Results: pain1.sas

Multivariate repeated measures analysis of the pain data

The Print Procedure

Data Set WORK.OUCH0

Obs Patient Drug1Dose1 Drug1Dose2 Drug1Dose3 Drug2Dose1 Drug2Dose2 Drug2Dose3
1 1 7 8 9 10 7 6.5
2 2 7.5 6 5.5 6 4.5 7.5
3 3 3 4.5 6 6.5 5.5 8.5
4 4 3 1.5 0 5 0 2
5 5 5 3.5 4.5 5.5 1.5 5.5
6 6 8 6 4 6.5 5.5 4.5
7 7 7.5 4.5 5.5 5 5.5 6
8 8 7.5 4 0.5 3.5 4.5 7.5
9 9 7.5 4.5 4 7.5 4.5 6
10 10 6 7.5 5.5 7.5 6 6.5

Multivariate repeated measures analysis of the pain data

The MEANS Procedure

The Means Procedure

Summary statistics

Variable Label N Mean Std Dev
Drug1Dose1
Drug1Dose2
Drug1Dose3
Drug2Dose1
Drug2Dose2
Drug2Dose3
Drug1
Drug2
Dose1
Dose2
Dose3
DrugEffect1
DrugEffect2
DrugEffect3
Drug1Dose1
Drug1Dose2
Drug1Dose3
Drug2Dose1
Drug2Dose2
Drug2Dose3
 
 
 
 
 
Drug effect for dose 1
Drug effect for dose 2
Drug effect for dose 3
10
10
10
10
10
10
10
10
10
10
10
10
10
10
6.200
5.000
4.450
6.300
4.450
6.050
5.217
5.600
6.250
4.725
5.250
-0.100
0.550
-1.600
1.903
1.929
2.629
1.783
2.127
1.817
1.759
1.524
1.374
1.952
1.926
2.459
1.117
2.366

Multivariate repeated measures analysis of the pain data

Overall test

The REG Procedure

Model: MODEL1

Multivariate Test: Overall

The Reg Procedure

MODEL1

Multivariate Test Overall

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=1.5 N=1.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.26024160 2.84 5 5 0.1381
Pillai's Trace 0.73975840 2.84 5 5 0.1381
Hotelling-Lawley Trace 2.84258317 2.84 5 5 0.1381
Roy's Greatest Root 2.84258317 2.84 5 5 0.1381

Multivariate repeated measures analysis of the pain data

Main Effect of Drug

The REG Procedure

Model: MODEL1

Multivariate Test: Drug

The Reg Procedure

MODEL1

Multivariate Test Drug

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=-0.5 N=3.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.82880259 1.86 1 9 0.2059
Pillai's Trace 0.17119741 1.86 1 9 0.2059
Hotelling-Lawley Trace 0.20655994 1.86 1 9 0.2059
Roy's Greatest Root 0.20655994 1.86 1 9 0.2059

Multivariate repeated measures analysis of the pain data

Main Effect of Dose Level

The REG Procedure

Model: MODEL1

Multivariate Test: Dose

The Reg Procedure

MODEL1

Multivariate Test Dose

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=0 N=3
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.33765103 7.85 2 8 0.0130
Pillai's Trace 0.66234897 7.85 2 8 0.0130
Hotelling-Lawley Trace 1.96163760 7.85 2 8 0.0130
Roy's Greatest Root 1.96163760 7.85 2 8 0.0130

Multivariate repeated measures analysis of the pain data

Drug by Dose Interaction

The REG Procedure

Model: MODEL1

Multivariate Test: Drug_by_Dose

The Reg Procedure

MODEL1

Multivariate Test Drug_by_Dose

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=0 N=3
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.43171577 5.27 2 8 0.0347
Pillai's Trace 0.56828423 5.27 2 8 0.0347
Hotelling-Lawley Trace 1.31633881 5.27 2 8 0.0347
Roy's Greatest Root 1.31633881 5.27 2 8 0.0347

Multivariate repeated measures analysis of the pain data

Follow up with matched t-tests

The MEANS Procedure

The Means Procedure

Summary statistics

Variable N Mean t Value Pr > |t|
d12
d13
d14
d15
d16
d23
d24
d25
d26
d34
d35
d36
d45
d46
d56
doseD12
doseD13
doseD23
int1
int2
int3
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
10
1.2000000
1.7500000
-0.1000000
1.7500000
0.1500000
0.5500000
-1.3000000
0.5500000
-1.0500000
-1.8500000
0
-1.6000000
1.8500000
0.2500000
-1.6000000
1.5250000
1.0000000
-0.5250000
-0.6500000
1.5000000
2.1500000
2.01
1.89
-0.13
2.84
0.20
1.04
-2.98
1.56
-1.72
-3.51
0.00
-2.14
3.08
0.33
-3.01
4.08
1.93
-1.33
-0.69
1.13
3.02
0.0754
0.0913
0.9005
0.0193
0.8427
0.3260
0.0154
0.1538
0.1204
0.0066
1.0000
0.0612
0.0132
0.7477
0.0147
0.0027
0.0862
0.2148
0.5054
0.2890
0.0144

Multivariate repeated measures analysis of the pain data

Specify new response variables within proc reg

The REG Procedure

Model: MODEL1

Multivariate Test: Overall

The Reg Procedure

MODEL1

Multivariate Test Overall

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=1.5 N=1.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.26024160 2.84 5 5 0.1381
Pillai's Trace 0.73975840 2.84 5 5 0.1381
Hotelling-Lawley Trace 2.84258317 2.84 5 5 0.1381
Roy's Greatest Root 2.84258317 2.84 5 5 0.1381

Multivariate repeated measures analysis of the pain data

Specify new response variables within proc reg

The REG Procedure

Model: MODEL1

Multivariate Test: Drug

Multivariate Test Drug

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=-0.5 N=3.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.82880259 1.86 1 9 0.2059
Pillai's Trace 0.17119741 1.86 1 9 0.2059
Hotelling-Lawley Trace 0.20655994 1.86 1 9 0.2059
Roy's Greatest Root 0.20655994 1.86 1 9 0.2059

Multivariate repeated measures analysis of the pain data

Specify new response variables within proc reg

The REG Procedure

Model: MODEL1

Multivariate Test: Dose

Multivariate Test Dose

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=0 N=3
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.33765103 7.85 2 8 0.0130
Pillai's Trace 0.66234897 7.85 2 8 0.0130
Hotelling-Lawley Trace 1.96163760 7.85 2 8 0.0130
Roy's Greatest Root 1.96163760 7.85 2 8 0.0130

Multivariate repeated measures analysis of the pain data

Specify new response variables within proc reg

The REG Procedure

Model: MODEL1

Multivariate Test: Interaction

Multivariate Test Interaction

Multivariate Statistics

Multivariate Statistics and Exact F Statistics
S=1 M=0 N=3
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.43171577 5.27 2 8 0.0347
Pillai's Trace 0.56828423 5.27 2 8 0.0347
Hotelling-Lawley Trace 1.31633881 5.27 2 8 0.0347
Roy's Greatest Root 1.31633881 5.27 2 8 0.0347

Multivariate repeated measures analysis of the pain data

Two-factor within cases the easy way

The GLM Procedure

Repeated Measures Analysis of Variance

The GLM Procedure

Repeated Measures Analysis

MANOVA

Model

Drug

Multivariate Tests

MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no Drug Effect
H = Type III SSCP Matrix for Drug
E = Error SSCP Matrix

S=1 M=-0.5 N=3.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.82880259 1.86 1 9 0.2059
Pillai's Trace 0.17119741 1.86 1 9 0.2059
Hotelling-Lawley Trace 0.20655994 1.86 1 9 0.2059
Roy's Greatest Root 0.20655994 1.86 1 9 0.2059

MANOVA

Model

Dosage

Multivariate Tests

MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no Dosage Effect
H = Type III SSCP Matrix for Dosage
E = Error SSCP Matrix

S=1 M=0 N=3
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.33765103 7.85 2 8 0.0130
Pillai's Trace 0.66234897 7.85 2 8 0.0130
Hotelling-Lawley Trace 1.96163760 7.85 2 8 0.0130
Roy's Greatest Root 1.96163760 7.85 2 8 0.0130

MANOVA

Model

Drug*Dosage

Multivariate Tests

MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no Drug*Dosage Effect
H = Type III SSCP Matrix for Drug*Dosage
E = Error SSCP Matrix

S=1 M=0 N=3
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.43171577 5.27 2 8 0.0347
Pillai's Trace 0.56828423 5.27 2 8 0.0347
Hotelling-Lawley Trace 1.31633881 5.27 2 8 0.0347
Roy's Greatest Root 1.31633881 5.27 2 8 0.0347

Multivariate repeated measures analysis of the pain data

Two-factor within cases the easy way

The GLM Procedure

Repeated Measures Analysis of Variance

Univariate Tests of Hypotheses for Within Subject Effects

Within

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F
Drug 1 2.20416667 2.20416667 1.86 0.2059
Error(Drug) 9 10.67083333 1.18564815    

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F Adj Pr > F
G - G H - F
Dosage 2 24.00833333 12.00416667 6.39 0.0080 0.0125 0.0080
Error(Dosage) 18 33.82500000 1.87916667        

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F Adj Pr > F
G - G H - F
Drug*Dosage 2 12.15833333 6.07916667 2.31 0.1278 0.1514 0.1463
Error(Drug*Dosage) 18 47.34166667 2.63009259        

Multivariate repeated measures analysis of the pain data

Overall test the easy way

The GLM Procedure

Repeated Measures Analysis of Variance

The GLM Procedure

Repeated Measures Analysis

MANOVA

Model

treatment

Multivariate Tests

MANOVA Test Criteria and Exact F Statistics for the Hypothesis of no treatment Effect
H = Type III SSCP Matrix for treatment
E = Error SSCP Matrix

S=1 M=1.5 N=1.5
Statistic Value F Value Num DF Den DF Pr > F
Wilks' Lambda 0.26024160 2.84 5 5 0.1381
Pillai's Trace 0.73975840 2.84 5 5 0.1381
Hotelling-Lawley Trace 2.84258317 2.84 5 5 0.1381
Roy's Greatest Root 2.84258317 2.84 5 5 0.1381

Multivariate repeated measures analysis of the pain data

Overall test the easy way

The GLM Procedure

Repeated Measures Analysis of Variance

Univariate Tests of Hypotheses for Within Subject Effects

Within

Type III Model ANOVA

Source DF Type III SS Mean Square F Value Pr > F Adj Pr > F
G - G H - F
treatment 5 38.37083333 7.67416667 3.76 0.0063 0.0207 0.0064
Error(treatment) 45 91.83750000 2.04083333