*******************************************************;
* hemophil.sas - MANOVA of Hemophilia data. *;
* Johnson and Wichern, 3rd Ed., Page 570. *;
*******************************************************;
Options PS=55 LS=90 PageNo=1 NoDate
FORMCHAR='|----|+|---+=|-/\<>*';
Title1 "Hemophilia Data";
Proc Format;
Value Groups 1="Noncarriers" 2="Carriers";
Run;
Data Hemophil;
Input Group Activity Antigen;
Format Group Groups.;
Label Group="Group" Activity="AHF Activity" Antigen="AHF Antigen";
Datalines;
1 -0.0056 -0.1657
1 -0.1698 -0.1585
1 -0.3469 -0.1879
1 -0.0894 0.0064
1 -0.1679 0.0713
1 -0.0836 0.0106
1 -0.1979 -0.0005
1 -0.0762 0.0392
1 -0.1913 -0.2123
1 -0.1092 -0.1190
1 -0.5268 -0.4773
1 -0.0842 0.0248
1 -0.0225 -0.0580
1 0.0084 0.0782
1 -0.1827 -0.1138
1 0.1237 0.2140
1 -0.4702 -0.3099
1 -0.1519 -0.0686
1 0.0006 -0.1153
1 -0.2015 -0.0498
1 -0.1932 -0.2293
1 0.1507 0.0933
1 -0.1259 -0.0669
1 -0.1551 -0.1232
1 -0.1952 -0.1007
1 0.0291 0.0442
1 -0.2280 -0.1710
1 -0.0997 -0.0733
1 -0.1972 -0.0607
1 -0.0867 -0.0560
2 -0.3478 0.1151
2 -0.3618 -0.2008
2 -0.4986 -0.0860
2 -0.5015 -0.2984
2 -0.1326 0.0097
2 -0.6911 -0.3390
2 -0.3608 0.1237
2 -0.4535 -0.1682
2 -0.3479 -0.1721
2 -0.3539 0.0722
2 -0.4719 -0.1079
2 -0.3610 -0.0399
2 -0.3226 0.1670
2 -0.4319 -0.0687
2 -0.2734 -0.0020
2 -0.5573 0.0548
2 -0.3755 -0.1865
2 -0.4950 -0.0153
2 -0.5107 -0.2483
2 -0.1652 0.2132
2 -0.2447 -0.0407
2 -0.4232 -0.0998
2 -0.2375 0.2876
2 -0.2205 0.0046
2 -0.2154 -0.0219
2 -0.3447 0.0097
2 -0.2540 -0.0573
2 -0.3778 -0.2682
2 -0.4046 -0.1162
2 -0.0639 0.1569
2 -0.3351 -0.1368
2 -0.0149 0.1539
2 -0.0312 0.1400
2 -0.1740 -0.0776
2 -0.1416 0.1642
2 -0.1508 0.1137
2 -0.0964 0.0531
2 -0.2642 0.0867
2 -0.0234 0.0804
2 -0.3352 0.0875
2 -0.1878 0.2510
2 -0.1744 0.1892
2 -0.4055 -0.2418
2 -0.2444 0.1614
2 -0.4784 0.0282
;
Proc Print Data=Hemophil;
Run;
Proc Univariate Data=Hemophil Plot Normal;
Var Activity Antigen;
Run;
Proc Plot Data=Hemophil;
Plot Activity*Antigen=Group;
Run; Quit;
Proc Corr Data=Hemophil;
Var Activity Antigen;
Run;
Proc GLM Data=Hemophil;
Class Group;
Model Activity Antigen = Group;
Output Out=Errs R=Eact Eant;
Manova H=Group / PrintE PrintH;
Means Group / CLM T;
Means Group / CLDIFF T;
Run;
Quit;
Proc Univariate Data=Errs Normal Plot;
Var Eact Eant;
Label Eact="Activity Residual" Eant="Antigen Residual";
Run;
Proc Plot Data=Errs;
Plot Eact*Eant;
Label Eact="Activity Residual" Eant="Antigen Residual";
Run;
Quit;
Hemophilia Data 1
OBS GROUP ACTIVITY ANTIGEN
1 Noncarriers -0.0056 -0.1657
2 Noncarriers -0.1698 -0.1585
3 Noncarriers -0.3469 -0.1879
4 Noncarriers -0.0894 0.0064
5 Noncarriers -0.1679 0.0713
6 Noncarriers -0.0836 0.0106
7 Noncarriers -0.1979 -0.0005
8 Noncarriers -0.0762 0.0392
9 Noncarriers -0.1913 -0.2123
10 Noncarriers -0.1092 -0.1190
11 Noncarriers -0.5268 -0.4773
12 Noncarriers -0.0842 0.0248
13 Noncarriers -0.0225 -0.0580
14 Noncarriers 0.0084 0.0782
15 Noncarriers -0.1827 -0.1138
16 Noncarriers 0.1237 0.2140
17 Noncarriers -0.4702 -0.3099
18 Noncarriers -0.1519 -0.0686
19 Noncarriers 0.0006 -0.1153
20 Noncarriers -0.2015 -0.0498
21 Noncarriers -0.1932 -0.2293
22 Noncarriers 0.1507 0.0933
23 Noncarriers -0.1259 -0.0669
24 Noncarriers -0.1551 -0.1232
25 Noncarriers -0.1952 -0.1007
26 Noncarriers 0.0291 0.0442
27 Noncarriers -0.2280 -0.1710
28 Noncarriers -0.0997 -0.0733
29 Noncarriers -0.1972 -0.0607
30 Noncarriers -0.0867 -0.0560
31 Carriers -0.3478 0.1151
32 Carriers -0.3618 -0.2008
33 Carriers -0.4986 -0.0860
34 Carriers -0.5015 -0.2984
35 Carriers -0.1326 0.0097
36 Carriers -0.6911 -0.3390
37 Carriers -0.3608 0.1237
38 Carriers -0.4535 -0.1682
39 Carriers -0.3479 -0.1721
40 Carriers -0.3539 0.0722
41 Carriers -0.4719 -0.1079
42 Carriers -0.3610 -0.0399
43 Carriers -0.3226 0.1670
44 Carriers -0.4319 -0.0687
45 Carriers -0.2734 -0.0020
46 Carriers -0.5573 0.0548
47 Carriers -0.3755 -0.1865
48 Carriers -0.4950 -0.0153
49 Carriers -0.5107 -0.2483
50 Carriers -0.1652 0.2132
51 Carriers -0.2447 -0.0407
Hemophilia Data 2
OBS GROUP ACTIVITY ANTIGEN
52 Carriers -0.4232 -0.0998
53 Carriers -0.2375 0.2876
54 Carriers -0.2205 0.0046
55 Carriers -0.2154 -0.0219
56 Carriers -0.3447 0.0097
57 Carriers -0.2540 -0.0573
58 Carriers -0.3778 -0.2682
59 Carriers -0.4046 -0.1162
60 Carriers -0.0639 0.1569
61 Carriers -0.3351 -0.1368
62 Carriers -0.0149 0.1539
63 Carriers -0.0312 0.1400
64 Carriers -0.1740 -0.0776
65 Carriers -0.1416 0.1642
66 Carriers -0.1508 0.1137
67 Carriers -0.0964 0.0531
68 Carriers -0.2642 0.0867
69 Carriers -0.0234 0.0804
70 Carriers -0.3352 0.0875
71 Carriers -0.1878 0.2510
72 Carriers -0.1744 0.1892
73 Carriers -0.4055 -0.2418
74 Carriers -0.2444 0.1614
75 Carriers -0.4784 0.0282
Hemophilia Data 3
Univariate Procedure
Variable=ACTIVITY AHF Activity
Moments Quantiles(Def=5)
N 75 Sum Wgts 75 100% Max 0.1507 99% 0.1507 Mean -0.23872 Sum -17.9037 75% Q3 -0.1092 95% 0.0084 Std Dev 0.172098 Variance 0.029618 50% Med -0.2015 90% -0.0225 Skewness -0.17877 Kurtosis -0.36072 25% Q1 -0.361 10% -0.4784 USS 6.465607 CSS 2.191707 0% Min -0.6911 5% -0.5107 CV -72.0931 Std Mean 0.019872 1% -0.6911 T:Mean=0 -12.0126 Pr>|T| 0.0001 Range 0.8418 Num ^= 0 75 Num > 0 5 Q3-Q1 0.2518 M(Sign) -32.5 Pr>=|M| 0.0001 Mode -0.6911 Sgn Rank -1374 Pr>=|S| 0.0001 W:Normal 0.978807 Pr
Extremes
Lowest Obs Highest Obs
-0.6911( 36) 0.0006( 19)
-0.5573( 46) 0.0084( 14)
-0.5268( 11) 0.0291( 26)
-0.5107( 49) 0.1237( 16)
-0.5015( 34) 0.1507( 22)
Stem Leaf # Boxplot
1 5 1 |
1 2 1 |
0 |
0 013 3 |
-0 32211 5 |
-0 998886 6 |
-1 433100 6 +-----+
-1 999877777655 12 | |
-2 4443220000 10 *--+--*
-2 765 3 | |
-3 4442 4 | |
-3 886665555 9 +-----+
-4 3210 4 |
-4 8775 4 |
-5 31000 5 |
-5 6 1 |
-6 |
-6 9 1 |
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Hemophilia Data 4
Univariate Procedure
Variable=ACTIVITY AHF Activity
Normal Probability Plot
0.175+ +*+
| *++
| +++
| +*+**
| ****
| *****
| **+
| ******
| ***++
| **+
| ****
| +***
| ++**
| +****
| **+*
| *+
| +++
-0.675++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Hemophilia Data 5
Univariate Procedure
Variable=ANTIGEN AHF Antigen
Moments Quantiles(Def=5)
N 75 Sum Wgts 75 100% Max 0.2876 99% 0.2876 Mean -0.03474 Sum -2.6053 75% Q3 0.0782 95% 0.2132 Std Dev 0.150233 Variance 0.02257 50% Med -0.0407 90% 0.1614 Skewness -0.24808 Kurtosis 0.028308 25% Q1 -0.1232 10% -0.2293 USS 1.760689 CSS 1.670187 0% Min -0.4773 5% -0.2984 CV -432.484 Std Mean 0.017347 1% -0.4773 T:Mean=0 -2.00244 Pr>|T| 0.0489 Range 0.7649 Num ^= 0 75 Num > 0 32 Q3-Q1 0.2014 M(Sign) -5.5 Pr>=|M| 0.2480 Mode 0.0097 Sgn Rank -338 Pr>=|S| 0.0741 W:Normal 0.98828 Pr
Extremes
Lowest Obs Highest Obs
-0.4773( 11) 0.1892( 72)
-0.339( 36) 0.2132( 50)
-0.3099( 17) 0.214( 16)
-0.2984( 34) 0.251( 71)
-0.2682( 58) 0.2876( 53)
Stem Leaf # Boxplot
2 59 2 |
2 11 2 |
1 566679 6 |
1 1224 4 |
0 557788999 9 +-----+
0 011112344 9 | |
-0 442200 6 *--+--*
-0 98777766665 11 | |
-1 422221100 9 +-----+
-1 9977776 7 |
-2 4310 4 |
-2 75 2 |
-3 410 3 |
-3
-4
-4 8 1 0
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Hemophilia Data 6
Univariate Procedure
Variable=ANTIGEN AHF Antigen
Normal Probability Plot
0.275+ +*++ *
| +**
| *****
0.125+ ***+
| *****
| ****
-0.025+ +***
| ****
| ****
-0.175+ ****
| ****
| *+*
-0.325+ *+*
| ++++
|+
-0.475+ *
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Hemophilia Data 7
Plot of ACTIVITY*ANTIGEN. Symbol is value of GROUP.
|
|
0.2 +
|
| N
| N
|
|
| N
0.0 + N N N
| N C CC
| C
| NN NN NC
A | N N
H | N N C C C
F | N N C N C C
-0.2 + N N N NN N C
A | N C C C
c | C C C C
t | C
i | C
v | N C C C C C C
i | C CC C C
t -0.4 + C C
y | C C
| N C
| C C C C
| N C C
|
| C
-0.6 +
|
|
| C
|
|
|
-0.8 +
|
-+---------+---------+---------+---------+---------+---------+---------+---------+-
-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
AHF Antigen
NOTE: 1 obs hidden.
Hemophilia Data 8
Correlation Analysis
2 'VAR' Variables: ACTIVITY ANTIGEN
Simple Statistics Variable N Mean Std Dev Sum Minimum Maximum Label
ACTIVITY 75 -0.2387 0.1721 -17.9037 -0.6911 0.1507 AHF Activity ANTIGEN 75 -0.0347 0.1502 -2.6053 -0.4773 0.2876 AHF Antigen
Pearson Correlation Coefficients / Prob > |R| under Ho: Rho=0 / N = 75
ACTIVITY ANTIGEN
ACTIVITY 1.00000 0.47176
AHF Activity 0.0 0.0001
ANTIGEN 0.47176 1.00000
AHF Antigen 0.0001 0.0
Hemophilia Data 9
General Linear Models Procedure
Class Level Information
Class Levels Values
GROUP 2 Carriers Noncarriers
Number of observations in data set = 75
Hemophilia Data 10
General Linear Models Procedure Dependent Variable: ACTIVITY AHF Activity Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 0.53919959 0.53919959 23.82 0.0001 Error 73 1.65250773 0.02263709 Corrected Total 74 2.19170732
R-Square C.V. Root MSE ACTIVITY Mean
0.246018 -63.02731 0.15045628 -0.23871600
Source DF Type I SS Mean Square F Value Pr > F
GROUP 1 0.53919959 0.53919959 23.82 0.0001
Source DF Type III SS Mean Square F Value Pr > F
GROUP 1 0.53919959 0.53919959 23.82 0.0001
Hemophilia Data 11
General Linear Models Procedure Dependent Variable: ANTIGEN AHF Antigen Source DF Sum of Squares Mean Square F Value Pr > F
Model 1 0.09296385 0.09296385 4.30 0.0416 Error 73 1.57722353 0.02160580 Corrected Total 74 1.67018738
R-Square C.V. Root MSE ANTIGEN Mean
0.055661 -423.1445 0.14698912 -0.03473733
Source DF Type I SS Mean Square F Value Pr > F
GROUP 1 0.09296385 0.09296385 4.30 0.0416
Source DF Type III SS Mean Square F Value Pr > F
GROUP 1 0.09296385 0.09296385 4.30 0.0416
E = Error SS&CP Matrix
ACTIVITY ANTIGEN
ACTIVITY 1.652507735 1.1264850597
ANTIGEN 1.1264850597 1.5772235301
Hemophilia Data 12
General Linear Models Procedure
Multivariate Analysis of Variance
Partial Correlation Coefficients from the Error SS&CP Matrix / Prob > |r|
DF = 73 ACTIVITY ANTIGEN
ACTIVITY 1.000000 0.697762
0.0001 0.0001
ANTIGEN 0.697762 1.000000
0.0001 0.0001
Hemophilia Data 13
General Linear Models Procedure
Multivariate Analysis of Variance
H = Type III SS&CP Matrix for GROUP
ACTIVITY ANTIGEN
ACTIVITY 0.5391995858 -0.223888514
ANTIGEN -0.223888514 0.0929638454
Characteristic Roots and Vectors of: E Inverse * H, where
H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix
Characteristic Percent Characteristic Vector V'EV=1
Root
ACTIVITY ANTIGEN
1.12791213 100.00 -1.05720774 0.93710218
0.00000000 0.00 0.24824920 0.59786839
Manova Test Criteria and Exact F Statistics for the Hypothesis of no Overall GROUP Effect
H = Type III SS&CP Matrix for GROUP E = Error SS&CP Matrix
S=1 M=0 N=35
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.46994422 40.6048 2 72 0.0001
Pillai's Trace 0.53005578 40.6048 2 72 0.0001
Hotelling-Lawley Trace 1.12791213 40.6048 2 72 0.0001
Roy's Greatest Root 1.12791213 40.6048 2 72 0.0001
Hemophilia Data 14
General Linear Models Procedure
T Confidence Intervals for variable: ACTIVITY
Alpha= 0.05 Confidence= 0.95 df= 73 MSE= 0.022637
Critical Value of T= 1.99
Lower Upper
GROUP N Confidence Mean Confidence
Limit Limit
Noncarriers 30 -0.18962 -0.13487 -0.08012
Carriers 45 -0.35265 -0.30795 -0.26325
Hemophilia Data 15
General Linear Models Procedure
T Confidence Intervals for variable: ANTIGEN
Alpha= 0.05 Confidence= 0.95 df= 73 MSE= 0.021606
Critical Value of T= 1.99
Lower Upper
GROUP N Confidence Mean Confidence
Limit Limit
Carriers 45 -0.04966 -0.00599 0.03768
Noncarriers 30 -0.13134 -0.07786 -0.02437
Hemophilia Data 16
General Linear Models Procedure
T tests (LSD) for variable: ACTIVITY
NOTE: This test controls the type I comparisonwise error rate not the
experimentwise error rate.
Alpha= 0.05 Confidence= 0.95 df= 73 MSE= 0.022637
Critical Value of T= 1.99300
Comparisons significant at the 0.05 level are indicated by '***'.
Lower Difference Upper
GROUP Confidence Between Confidence
Comparison Limit Means Limit
Noncarriers - Carriers 0.10240 0.17308 0.24375 ***
Carriers - Noncarriers -0.24375 -0.17308 -0.10240 ***
Hemophilia Data 17
General Linear Models Procedure
T tests (LSD) for variable: ANTIGEN
NOTE: This test controls the type I comparisonwise error rate not the
experimentwise error rate.
Alpha= 0.05 Confidence= 0.95 df= 73 MSE= 0.021606
Critical Value of T= 1.99300
Comparisons significant at the 0.05 level are indicated by '***'.
Lower Difference Upper
GROUP Confidence Between Confidence
Comparison Limit Means Limit
Carriers - Noncarriers 0.00282 0.07187 0.14091 ***
Noncarriers - Carriers -0.14091 -0.07187 -0.00282 ***
Hemophilia Data 18
Univariate Procedure
Variable=EACT Activity Residual
Moments Quantiles(Def=5)
N 75 Sum Wgts 75 100% Max 0.293047 99% 0.293047 Mean 0 Sum 0 75% Q3 0.11237 95% 0.276747 Std Dev 0.149436 Variance 0.022331 50% Med -0.02023 90% 0.175347 Skewness -0.23194 Kurtosis 0.235909 25% Q1 -0.06755 10% -0.19065 USS 1.652508 CSS 1.652508 0% Min -0.39193 5% -0.24935 CV . Std Mean 0.017255 1% -0.39193 T:Mean=0 0 Pr>|T| 1.0000 Range 0.684977 Num ^= 0 75 Num > 0 35 Q3-Q1 0.179923 M(Sign) -2.5 Pr>=|M| 0.6445 Mode -0.39193 Sgn Rank 15 Pr>=|S| 0.9375 W:Normal 0.96863 Pr
Extremes
Lowest Obs Highest Obs
-0.39193( 11) 0.25857( 16)
-0.38315( 36) 0.276747( 63)
-0.33533( 17) 0.284547( 69)
-0.24935( 46) 0.28557( 22)
-0.21203( 3) 0.293047( 62)
Stem Leaf # Boxplot
2 68899 5 |
2 14 2 |
1 6678 4 |
1 12333444 8 +-----+
0 55555666799 11 | |
0 13344 5 | + |
-0 4443333221 10 *-----*
-0 97776666655555 14 +-----+
-1 2200 4 |
-1 999765 6 |
-2 10 2 |
-2 5 1 |
-3 4 1 |
-3 98 2 0
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Hemophilia Data 19
Univariate Procedure
Variable=EACT Activity Residual
Normal Probability Plot
0.275+ * **+* *
| *++
| ***
| ****
| ****
| +***
| *****
| *******
| **++
| ****
| *+**
| ++++
| +++ *
-0.375++* *
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Hemophilia Data 20
Univariate Procedure
Variable=EANT Antigen Residual
Moments Quantiles(Def=5)
N 75 Sum Wgts 75 100% Max 0.293591 99% 0.293591 Mean 0 Sum 0 75% Q3 0.117057 95% 0.219191 Std Dev 0.145993 Variance 0.021314 50% Med 0.010591 90% 0.170191 Skewness -0.37135 Kurtosis -0.03439 25% Q1 -0.09314 10% -0.19481 USS 1.577224 CSS 1.577224 0% Min -0.39944 5% -0.26221 CV . Std Mean 0.016858 1% -0.39944 T:Mean=0 0 Pr>|T| 1.0000 Range 0.693034 Num ^= 0 75 Num > 0 41 Q3-Q1 0.2102 M(Sign) 3.5 Pr>=|M| 0.4887 Mode 0.015691 Sgn Rank 50 Pr>=|S| 0.7938 W:Normal 0.977938 Pr
Extremes
Lowest Obs Highest Obs
-0.39944( 11) 0.195191( 72)
-0.33301( 36) 0.219191( 50)
-0.29241( 34) 0.256991( 71)
-0.26221( 58) 0.291857( 16)
-0.24231( 49) 0.293591( 53)
Stem Leaf # Boxplot
2 699 3 |
2 02 2 |
1 556667777 9 |
1 022223 6 +-----+
0 668889999 9 | |
0 001112222233 12 *--+--*
-0 44433221 8 | |
-0 999887655 9 +-----+
-1 33110 5 |
-1 98765 5 |
-2 443 3 |
-2 96 2 |
-3 3 1 |
-3 |
-4 0 1 |
----+----+----+----+
Multiply Stem.Leaf by 10**-1
Hemophilia Data 21
Univariate Procedure
Variable=EANT Antigen Residual
Normal Probability Plot
0.275+ *+* *
| +++*
| ******
| *****
| ****
| *****
| ****
-0.075+ ****
| ***+
| ****
| ++**
| ++**
| +++*
|+*
-0.425+
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Hemophilia Data 22
Plot of EACT*EANT. Legend: A = 1 obs, B = 2 obs, etc.
|
0.3 + A
| A A A
| A
| A
|
| A
0.2 +
| A
| A A
| A A A
| A A A A
| A A
0.1 + A
A | A
c | A A A A
t | A A ABA
i | A AA
v | A
i 0.0 +
t | A A A
y | A A A A A A A
| A A A B A A
R | A A A AA A
e |
s -0.1 + A A A
i | A A
d |
u | A
a | A A
l | A A
-0.2 + A A
| A
|
| A
|
|
-0.3 +
|
| A
|
|
| A
-0.4 + A
|
---+----------+----------+----------+----------+----------+----------+----------+--
-0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3
Antigen Residual