.86 10 22.909 <.0001
Roy's Greatest Root 9.75729573 35.13 5 18 <.0001

Contrasts

AllBut198

Characteristic Structure

Characteristic Roots and Vectors of: E Inverse * H, where
H = Contrast SSCP Matrix for AllBut198
E = Error SSCP Matrix
Characteristic Root Percent Characteristic Vector V'EV=1
length10 weight
4.99846050 78.08 -0.23260290 0.05994775
1.40322455 21.92 0.32034296 0.02990881

Multivariate Tests

MANOVA Test Criteria and F Approximations for the Hypothesis of No Overall AllBut198 Effect
H = Contrast SSCP Matrix for AllBut198
E = Error SSCP Matrix

S=2 M=0.5 N=7.5
Statistic Value F Value Num DF Den DF Pr > F
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
Wilks' Lambda 0.06936907 11.89 8 34 <.0001
Pillai's Trace 1.41718296 10.94 8 36 <.0001
Hotelling-Lawley Trace 6.40168505 13.20 8 22.087 <.0001
Roy's Greatest Root 4.99846050 22.49 4 18 <.0001

Multivariate tests on Little Fungus Tube data

Manova with proc reg and effect coding;

The REG Procedure

Model: MODEL1

Dependent Variable: length10

The Reg Procedure

MODEL1

Fit

length10

Number of Observations

Number of Observations Read 24
Number of Observations Used 24

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 52.49177 10.49835 28.81 <.0001
Error 18 6.55813 0.36434    
Corrected Total 23 59.04990      

Fit Statistics

Root MSE 0.60361 R-Square 0.8889
Dependent Mean 24.93958 Adj R-Sq 0.8581
Coeff Var 2.42027    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 24.93958 0.12321 202.41 <.0001
fungus1 1 2.83542 0.27551 10.29 <.0001
fungus2 1 0.39792 0.27551 1.44 0.1658
fungus3 1 0.12292 0.27551 0.45 0.6608
fungus4 1 -1.98958 0.27551 -7.22 <.0001
fungus5 1 -0.58958 0.27551 -2.14 0.0463

Multivariate tests on Little Fungus Tube data

Manova with proc reg and effect coding;

The REG Procedure

Model: MODEL1

Dependent Variable: weight

weight

Number of Observations

Number of Observations Read 24
Number of Observations Used 24

Analysis of Variance

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 5 872.45833 174.49167 13.72 <.0001
Error 18 229.00000 12.72222    
Corrected Total 23 1101.45833      

Fit Statistics

Root MSE 3.56682 R-Square 0.7921
Dependent Mean 27.95833 Adj R-Sq 0.7343
Coeff Var 12.75764    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
Intercept 1 27.95833 0.72807 38.40 <.0001
fungus1 1 -1.58333 1.62802 -0.97 0.3437
fungus2 1 0.04167 1.62802 0.03 0.9799
fungus3 1 3.16667 1.62802 1.95 0.0676
fungus4 1 8.91667 1.62802 5.48 <.0001
fungus5 1 -11.20833 1.62802 -6.88 <.0001

Multivariate tests on Little Fungus Tube data

Manova with proc reg and effect coding;

The REG Procedure

Model: MODEL1

Multivariate Test: overall

Multivariate Test overall

Multivariate Statistics

Multivariate Statistics and F Approximations
S=2 M=1 N=7.5
Statistic Value F Value Num DF Den DF Pr > F
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
Wilks' Lambda 0.02362750 18.72 10 34 <.0001
Pillai's Trace 1.65287182 17.14 10 36 <.0001
Hotelling-Lawley Trace 12.69170110 20.86 10 22.909 <.0001
Roy's Greatest Root 9.75729573 35.13 5 18 <.0001

Multivariate tests on Little Fungus Tube data

Manova with proc reg and cell means coding

The REG Procedure

Model: MODEL1

Dependent Variable: length10

The Reg Procedure

MODEL1

Fit

length10

Number of Observations

Number of Observations Read 24
Number of Observations Used 24

Analysis of Variance

Note:No intercept in model. R-Square is redefined.

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 6 14980 2496.67990 6852.60 <.0001
Error 18 6.55813 0.36434    
Uncorrected Total 24 14987      

Fit Statistics

Root MSE 0.60361 R-Square 0.9996
Dependent Mean 24.93958 Adj R-Sq 0.9994
Coeff Var 2.42027    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
mcg198 1 27.77500 0.30180 92.03 <.0001
mcg205 1 25.33750 0.30180 83.95 <.0001
mcg213 1 25.06250 0.30180 83.04 <.0001
mcg221 1 22.95000 0.30180 76.04 <.0001
mcg223 1 24.35000 0.30180 80.68 <.0001
mcg225 1 24.16250 0.30180 80.06 <.0001

Multivariate tests on Little Fungus Tube data

Manova with proc reg and cell means coding

The REG Procedure

Model: MODEL1

Dependent Variable: weight

weight

Number of Observations

Number of Observations Read 24
Number of Observations Used 24

Analysis of Variance

Note:No intercept in model. R-Square is redefined.

Analysis of Variance
Source DF Sum of
Squares		 Mean
Square		 F Value Pr > F
Model 6 19633 3272.08333 257.19 <.0001
Error 18 229.00000 12.72222    
Uncorrected Total 24 19862      

Fit Statistics

Root MSE 3.56682 R-Square 0.9885
Dependent Mean 27.95833 Adj R-Sq 0.9846
Coeff Var 12.75764    

Parameter Estimates

Parameter Estimates
Variable DF Parameter
Estimate		 Standard
Error		 t Value Pr > |t|
mcg198 1 26.37500 1.78341 14.79 <.0001
mcg205 1 28.00000 1.78341 15.70 <.0001
mcg213 1 31.12500 1.78341 17.45 <.0001
mcg221 1 36.87500 1.78341 20.68 <.0001
mcg223 1 16.75000 1.78341 9.39 <.0001
mcg225 1 28.62500 1.78341 16.05 <.0001

Multivariate tests on Little Fungus Tube data

Manova with proc reg and cell means coding

The REG Procedure

Model: MODEL1

Test Overall

Results

Test Overall results
Dependent
Variable		 Source DF Mean
Square		 F Value Pr > F
length10 Numerator 5 10.49835 28.81 <.0001
  Denominator 18 0.36434    
weight Numerator 5 174.49167 13.72 <.0001
  Denominator 18 12.72222    

Multivariate tests on Little Fungus Tube data

Manova with proc reg and cell means coding

The REG Procedure

Model: MODEL1

Multivariate Test: mOverall

Multivariate Test mOverall

Multivariate Statistics

Multivariate Statistics and F Approximations
S=2 M=1 N=7.5
Statistic Value F Value Num DF Den DF Pr > F
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
Wilks' Lambda 0.02362750 18.72 10 34 <.0001
Pillai's Trace 1.65287182 17.14 10 36 <.0001
Hotelling-Lawley Trace 12.69170110 20.86 10 22.909 <.0001
Roy's Greatest Root 9.75729573 35.13 5 18 <.0001

Multivariate tests on Little Fungus Tube data

Manova with proc reg and cell means coding

The REG Procedure

Model: MODEL1

Test AllBut198

Results

Test AllBut198 results
Dependent
Variable		 Source DF Mean
Square		 F Value Pr > F
length10 Numerator 4 3.47544 9.54 0.0003
  Denominator 18 0.36434    
weight Numerator 4 215.10625 16.91 <.0001
  Denominator 18 12.72222    

Multivariate tests on Little Fungus Tube data

Manova with proc reg and cell means coding

The REG Procedure

Model: MODEL1

Multivariate Test: mAllBut198

Multivariate Test mAllBut198

Multivariate Statistics

Multivariate Statistics and F Approximations
S=2 M=0.5 N=7.5
Statistic Value F Value Num DF Den DF Pr > F
NOTE: F Statistic for Roy's Greatest Root is an upper bound.
NOTE: F Statistic for Wilks' Lambda is exact.
Wilks' Lambda 0.06936907 11.89 8 34 <.0001
Pillai's Trace 1.41718296 10.94 8 36 <.0001
Hotelling-Lawley Trace 6.40168505 13.20 8 22.087 <.0001
Roy's Greatest Root 4.99846050 22.49 4 18 <.0001