Descriptives and Plots
How
to do this
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE1
Moments
N 29 Sum Wgts 29
Mean 9.62069 Sum 279
Std Dev 0.727706 Variance 0.529557
Skewness -1.64689 Kurtosis 1.147437
USS 2699 CSS 14.82759
CV 7.563974 Std Mean 0.135132
T:Mean=0 71.19492 Pr>|T| 0.0001
Num ^= 0 29 Num > 0 29
M(Sign) 14.5 Pr>=|M| 0.0001
Sgn Rank 217.5 Pr>=|S| 0.0001
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE1
Quantiles(Def=5)
100% Max 10 99% 10
75% Q3 10 95% 10
50% Med 10 90% 10
25% Q1 10 10% 8
0% Min 8 5% 8
1% 8
Range 2
Q3-Q1 0
Mode 10
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE1
Extremes
Lowest Obs Highest Obs
8( 29) 10( 24)
8( 19) 10( 25)
8( 16) 10( 26)
8( 3) 10( 27)
9( 22) 10( 28)
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE1
Stem Leaf # Boxplot
100 0000000000000000000000 22 +-----+
98
96 +
94
92
90 000 3 *
88
86
84
82
80 0000 4 *
----+----+----+----+--
Multiply Stem.Leaf by 10**-1
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE1
Normal Probability Plot
10.1+ *************+*** ** * *
| +++
| +++
| +++
| ++
9.1+ ***++
| +++
| +++
| ++
| +++
8.1+ ++* * **
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE2
Moments
N 29 Sum Wgts 29
Mean 4.37931 Sum 127
Std Dev 3.144312 Variance 9.8867
Skewness 0.540974 Kurtosis -0.54648
USS 833 CSS 276.8276
CV 71.79926 Std Mean 0.583884
T:Mean=0 7.500307 Pr>|T| 0.0001
Num ^= 0 25 Num > 0 25
M(Sign) 12.5 Pr>=|M| 0.0001
Sgn Rank 162.5 Pr>=|S| 0.0001
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE2
Quantiles(Def=5)
100% Max 10 99% 10
75% Q3 6 95% 10
50% Med 4 90% 10
25% Q1 2 10% 0
0% Min 0 5% 0
1% 0
Range 10
Q3-Q1 4
Mode 4
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE2
Extremes
Lowest Obs Highest Obs
0( 20) 9( 24)
0( 18) 10( 25)
0( 4) 10( 26)
0( 1) 10( 27)
2( 19) 10( 28)
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE2
Stem Leaf # Boxplot
10 0000 4 |
9 0 1 |
8 |
7 00 2 |
6 0 1 +-----+
5 000 3 | |
4 000000 6 *--+--*
3 000 3 | |
2 00000 5 +-----+
1 |
0 0000 4 |
----+----+----+----+
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=SCORE2
Normal Probability Plot
10.5+ ** * ++*+
| * +++
| +++
| **++
| *++
5.5+ +***
| ******
| **+
| ***+**
| +++
0.5+ * * **+
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=CHANGE
Moments
N 29 Sum Wgts 29
Mean 5.241379 Sum 152
Std Dev 3.236568 Variance 10.47537
Skewness -0.33468 Kurtosis -0.82948
USS 1090 CSS 293.3103
CV 61.7503 Std Mean 0.601016
T:Mean=0 8.720872 Pr>|T| 0.0001
Num ^= 0 25 Num > 0 25
M(Sign) 12.5 Pr>=|M| 0.0001
Sgn Rank 162.5 Pr>=|S| 0.0001
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=CHANGE
Quantiles(Def=5)
100% Max 10 99% 10
75% Q3 7 95% 10
50% Med 6 90% 10
25% Q1 4 10% 0
0% Min 0 5% 0
1% 0
Range 10
Q3-Q1 3
Mode 6
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=CHANGE
Extremes
Lowest Obs Highest Obs
0( 28) 8( 12)
0( 27) 10( 1)
0( 26) 10( 4)
0( 25) 10( 18)
1( 29) 10( 20)
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=CHANGE
Stem Leaf # Boxplot
10 0000 4 |
9 |
8 000 3 |
7 000 3 +-----+
6 000000 6 *-----*
5 0000 4 | + |
4 00 2 +-----+
3 |
2 |
1 000 3 |
0 0000 4 |
----+----+----+----+
--------------------------------- ACTIVE=1 ---------------------------------
Univariate Procedure
Variable=CHANGE
Normal Probability Plot
10.5+ ** +*+ *
| +++
| ***+
| ***++
| *****++
5.5+ *** +++
| ** +++
| +++
| ++++
| +++***
0.5+ * *++**
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE1
Moments
N 21 Sum Wgts 21
Mean 9.52381 Sum 200
Std Dev 0.872872 Variance 0.761905
Skewness -1.82512 Kurtosis 2.582689
USS 1920 CSS 15.2381
CV 9.165151 Std Mean 0.190476
T:Mean=0 50 Pr>|T| 0.0001
Num ^= 0 21 Num > 0 21
M(Sign) 10.5 Pr>=|M| 0.0001
Sgn Rank 115.5 Pr>=|S| 0.0001
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE1
Quantiles(Def=5)
100% Max 10 99% 10
75% Q3 10 95% 10
50% Med 10 90% 10
25% Q1 9 10% 8
0% Min 7 5% 8
1% 7
Range 3
Q3-Q1 1
Mode 10
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE1
Extremes
Lowest Obs Highest Obs
7( 10) 10( 16)
8( 12) 10( 18)
8( 1) 10( 19)
9( 17) 10( 20)
9( 7) 10( 21)
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE1
Stem Leaf # Boxplot
10 000000000000000 15 +-----+
9 | + |
9 000 3 +-----+
8 |
8 00 2 |
7
7 0 1 0
----+----+----+----+
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE1
Normal Probability Plot
10.25+ ** ***** ***+*+*+* * *
| ++++++
| * * *+++++
8.75+ +++++
| +++*+*
| ++++++
7.25+++ *
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE2
Moments
N 21 Sum Wgts 21
Mean 8.428571 Sum 177
Std Dev 1.859339 Variance 3.457143
Skewness -1.0622 Kurtosis 0.175307
USS 1561 CSS 69.14286
CV 22.05996 Std Mean 0.405741
T:Mean=0 20.77327 Pr>|T| 0.0001
Num ^= 0 21 Num > 0 21
M(Sign) 10.5 Pr>=|M| 0.0001
Sgn Rank 115.5 Pr>=|S| 0.0001
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE2
Quantiles(Def=5)
100% Max 10 99% 10
75% Q3 10 95% 10
50% Med 9 90% 10
25% Q1 8 10% 6
0% Min 4 5% 5
1% 4
Range 6
Q3-Q1 2
Mode 10
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE2
Extremes
Lowest Obs Highest Obs
4( 1) 10( 14)
5( 3) 10( 15)
6( 10) 10( 16)
6( 6) 10( 19)
7( 2) 10( 20)
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE2
Stem Leaf # Boxplot
10 000000000 9 +-----+
9 000 3 *-----*
8 0000 4 +--+--+
7 0 1 |
6 00 2 |
5 0 1 |
4 0 1 0
----+----+----+----+
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=SCORE2
Normal Probability Plot
10.5+ * *** *+*+*+* *
| *** +++++
| *** *+++++
7.5+ *+++++
| +*+*++
| ++++*
4.5+ ++++*
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=CHANGE
Moments
N 21 Sum Wgts 21
Mean 1.095238 Sum 23
Std Dev 1.578124 Variance 2.490476
Skewness 1.430701 Kurtosis 0.896441
USS 75 CSS 49.80952
CV 144.0896 Std Mean 0.344375
T:Mean=0 3.180365 Pr>|T| 0.0047
Num ^= 0 10 Num > 0 10
M(Sign) 5 Pr>=|M| 0.0020
Sgn Rank 27.5 Pr>=|S| 0.0020
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=CHANGE
Quantiles(Def=5)
100% Max 5 99% 5
75% Q3 1 95% 4
50% Med 0 90% 4
25% Q1 0 10% 0
0% Min 0 5% 0
1% 0
Range 5
Q3-Q1 1
Mode 0
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=CHANGE
Extremes
Lowest Obs Highest Obs
0( 20) 2( 4)
0( 19) 3( 2)
0( 17) 4( 1)
0( 16) 4( 6)
0( 15) 5( 3)
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=CHANGE
Stem Leaf # Boxplot
5 0 1 *
4 00 2 0
3 0 1 0
2 0 1 |
1 00000 5 +--+--+
0 00000000000 11 *-----*
----+----+----+----+
--------------------------------- ACTIVE=2 ---------------------------------
Univariate Procedure
Variable=CHANGE
Normal Probability Plot
5.5+ * +
| * * ++++++
| * ++++++
| ++*++++
| +**+***
0.5+ * * * * * ***+***
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
Univariate Procedure
Schematic Plots
Variable=SCORE1
|
10 + *-----* *-----*
| + | + |
| | |
9 + * +-----+
| |
| |
8 + * |
|
|
7 + 0
------------+-----------+-----------
ACTIVE 1 2
Univariate Procedure
Schematic Plots
Variable=SCORE2
10 + | +-----+
| | *-----*
| | +--+--+
7.5 + | |
| | |
| +-----+ |
5 + | | |
| *--+--* 0
| | |
2.5 + | |
| +-----+
| |
0 + |
------------+-----------+-----------
ACTIVE 1 2
Univariate Procedure
Schematic Plots
Variable=CHANGE
10 + |
| |
| |
7.5 + |
| +-----+
| *-----*
5 + | + | *
| +-----+ 0
| | 0
2.5 + |
| | |
| | +--+--+
0 + | *-----*
------------+-----------+-----------
ACTIVE 1 2
TTEST PROCEDURE
How to do this
Variable: SCORE1
ACTIVE N Mean Std Dev Std Error
--------------------------------------------------------------------------
1 29 9.62068966 0.72770643 0.13513169
2 21 9.52380952 0.87287156 0.19047619
Variances T DF Prob>|T|
---------------------------------------
Unequal 0.4148 38.3 0.6806
Equal 0.4272 48.0 0.6711
For H0: Variances are equal, F' = 1.44 DF = (20,28) Prob>F' = 0.3687
TTEST PROCEDURE
Variable: SCORE2
ACTIVE N Mean Std Dev Std Error
--------------------------------------------------------------------------
1 29 4.37931034 3.14431225 0.58388413
2 21 8.42857143 1.85933936 0.40574111
Variances T DF Prob>|T|
---------------------------------------
Unequal -5.6950 46.4 0.0001
Equal -5.2638 48.0 0.0000
For H0: Variances are equal, F' = 2.86 DF = (28,20) Prob>F' = 0.0178
TTEST PROCEDURE
Variable: CHANGE
ACTIVE N Mean Std Dev Std Error
--------------------------------------------------------------------------
1 29 5.24137931 3.23656754 0.60101550
2 21 1.09523810 1.57812426 0.34437495
Variances T DF Prob>|T|
---------------------------------------
Unequal 5.9856 42.9 0.0001
Equal 5.4121 48.0 0.0000
For H0: Variances are equal, F' = 4.21 DF = (28,20) Prob>F' = 0.0015
General Linear Models Procedure
How to do this
Class Level Information
Class Levels Values
ACTIVE 2 1 2
Number of observations in data set = 50
General Linear Models Procedure
Dependent Variable: SCORE1
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 0.11431856 0.11431856 0.18 0.6711
Error 48 30.06568144 0.62636836
Corrected Total 49 30.18000000
R-Square C.V. Root MSE SCORE1 Mean
0.003788 8.261319 0.79143 9.58000
General Linear Models Procedure
Dependent Variable: SCORE1
Source DF Type I SS Mean Square F Value Pr > F
ACTIVE 1 0.11431856 0.11431856 0.18 0.6711
Source DF Type III SS Mean Square F Value Pr > F
ACTIVE 1 0.11431856 0.11431856 0.18 0.6711
General Linear Models Procedure
Dependent Variable: SCORE2
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 1 199.709557 199.709557 27.71 0.0001
Error 48 345.970443 7.207718
Corrected Total 49 545.680000
R-Square C.V. Root MSE SCORE2 Mean
0.365983 44.15657 2.68472 6.08000
General Linear Models Procedure
Dependent Variable: SCORE2
Source DF Type I SS Mean Square F Value Pr > F
ACTIVE 1 199.709557 199.709557 27.71 0.0001
Source DF Type III SS Mean Square F Value Pr > F
ACTIVE 1 199.709557 199.709557 27.71 0.0001
General Linear Models Procedure
Repeated Measures Analysis of Variance
Repeated Measures Level Information
Dependent Variable SCORE1 SCORE2
Level of TIME 1 2
General Linear Models Procedure
Repeated Measures Analysis of Variance
Manova Test Criteria and Exact F Statistics for
the Hypothesis of no TIME Effect
H = Type III SS&CP Matrix for TIME E = Error SS&CP Matrix
S=1 M=-0.5 N=23
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.41231449 68.4160 1 48 0.0001
Pillai's Trace 0.58768551 68.4160 1 48 0.0001
Hotelling-Lawley Trace 1.42533317 68.4160 1 48 0.0001
Roy's Greatest Root 1.42533317 68.4160 1 48 0.0001
General Linear Models Procedure
Repeated Measures Analysis of Variance
Manova Test Criteria and Exact F Statistics for
the Hypothesis of no TIME*ACTIVE Effect
H = Type III SS&CP Matrix for TIME*ACTIVE E = Error SS&CP Matrix
S=1 M=-0.5 N=23
Statistic Value F Num DF Den DF Pr > F
Wilks' Lambda 0.62103144 29.2908 1 48 0.0001
Pillai's Trace 0.37896856 29.2908 1 48 0.0001
Hotelling-Lawley Trace 0.61022444 29.2908 1 48 0.0001
Roy's Greatest Root 0.61022444 29.2908 1 48 0.0001
General Linear Models Procedure
Repeated Measures Analysis of Variance
Tests of Hypotheses for Between Subjects Effects
Source DF Type III SS Mean Square F Value Pr > F
ACTIVE 1 95.133810 95.133810 22.33 0.0001
Error 48 204.476190 4.259921
General Linear Models Procedure
Repeated Measures Analysis of Variance
Univariate Tests of Hypotheses for Within Subject Effects
Source: TIME
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 244.53006568 244.53006568 68.42 0.0001 . .
Source: TIME*ACTIVE
Adj Pr > F
DF Type III SS Mean Square F Value Pr > F G - G H - F
1 104.69006568 104.69006568 29.29 0.0001 . .
Source: Error(TIME)
DF Type III SS Mean Square
48 171.55993432 3.57416530
The SAS System 11
09:02 Monday, June 29, 1998
General Linear Models Procedure
Level of -----------SCORE1----------- -----------SCORE2-----------
ACTIVE N Mean SD Mean SD
1 29 9.62068966 0.72770643 4.37931034 3.14431225
2 21 9.52380952 0.87287156 8.42857143 1.85933936
Chi-Square: Reporting Pain improvement by magnetic activity
How to do this
TABLE OF IMP BY ACTIV
IMP ACTIV
Frequency|
Percent |
Row Pct |
Col Pct | 1| 2| Total
---------+--------+--------+
1 | 22 | 4 | 26
| 44.00 | 8.00 | 52.00
| 84.62 | 15.38 |
| 75.86 | 19.05 |
---------+--------+--------+
Total 29 21 50
58.00 42.00 100.00
(Continued)
Chi-Square: Reporting Pain improvement by magnetic activity
TABLE OF IMP BY ACTIV
IMP ACTIV
Frequency|
Percent |
Row Pct |
Col Pct | 1| 2| Total
---------+--------+--------+
2 | 7 | 17 | 24
| 14.00 | 34.00 | 48.00
| 29.17 | 70.83 |
| 24.14 | 80.95 |
---------+--------+--------+
Total 29 21 50
58.00 42.00 100.00
Chi-Square: Reporting Pain improvement by magnetic activity
STATISTICS FOR TABLE OF IMP BY ACTIV
Statistic DF Value Prob
------------------------------------------------------
Chi-Square 1 15.751 0.001
Likelihood Ratio Chi-Square 1 16.730 0.001
Continuity Adj. Chi-Square 1 13.557 0.001
Mantel-Haenszel Chi-Square 1 15.436 0.001
Fisher's Exact Test (Left) 1.000
(Right) 8.23E-05
(2-Tail) 1.32E-04
Phi Coefficient 0.561
Contingency Coefficient 0.489
Cramer's V 0.561
Chi-Square: Reporting Pain improvement by magnetic activity
Statistic Value ASE
------------------------------------------------------
Gamma 0.861 0.091
Kendall's Tau-b 0.561 0.116
Stuart's Tau-c 0.554 0.117
Somers' D C|R 0.554 0.117
Somers' D R|C 0.568 0.117
Pearson Correlation 0.561 0.116
Spearman Correlation 0.561 0.116
Lambda Asymmetric C|R 0.476 0.169
Lambda Asymmetric R|C 0.542 0.129
Lambda Symmetric 0.511 0.143
Uncertainty Coefficient C|R 0.246 0.108
Uncertainty Coefficient R|C 0.242 0.107
Uncertainty Coefficient Symmetric 0.244 0.108
Chi-Squre: Reporting Pain improvement by magnetic activity
Estimates of the Relative Risk (Row1/Row2)
95%
Type of Study Value Confidence Bounds
------------------------------------------------------
Case-Control 13.357 3.354 53.196
Cohort (Col1 Risk) 2.901 1.523 5.528
Cohort (Col2 Risk) 0.217 0.085 0.555
Sample Size = 50
ANCOVA
How to do this
General Linear Models Procedure
Class Level Information
Class Levels Values
ACTIVE 2 1 2
Number of observations in data set = 50
General Linear Models Procedure
Dependent Variable: SCORE2
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 3 219.364230 73.121410 10.31 0.0001
Error 46 326.315770 7.093821
Corrected Total 49 545.680000
R-Square C.V. Root MSE SCORE2 Mean
0.402002 43.80630 2.66342 6.08000
General Linear Models Procedure
Dependent Variable: SCORE2
Source DF Type I SS Mean Square F Value Pr > F
SCORE1 1 4.520292 4.520292 0.64 0.4288
ACTIVE 1 204.198540 204.198540 28.79 0.0001
SCORE1*ACTIVE 1 10.645398 10.645398 1.50 0.2268
Source DF Type III SS Mean Square F Value Pr > F
SCORE1 1 8.7421761 8.7421761 1.23 0.2727
ACTIVE 1 4.3303623 4.3303623 0.61 0.4386
SCORE1*ACTIVE 1 10.6453984 10.6453984 1.50 0.2268
General Linear Models Procedure
Level of -----------SCORE2----------- -----------SCORE1-----------
ACTIVE N Mean SD Mean SD
1 29 4.37931034 3.14431225 9.62068966 0.72770643
2 21 8.42857143 1.85933936 9.52380952 0.87287156
The SAS System 5
11:13 Tuesday, June 30, 1998
General Linear Models Procedure
Class Level Information
Class Levels Values
ACTIVE 2 1 2
Number of observations in data set = 50
General Linear Models Procedure
Dependent Variable: SCORE2
Sum of Mean
Source DF Squares Square F Value Pr > F
Model 2 208.718831 104.359416 14.56 0.0001
Error 47 336.961169 7.169387
Corrected Total 49 545.680000
R-Square C.V. Root MSE SCORE2 Mean
0.382493 44.03900 2.67757 6.08000
General Linear Models Procedure
Dependent Variable: SCORE2
Source DF Type I SS Mean Square F Value Pr > F
SCORE1 1 4.520292 4.520292 0.63 0.4312
ACTIVE 1 204.198540 204.198540 28.48 0.0001
Source DF Type III SS Mean Square F Value Pr > F
SCORE1 1 9.009275 9.009275 1.26 0.2680
ACTIVE 1 204.198540 204.198540 28.48 0.0001
General Linear Models Procedure
Level of -----------SCORE2----------- -----------SCORE1-----------
ACTIVE N Mean SD Mean SD
1 29 4.37931034 3.14431225 9.62068966 0.72770643
2 21 8.42857143 1.85933936 9.52380952 0.87287156