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
mcg198	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
mcg205	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
mcg213	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
mcg221	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
mcg223	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
mcg225	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

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	0.04792249	0.00958450	5.81	0.0023
Error	18	0.02971930	0.00165107
Corrected Total	23	0.07764179

Fit Statistics


R-Square	Coeff Var	Root MSE	weight Mean
0.617225	6.477806	0.040633	0.627271

Type I Model ANOVA


Source	DF	Type I SS	Mean Square	F Value	Pr > F
mcg	5	0.04792249	0.00958450	5.81	0.0023

Type III Model ANOVA


Source	DF	Type III SS	Mean Square	F Value	Pr > F
mcg	5	0.04792249	0.00958450	5.81	0.0023

Contrasts


Contrast	DF	Contrast SS	Mean Square	F Value	Pr > F
AllBut198	4	0.04585662	0.01146415	6.94	0.0015

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
Characteristic Root	Percent	length10	weight
9.71615392	85.97	0.42673886	2.91375733
1.58536355	14.03	-0.02469610	5.64178530

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	0.03609437	14.50	10	34	<.0001
Pillai's Trace	1.51989014	11.40	10	36	<.0001
Hotelling-Lawley Trace	11.30151747	18.57	10	22.909	<.0001
Roy's Greatest Root	9.71615392	34.98	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
Characteristic Root	Percent	length10	weight
3.81724843	79.68	0.38225907	4.90580188
0.97343897	20.32	-0.19129547	4.03148002

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	0.10519068	8.85	8	34	<.0001
Pillai's Trace	1.28568299	8.10	8	36	<.0001
Hotelling-Lawley Trace	4.79068740	9.88	8	22.087	<.0001
Roy's Greatest Root	3.81724843	17.18	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	0.04792	0.00958	5.81	0.0023
Error	18	0.02972	0.00165
Corrected Total	23	0.07764

Fit Statistics


Root MSE	0.04063	R-Square	0.6172
Dependent Mean	0.62727	Adj R-Sq	0.5109
Coeff Var	6.47781

Parameter Estimates


Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
Intercept	1	0.62727	0.00829	75.63	<.0001
fungus1	1	-0.02075	0.01855	-1.12	0.2780
fungus2	1	0.05088	0.01855	2.74	0.0134
fungus3	1	0.04093	0.01855	2.21	0.0406
fungus4	1	0.02635	0.01855	1.42	0.1724
fungus5	1	-0.07910	0.01855	-4.26	0.0005

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	0.03609437	14.50	10	34	<.0001
Pillai's Trace	1.51989014	11.40	10	36	<.0001
Hotelling-Lawley Trace	11.30151747	18.57	10	22.909	<.0001
Roy's Greatest Root	9.71615392	34.98	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	9.49117	1.58186	958.08	<.0001
Error	18	0.02972	0.00165
Uncorrected Total	24	9.52089

Fit Statistics


Root MSE	0.04063	R-Square	0.9969
Dependent Mean	0.62727	Adj R-Sq	0.9958
Coeff Var	6.47781

Parameter Estimates


Parameter Estimates
Variable	DF	Parameter Estimate	Standard Error	t Value	Pr > \|t\|
mcg198	1	0.60653	0.02032	29.85	<.0001
mcg205	1	0.67815	0.02032	33.38	<.0001
mcg213	1	0.66820	0.02032	32.89	<.0001
mcg221	1	0.65363	0.02032	32.17	<.0001
mcg223	1	0.54818	0.02032	26.98	<.0001
mcg225	1	0.60895	0.02032	29.97	<.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	0.00958	5.81	0.0023
	Denominator	18	0.00165

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	0.03609437	14.50	10	34	<.0001
Pillai's Trace	1.51989014	11.40	10	36	<.0001
Hotelling-Lawley Trace	11.30151747	18.57	10	22.909	<.0001
Roy's Greatest Root	9.71615392	34.98	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	0.01146	6.94	0.0015
	Denominator	18	0.00165

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	0.10519068	8.85	8	34	<.0001
Pillai's Trace	1.28568299	8.10	8	36	<.0001
Hotelling-Lawley Trace	4.79068740	9.88	8	22.087	<.0001
Roy's Greatest Root	3.81724843	17.18	4	18	<.0001