Computer Project 2
1. (Bivariate Association) Compute the Pearson and Spearman Correlation coefficients between log(salary) and every continuous performance measures. Assess the strength of the association based on p-values from formal statistical tests.
/*This will calculate the Pearson and Spearman Correlation Coefficients
between log(salary) and every continous performance measures*/
/* Assess Normailty */
PROC UNIVARIATE Normal;
var logsalary X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12;
Run;
/* Check linear association */
Proc plot HPCT=50 VPCT=75;
Plot logsalary*X1;
Plot logsalary*X2;
Plot logsalary*X3;
Plot logsalary*X4;
Plot logsalary*X5;
Plot logsalary*X6;
Plot logsalary*X7;
Plot logsalary*X8;
Plot logsalary*X9;
Plot logsalary*X10;
Plot logsalary*X11;
Plot logsalary*X12;
Run;
/* Compute Pearson Correlation Coefficient */
Proc corr;
var logsalary X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12;
Run;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 69
The CORR Procedure
13 Variables: logsalary X1 X2 X3 X4 X5 X6 X7
X8 X9 X10 X11 X12
Simple Statistics
Variable N Mean Std Dev Sum Minimum Maximum
logsalary 337 6.53542 1.17654 2202 4.69135 8.71604
X1 337 0.25782 0.03955 86.88700 0.06300 0.45700
X2 337 0.32397 0.04713 109.17900 0.06300 0.48600
X3 337 46.69733 29.02017 15737 0 133.00000
X4 337 92.83383 51.89632 31285 1.00000 216.00000
X5 337 16.67359 10.45200 5619 0 49.00000
X6 337 2.33828 2.54334 788.00000 0 15.00000
X7 337 9.09792 9.28993 3066 0 44.00000
X8 337 44.02077 29.55941 14835 0 133.00000
X9 337 35.01780 24.84247 11801 0 138.00000
X10 337 56.70623 33.82878 19110 1.00000 175.00000
X11 337 8.24629 11.66478 2779 0 76.00000
X12 337 6.77151 5.92749 2282 0 31.00000
Simple Statistics
Variable Label
logsalary
X1 BattingAverage
X2 OnBasePercentage
X3 Runs
X4 Hits
X5 Doubles
X6 Triples
X7 HomeRuns
X8 RunsBattedIn
X9 Walks
X10 StrikeOuts
X11 StolenBases
X12 Errors
The SAS System 13:29 Friday, October 25, 2002 70
The CORR Procedure
Pearson Correlation Coefficients, N = 337
Prob > |r| under H0: Rho=0
logsalary X1 X2 X3 X4 X5 X6
logsalary 1.00000 0.26610 0.30622 0.64711 0.66753 0.59876 0.27363
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X1 0.26610 1.00000 0.80596 0.43674 0.50779 0.45168 0.26380
BattingAverage <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X2 0.30622 0.80596 1.00000 0.51357 0.45661 0.40398 0.19855
OnBasePercentage <.0001 <.0001 <.0001 <.0001 <.0001 0.0002
X3 0.64711 0.43674 0.51357 1.00000 0.92317 0.83224 0.54922
Runs <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X4 0.66753 0.50779 0.45661 0.92317 1.00000 0.88930 0.54428
Hits <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X5 0.59876 0.45168 0.40398 0.83224 0.88930 1.00000 0.41651
Doubles <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X6 0.27363 0.26380 0.19855 0.54922 0.54428 0.41651 1.00000
Triples <.0001 <.0001 0.0002 <.0001 <.0001 <.0001
X7 0.53118 0.21273 0.31121 0.68106 0.61400 0.63515 0.12468
HomeRuns <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 0.0221
X8 0.65223 0.36954 0.39942 0.83348 0.85162 0.82537 0.33118
RunsBattedIn <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X9 0.57211 0.27989 0.59046 0.82839 0.72301 0.64030 0.30773
Walks <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X10 0.41406 0.07625 0.20827 0.68490 0.64626 0.60070 0.32898
StrikeOuts <.0001 0.1626 0.0001 <.0001 <.0001 <.0001 <.0001
X11 0.24215 0.20090 0.23008 0.52612 0.42902 0.29264 0.52877
StolenBases <.0001 0.0002 <.0001 <.0001 <.0001 <.0001 <.0001
X12 0.18394 0.14537 0.09549 0.34226 0.41589 0.33900 0.19802
Errors 0.0007 0.0075 0.0800 <.0001 <.0001 <.0001 0.0003
The SAS System 13:29 Friday, October 25, 2002 71
The CORR Procedure
Pearson Correlation Coefficients, N = 337
Prob > |r| under H0: Rho=0
X7 X8 X9 X10 X11 X12
logsalary 0.53118 0.65223 0.57211 0.41406 0.24215 0.18394
<.0001 <.0001 <.0001 <.0001 <.0001 0.0007
X1 0.21273 0.36954 0.27989 0.07625 0.20090 0.14537
BattingAverage <.0001 <.0001 <.0001 0.1626 0.0002 0.0075
X2 0.31121 0.39942 0.59046 0.20827 0.23008 0.09549
OnBasePercentage <.0001 <.0001 <.0001 0.0001 <.0001 0.0800
X3 0.68106 0.83348 0.82839 0.68490 0.52612 0.34226
Runs <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X4 0.61400 0.85162 0.72301 0.64626 0.42902 0.41589
Hits <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X5 0.63515 0.82537 0.64030 0.60070 0.29264 0.33900
Doubles <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X6 0.12468 0.33118 0.30773 0.32898 0.52877 0.19802
Triples 0.0221 <.0001 <.0001 <.0001 <.0001 0.0003
X7 1.00000 0.87738 0.62498 0.74882 0.07800 0.15239
HomeRuns <.0001 <.0001 <.0001 0.1531 0.0051
X8 0.87738 1.00000 0.72706 0.74545 0.20596 0.29305
RunsBattedIn <.0001 <.0001 <.0001 0.0001 <.0001
X9 0.62498 0.72706 1.00000 0.66633 0.35483 0.24301
Walks <.0001 <.0001 <.0001 <.0001 <.0001
X10 0.74882 0.74545 0.66633 1.00000 0.27865 0.30159
StrikeOuts <.0001 <.0001 <.0001 <.0001 <.0001
X11 0.07800 0.20596 0.35483 0.27865 1.00000 0.17028
StolenBases 0.1531 0.0001 <.0001 <.0001 0.0017
X12 0.15239 0.29305 0.24301 0.30159 0.17028 1.00000
Errors 0.0051 <.0001 <.0001 <.0001 0.0017
/* Spearman Correlation Coefficient */
PROC CORR SPEARMAN;
VAR logsalary X1 X2 X3 X4 X5 X6 X7 X8 X9 X10 X11 X12;
Run;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 78
The CORR Procedure
13 Variables: logsalary X1 X2 X3 X4 X5 X6 X7
X8 X9 X10 X11 X12
Simple Statistics
Variable N Mean Std Dev Median Minimum Maximum
logsalary 337 6.53542 1.17654 6.60665 4.69135 8.71604
X1 337 0.25782 0.03955 0.26000 0.06300 0.45700
X2 337 0.32397 0.04713 0.32300 0.06300 0.48600
X3 337 46.69733 29.02017 41.00000 0 133.00000
X4 337 92.83383 51.89632 91.00000 1.00000 216.00000
X5 337 16.67359 10.45200 15.00000 0 49.00000
X6 337 2.33828 2.54334 2.00000 0 15.00000
X7 337 9.09792 9.28993 6.00000 0 44.00000
X8 337 44.02077 29.55941 39.00000 0 133.00000
X9 337 35.01780 24.84247 30.00000 0 138.00000
X10 337 56.70623 33.82878 49.00000 1.00000 175.00000
X11 337 8.24629 11.66478 4.00000 0 76.00000
X12 337 6.77151 5.92749 5.00000 0 31.00000
Simple Statistics
Variable Label
logsalary
X1 BattingAverage
X2 OnBasePercentage
X3 Runs
X4 Hits
X5 Doubles
X6 Triples
X7 HomeRuns
X8 RunsBattedIn
X9 Walks
X10 StrikeOuts
X11 StolenBases
X12 Errors
The SAS System 13:29 Friday, October 25, 2002 79
The CORR Procedure
Spearman Correlation Coefficients, N = 337
Prob > |r| under H0: Rho=0
logsalary X1 X2 X3 X4 X5 X6
logsalary 1.00000 0.31464 0.34096 0.66218 0.67126 0.61791 0.33701
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X1 0.31464 1.00000 0.73065 0.47004 0.54789 0.48025 0.28906
BattingAverage <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X2 0.34096 0.73065 1.00000 0.52780 0.45553 0.40368 0.25081
OnBasePercentage <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X3 0.66218 0.47004 0.52780 1.00000 0.93111 0.85502 0.59683
Runs <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X4 0.67126 0.54789 0.45553 0.93111 1.00000 0.90628 0.56720
Hits <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X5 0.61791 0.48025 0.40368 0.85502 0.90628 1.00000 0.46651
Doubles <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X6 0.33701 0.28906 0.25081 0.59683 0.56720 0.46651 1.00000
Triples <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X7 0.55863 0.25559 0.32183 0.70460 0.65957 0.69279 0.22444
HomeRuns <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X8 0.67539 0.40710 0.40005 0.86586 0.89225 0.87453 0.41543
RunsBattedIn <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X9 0.61785 0.30357 0.61867 0.86424 0.78706 0.72234 0.45490
Walks <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X10 0.46050 0.08966 0.19676 0.73729 0.70850 0.68638 0.39461
StrikeOuts <.0001 0.1004 0.0003 <.0001 <.0001 <.0001 <.0001
X11 0.32760 0.25311 0.26060 0.59317 0.51750 0.40239 0.60053
StolenBases <.0001 <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X12 0.23869 0.15070 0.07321 0.37819 0.44014 0.38978 0.29039
Errors <.0001 0.0056 0.1800 <.0001 <.0001 <.0001 <.0001
The SAS System 13:29 Friday, October 25, 2002 80
The CORR Procedure
Spearman Correlation Coefficients, N = 337
Prob > |r| under H0: Rho=0
X7 X8 X9 X10 X11 X12
logsalary 0.55863 0.67539 0.61785 0.46050 0.32760 0.23869
<.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X1 0.25559 0.40710 0.30357 0.08966 0.25311 0.15070
BattingAverage <.0001 <.0001 <.0001 0.1004 <.0001 0.0056
X2 0.32183 0.40005 0.61867 0.19676 0.26060 0.07321
OnBasePercentage <.0001 <.0001 <.0001 0.0003 <.0001 0.1800
X3 0.70460 0.86586 0.86424 0.73729 0.59317 0.37819
Runs <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X4 0.65957 0.89225 0.78706 0.70850 0.51750 0.44014
Hits <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X5 0.69279 0.87453 0.72234 0.68638 0.40239 0.38978
Doubles <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X6 0.22444 0.41543 0.45490 0.39461 0.60053 0.29039
Triples <.0001 <.0001 <.0001 <.0001 <.0001 <.0001
X7 1.00000 0.85543 0.64377 0.76129 0.20358 0.23461
HomeRuns <.0001 <.0001 <.0001 0.0002 <.0001
X8 0.85543 1.00000 0.78294 0.78425 0.34717 0.36332
RunsBattedIn <.0001 <.0001 <.0001 <.0001 <.0001
X9 0.64377 0.78294 1.00000 0.70795 0.44102 0.31638
Walks <.0001 <.0001 <.0001 <.0001 <.0001
X10 0.76129 0.78425 0.70795 1.00000 0.37602 0.33672
StrikeOuts <.0001 <.0001 <.0001 <.0001 <.0001
X11 0.20358 0.34717 0.44102 0.37602 1.00000 0.28014
StolenBases 0.0002 <.0001 <.0001 <.0001 <.0001
X12 0.23461 0.36332 0.31638 0.33672 0.28014 1.00000
Errors <.0001 <.0001 <.0001 <.0001 <.0001
2. (Comparing Two Populations) Use both a parametric t test and a nonparametric procedure to compare salaries between players who have free agent eligibility and those who do not.
/*Question 2*/
/*This will give the status and the players name with their salary*/
DATA salary1;
SET baseball;
IF X13=1 THEN STATUS='free';
ELSE IF X15=1 THEN STATUS='arb';
ELSE STATUS='none';
proc print;
VAR status;
ID ID Y;
run;
/*This will sort salary1 by status*/
PROC SORT DATA=salary1;
BY Status;
RUN;
/*Parametric T Test to compare salaries and status*/
Proc TTest Data=salary1 CI=NONE;
By STATUS;
Var Y;
run;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 150
------------------------------------------ STATUS=arb ------------------------------------------
The TTEST Procedure
Statistics
Lower CL Upper CL
Variable N Mean Mean Mean Std Dev Std Err Minimum Maximum
Y 65 1312.2 1567.6 1822.9 1030.5 127.82 109 5150
T-Tests
Variable DF t Value Pr > |t|
Y 64 12.26 <.0001
The SAS System 13:29 Friday, October 25, 2002 151
----------------------------------------- STATUS=free ------------------------------------------
The TTEST Procedure
Statistics
Lower CL Upper CL
Variable N Mean Mean Mean Std Dev Std Err Minimum Maximum
Y 134 1896.9 2108.9 2321 1241.2 107.22 109 6100
T-Tests
Variable DF t Value Pr > |t|
Y 133 19.67 <.0001
The SAS System 13:29 Friday, October 25, 2002 152
----------------------------------------- STATUS=none ------------------------------------------
The TTEST Procedure
Statistics
Lower CL Upper CL
Variable N Mean Mean Mean Std Dev Std Err Minimum Maximum
Y 138 234.49 262.78 291.08 168.11 14.31 109 935
T-Tests
Variable DF t Value Pr > |t|
Y 137 18.36 <.0001
/*Check Statistical Assumptions - Normality */
/* The assumption of equal variances has been checked in PROC TTEST */
Proc UNIVARIATE DATA=salary1 Normal plot;
By STATUS;
Var Y;
Run;
Results
The SAS System 13:29 Friday, October 25, 2002 164
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Moments
N 65 Sum Weights 65
Mean 1567.56923 Sum Observations 101892
Std Deviation 1030.52578 Variance 1061983.37
Skewness 1.45078254 Kurtosis 2.63021668
Uncorrected SS 227689700 Corrected SS 67966935.9
Coeff Variation 65.7403677 Std Error Mean 127.820991
Basic Statistical Measures
Location Variability
Mean 1567.569 Std Deviation 1031
Median 1262.000 Variance 1061983
Mode 1000.000 Range 5041
Interquartile Range 1200
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 12.26379 Pr > |t| <.0001
Sign M 32.5 Pr >= |M| <.0001
Signed Rank S 1072.5 Pr >= |S| <.0001
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.882636 Pr < W <0.0001
Kolmogorov-Smirnov D 0.140892 Pr > D <0.0100
Cramer-von Mises W-Sq 0.332383 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 2.016276 Pr > A-Sq <0.0050
Quantiles (Definition 5)
Quantile Estimate
100% Max 5150
99% 5150
95% 3300
90% 2833
75% Q3 2050
The SAS System 13:29 Friday, October 25, 2002 165
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Quantiles (Definition 5)
Quantile Estimate
50% Median 1262
25% Q1 850
10% 650
5% 425
1% 109
0% Min 109
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
109 51 3050 36
125 30 3300 26
370 16 3850 65
425 54 5000 58
500 15 5150 8
The SAS System 13:29 Friday, October 25, 2002 166
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Stem Leaf # Boxplot
50 05 2 0
48
46
44
42
40
38 5 1 |
36 |
34 |
32 0 1 |
30 5 1 |
28 38 2 |
26 05 2 |
24 837 3 |
22 1 1 |
20 0055057 7 +-----+
18 03 2 | |
16 055 3 | |
14 46035 5 | + |
12 01600 5 *-----*
10 0008859 7 | |
8 05884559 8 +-----+
6 562344668 9 |
4 209 3 |
2 7 1 |
0 12 2 |
----+----+----+----+
Multiply Stem.Leaf by 10**+2
The SAS System 13:29 Friday, October 25, 2002 167
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Normal Probability Plot
5100+ * *
|
|
|
|
4100+ ++
| * ++
| ++
| ++
| *+
3100+ +*
| +**
| **
| **
| ++*
2100+ ****
| +**
| ++**
| ++***
| ++**
1100+ +****
| ****
| ******
| *** ++
| * ++
100+ * * ++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
The SAS System 13:29 Friday, October 25, 2002 168
----------------------------------------- STATUS=free ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Moments
N 134 Sum Weights 134
Mean 2108.9403 Sum Observations 282598
Std Deviation 1241.19395 Variance 1540562.42
Skewness 0.41272592 Kurtosis -0.2517405
Uncorrected SS 800877112 Corrected SS 204894802
Coeff Variation 58.8539158 Std Error Mean 107.222826
Basic Statistical Measures
Location Variability
Mean 2108.940 Std Deviation 1241
Median 2171.000 Variance 1540562
Mode 2500.000 Range 5991
Interquartile Range 1910
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 19.66876 Pr > |t| <.0001
Sign M 67 Pr >= |M| <.0001
Signed Rank S 4522.5 Pr >= |S| <.0001
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.968001 Pr < W 0.0030
Kolmogorov-Smirnov D 0.088906 Pr > D 0.0100
Cramer-von Mises W-Sq 0.139511 Pr > W-Sq 0.0341
Anderson-Darling A-Sq 1.020792 Pr > A-Sq 0.0108
Quantiles (Definition 5)
Quantile Estimate
100% Max 6100
99% 5300
95% 4275
90% 3650
75% Q3 2900
The SAS System 13:29 Friday, October 25, 2002 169
----------------------------------------- STATUS=free ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Quantiles (Definition 5)
Quantile Estimate
50% Median 2171
25% Q1 990
10% 550
5% 350
1% 109
0% Min 109
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
109 129 4350 39
109 112 4450 25
109 79 4500 70
284 85 5300 86
300 84 6100 10
Stem Leaf # Boxplot
6 1 1 0
5
5 3 1 |
4 5 1 |
4 01123344 8 |
3 5566666678 10 |
3 011222233444 12 |
2 5555566677888889 16 +-----+
2 0000001222222233333444444444 28 *--+--*
1 6666668889 10 | |
1 000012222223444 15 +-----+
0 556666667778888899999 21 |
0 11133344444 11 |
----+----+----+----+----+---
Multiply Stem.Leaf by 10**+3
The SAS System 13:29 Friday, October 25, 2002 170
----------------------------------------- STATUS=free ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Normal Probability Plot
6250+ *
|
| *++
| +*++
| ******
| ****+
3250+ ****+
| ****
| ******
| ***+
| ++***
| ********
250+* * * *****++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
The SAS System 13:29 Friday, October 25, 2002 171
----------------------------------------- STATUS=none ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Moments
N 138 Sum Weights 138
Mean 262.782609 Sum Observations 36264
Std Deviation 168.105795 Variance 28259.5582
Skewness 1.52966616 Kurtosis 2.06178012
Uncorrected SS 13401108 Corrected SS 3871559.48
Coeff Variation 63.9714308 Std Error Mean 14.3101156
Basic Statistical Measures
Location Variability
Mean 262.7826 Std Deviation 168.10579
Median 195.0000 Variance 28260
Mode 109.0000 Range 826.00000
Interquartile Range 210.00000
NOTE: The mode displayed is the smallest of 5 modes with a count of 5.
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 18.36342 Pr > |t| <.0001
Sign M 69 Pr >= |M| <.0001
Signed Rank S 4795.5 Pr >= |S| <.0001
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.816707 Pr < W <0.0001
Kolmogorov-Smirnov D 0.181833 Pr > D <0.0100
Cramer-von Mises W-Sq 1.396782 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 8.222419 Pr > A-Sq <0.0050
Quantiles (Definition 5)
Quantile Estimate
100% Max 935
99% 750
95% 640
The SAS System 13:29 Friday, October 25, 2002 172
----------------------------------------- STATUS=none ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Quantiles (Definition 5)
Quantile Estimate
90% 525
75% Q3 350
50% Median 195
25% Q1 140
10% 117
5% 113
1% 109
0% Min 109
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
109 138 687 63
109 97 700 74
109 91 750 38
109 62 750 87
109 61 935 42
Stem Leaf # Boxplot
9 4 1 0
8
8
7 55 2 0
7 0 1 0
6 59 2 0
6 234 3 |
5 6668 4 |
5 0222 4 |
4 56 2 |
4 0003 4 |
3 555666666789 12 +-----+
3 0002222234 10 | |
2 5666888899 10 | + |
2 00000022333344 14 *-----*
1 555555555666667778888888889 27 | |
1 111111111222222222223333333444444444444444 42 +-----+
----+----+----+----+----+----+----+----+--
Multiply Stem.Leaf by 10**+2
The SAS System 13:29 Friday, October 25, 2002 173
----------------------------------------- STATUS=none ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Normal Probability Plot
925+ *
|
|
| * *
| *
| ** ++
| *** +++
| *** +++
525+ * +++
| *+++
| +**
| +****
| ++***
| +++**
| +++***
| ++*****
125+* * * *** ***********
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
The SAS System 13:29 Friday, October 25, 2002 174
The UNIVARIATE Procedure
Variable: Y (Salary)
Schematic Plots
|
6000 + 0
|
|
| 0 |
5000 + 0 |
| |
| |
| |
4000 + |
| | |
| | |
| | |
3000 + | +-----+
| | | |
| | | |
| | *-----*
2000 + +-----+ | + |
| | | | |
| | + | | |
| *-----* | |
1000 + | | +-----+ 0
| +-----+ | 0
| | | |
| | | *--+--*
0 + | | |
------------+-----------+-----------+-----------
STATUS arb free none
/*Nonparametric procedure to compare salaries of players
and their status using Wilcoxon Rank-Sum Test */
PROC NPAR1WAY DATA=salary1 WILCOXON;
Class STATUS;
Var Y;
RUN;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 176
The NPAR1WAY Procedure
Wilcoxon Scores (Rank Sums) for Variable Y
Classified by Variable STATUS
Sum of Expected Std Dev Mean
STATUS N Scores Under H0 Under H0 Score
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
arb 65 13971.00 10985.0 705.657420 214.938462
free 134 32252.50 22646.0 875.292486 240.690299
none 138 10729.50 23322.0 879.465613 77.750000
Average scores were used for ties.
Kruskal-Wallis Test
Chi-Square 208.0733
DF 2
Pr > Chi-Square <.0001
3. (Comparing more than two populations) Define a new variable status such that status = “free”, if a player has free agency eligibility; “arb”, if he has arbitration eligibility; and “none”, otherwise. Then apply ANOVA techniques and its nonparametric alternative method to compare salary in these two groups. If their differences are found significant, then perform further analysis such as multiple comparisons to find out what have led to the rejection to the null hypothesis.
/* ANOVA with Multiple Comparison */
PROC GLM DATA=salary1;
CLASS ID STATUS;
MODEL Y = ID STATUS;
MEANS STATUS / TUKEY
CLDIFF ALPHA=0.05;
RUN;
****Gives an output but has limitations and seems strange***
/*Checking Assumptions*/
PROC MEANS DATA=salary1;
BY STATUS;
VAR Y;
RUN;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 220
------------------------------------------ STATUS=arb ------------------------------------------
The MEANS Procedure
Analysis Variable : Y Salary
N Mean Std Dev Minimum Maximum
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
65 1567.57 1030.53 109.0000000 5150.00
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
----------------------------------------- STATUS=free ------------------------------------------
Analysis Variable : Y Salary
N Mean Std Dev Minimum Maximum
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
134 2108.94 1241.19 109.0000000 6100.00
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
----------------------------------------- STATUS=none ------------------------------------------
Analysis Variable : Y Salary
N Mean Std Dev Minimum Maximum
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
138 262.7826087 168.1057948 109.0000000 935.0000000
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
/*Check for normality */
/* Parallel Boxplot */
PROC UNIVARIATE NORMAL PLOT DATA=salary1;
BY STATUS;
VAR Y;
RUN;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 232
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Moments
N 65 Sum Weights 65
Mean 1567.56923 Sum Observations 101892
Std Deviation 1030.52578 Variance 1061983.37
Skewness 1.45078254 Kurtosis 2.63021668
Uncorrected SS 227689700 Corrected SS 67966935.9
Coeff Variation 65.7403677 Std Error Mean 127.820991
Basic Statistical Measures
Location Variability
Mean 1567.569 Std Deviation 1031
Median 1262.000 Variance 1061983
Mode 1000.000 Range 5041
Interquartile Range 1200
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 12.26379 Pr > |t| <.0001
Sign M 32.5 Pr >= |M| <.0001
Signed Rank S 1072.5 Pr >= |S| <.0001
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.882636 Pr < W <0.0001
Kolmogorov-Smirnov D 0.140892 Pr > D <0.0100
Cramer-von Mises W-Sq 0.332383 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 2.016276 Pr > A-Sq <0.0050
Quantiles (Definition 5)
Quantile Estimate
100% Max 5150
99% 5150
95% 3300
90% 2833
75% Q3 2050
The SAS System 13:29 Friday, October 25, 2002 233
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Quantiles (Definition 5)
Quantile Estimate
50% Median 1262
25% Q1 850
10% 650
5% 425
1% 109
0% Min 109
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
109 51 3050 36
125 30 3300 26
370 16 3850 65
425 54 5000 58
500 15 5150 8
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Stem Leaf # Boxplot
50 05 2 0
48
46
44
42
40
38 5 1 |
36 |
34 |
32 0 1 |
30 5 1 |
28 38 2 |
26 05 2 |
24 837 3 |
22 1 1 |
20 0055057 7 +-----+
18 03 2 | |
16 055 3 | |
14 46035 5 | + |
12 01600 5 *-----*
10 0008859 7 | |
8 05884559 8 +-----+
6 562344668 9 |
4 209 3 |
2 7 1 |
0 12 2 |
----+----+----+----+
Multiply Stem.Leaf by 10**+2
The SAS System 13:29 Friday, October 25, 2002 235
------------------------------------------ STATUS=arb ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Normal Probability Plot
5100+ * *
|
|
|
|
4100+ ++
| * ++
| ++
| ++
| *+
3100+ +*
| +**
| **
| **
| ++*
2100+ ****
| +**
| ++**
| ++***
| ++**
1100+ +****
| ****
| ******
| *** ++
| * ++
100+ * * ++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
The SAS System 13:29 Friday, October 25, 2002 236
----------------------------------------- STATUS=free ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Moments
N 134 Sum Weights 134
Mean 2108.9403 Sum Observations 282598
Std Deviation 1241.19395 Variance 1540562.42
Skewness 0.41272592 Kurtosis -0.2517405
Uncorrected SS 800877112 Corrected SS 204894802
Coeff Variation 58.8539158 Std Error Mean 107.222826
Basic Statistical Measures
Location Variability
Mean 2108.940 Std Deviation 1241
Median 2171.000 Variance 1540562
Mode 2500.000 Range 5991
Interquartile Range 1910
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 19.66876 Pr > |t| <.0001
Sign M 67 Pr >= |M| <.0001
Signed Rank S 4522.5 Pr >= |S| <.0001
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.968001 Pr < W 0.0030
Kolmogorov-Smirnov D 0.088906 Pr > D 0.0100
Cramer-von Mises W-Sq 0.139511 Pr > W-Sq 0.0341
Anderson-Darling A-Sq 1.020792 Pr > A-Sq 0.0108
Quantiles (Definition 5)
Quantile Estimate
100% Max 6100
99% 5300
95% 4275
90% 3650
75% Q3 2900
The SAS System 13:29 Friday, October 25, 2002 237
----------------------------------------- STATUS=free ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Quantiles (Definition 5)
Quantile Estimate
50% Median 2171
25% Q1 990
10% 550
5% 350
1% 109
0% Min 109
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
109 129 4350 39
109 112 4450 25
109 79 4500 70
284 85 5300 86
300 84 6100 10
Stem Leaf # Boxplot
6 1 1 0
5
5 3 1 |
4 5 1 |
4 01123344 8 |
3 5566666678 10 |
3 011222233444 12 |
2 5555566677888889 16 +-----+
2 0000001222222233333444444444 28 *--+--*
1 6666668889 10 | |
1 000012222223444 15 +-----+
0 556666667778888899999 21 |
0 11133344444 11 |
----+----+----+----+----+---
Multiply Stem.Leaf by 10**+3
The SAS System 13:29 Friday, October 25, 2002 238
----------------------------------------- STATUS=free ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Normal Probability Plot
6250+ *
|
| *++
| +*++
| ******
| ****+
3250+ ****+
| ****
| ******
| ***+
| ++***
| ********
250+* * * *****++
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
The SAS System 13:29 Friday, October 25, 2002 239
----------------------------------------- STATUS=none ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Moments
N 138 Sum Weights 138
Mean 262.782609 Sum Observations 36264
Std Deviation 168.105795 Variance 28259.5582
Skewness 1.52966616 Kurtosis 2.06178012
Uncorrected SS 13401108 Corrected SS 3871559.48
Coeff Variation 63.9714308 Std Error Mean 14.3101156
Basic Statistical Measures
Location Variability
Mean 262.7826 Std Deviation 168.10579
Median 195.0000 Variance 28260
Mode 109.0000 Range 826.00000
Interquartile Range 210.00000
NOTE: The mode displayed is the smallest of 5 modes with a count of 5.
Tests for Location: Mu0=0
Test -Statistic- -----p Value------
Student's t t 18.36342 Pr > |t| <.0001
Sign M 69 Pr >= |M| <.0001
Signed Rank S 4795.5 Pr >= |S| <.0001
Tests for Normality
Test --Statistic--- -----p Value------
Shapiro-Wilk W 0.816707 Pr < W <0.0001
Kolmogorov-Smirnov D 0.181833 Pr > D <0.0100
Cramer-von Mises W-Sq 1.396782 Pr > W-Sq <0.0050
Anderson-Darling A-Sq 8.222419 Pr > A-Sq <0.0050
Quantiles (Definition 5)
Quantile Estimate
100% Max 935
99% 750
95% 640
The SAS System 13:29 Friday, October 25, 2002 240
----------------------------------------- STATUS=none ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Quantiles (Definition 5)
Quantile Estimate
90% 525
75% Q3 350
50% Median 195
25% Q1 140
10% 117
5% 113
1% 109
0% Min 109
Extreme Observations
----Lowest---- ----Highest---
Value Obs Value Obs
109 138 687 63
109 97 700 74
109 91 750 38
109 62 750 87
109 61 935 42
Stem Leaf # Boxplot
9 4 1 0
8
8
7 55 2 0
7 0 1 0
6 59 2 0
6 234 3 |
5 6668 4 |
5 0222 4 |
4 56 2 |
4 0003 4 |
3 555666666789 12 +-----+
3 0002222234 10 | |
2 5666888899 10 | + |
2 00000022333344 14 *-----*
1 555555555666667778888888889 27 | |
1 111111111222222222223333333444444444444444 42 +-----+
----+----+----+----+----+----+----+----+--
Multiply Stem.Leaf by 10**+2
The SAS System 13:29 Friday, October 25, 2002 241
----------------------------------------- STATUS=none ------------------------------------------
The UNIVARIATE Procedure
Variable: Y (Salary)
Normal Probability Plot
925+ *
|
|
| * *
| *
| ** ++
| *** +++
| *** +++
525+ * +++
| *+++
| +**
| +****
| ++***
| +++**
| +++***
| ++*****
125+* * * *** ***********
+----+----+----+----+----+----+----+----+----+----+
-2 -1 0 +1 +2
The SAS System 13:29 Friday, October 25, 2002 242
The UNIVARIATE Procedure
Variable: Y (Salary)
Schematic Plots
|
6000 + 0
|
|
| 0 |
5000 + 0 |
| |
| |
| |
4000 + |
| | |
| | |
| | |
3000 + | +-----+
| | | |
| | | |
| | *-----*
2000 + +-----+ | + |
| | | | |
| | + | | |
| *-----* | |
1000 + | | +-----+ 0
| +-----+ | 0
| | | |
| | | *--+--*
0 + | | |
------------+-----------+-----------+-----------
STATUS arb free none
/* High solution plot of the data */
PROC GPLOT DATA=salary1;
PLOT Y*STATUS;
RUN;
RESULTS
/*One-Way ANOVA*/
PROC GLM DATA=salary1;
CLASS STATUS;
MODEL Y = STATUS;
OUTPUT OUT=rdata r=resid;
RUN;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 243
The GLM Procedure
Class Level Information
Class Levels Values
STATUS 3 arb free none
Number of observations 337
The SAS System 13:29 Friday, October 25, 2002 244
The GLM Procedure
Dependent Variable: Y Salary
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 2 239911393.0 119955696.5 144.78 <.0001
Error 334 276733296.9 828542.8
Corrected Total 336 516644690.0
R-Square Coeff Var Root MSE Y Mean
0.464364 72.90530 910.2433 1248.528
Source DF Type I SS Mean Square F Value Pr > F
STATUS 2 239911393.0 119955696.5 144.78 <.0001
Source DF Type III SS Mean Square F Value Pr > F
STATUS 2 239911393.0 119955696.5 144.78 <.0001
/* Another way of checking homogeniety or equal varainces */
PROC PRINT DATA=rdata; RUN;
PROC GPLOT DATA=rdata;
PLOT resid*STATUS;
RUN;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 245
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
1 2475 0.260 0.292 59 128 22 7 12 50 23 64 21 21 0 0 1 0 Shawon Dunston arb 907.43
2 2313 0.273 0.346 87 169 28 5 8 58 70 53 3 8 0 0 1 0 Mark Grace arb 745.43
3 1190 0.255 0.321 39 108 22 8 3 26 42 61 2 8 0 0 1 0 Spike Owen arb -377.57
4 775 0.272 0.300 18 62 14 2 5 35 9 19 0 3 0 0 1 0 Mackey Sasser arb -792.57
5 760 0.241 0.320 33 84 16 2 6 36 40 53 2 14 0 0 1 1 Kevin Elster arb -807.57
6 2567 0.196 0.297 36 56 12 0 12 42 41 66 5 8 0 0 1 0 Darren Daulton arb 999.43
7 660 0.272 0.304 38 82 21 3 9 49 14 49 0 9 0 0 1 0 Ricky Jordan arb -907.57
8 5150 0.292 0.410 95 149 28 5 25 116 107 73 43 3 0 0 1 0 Barry Bonds arb 3582.43
9 2000 0.265 0.306 53 133 16 6 3 54 30 56 7 9 0 0 1 1 Jose Lind arb 432.43
10 875 0.270 0.330 96 164 32 8 16 67 52 99 10 24 0 0 1 1 Jay Bell arb -692.57
11 992 0.264 0.319 38 121 24 5 2 57 36 63 9 7 0 0 1 0 Tom Pagnozzi arb -575.57
12 2700 0.251 0.338 101 141 35 3 32 105 71 104 34 6 0 0 1 0 Ron Gant arb 1132.43
13 1262 0.320 0.368 41 98 17 2 3 32 23 19 2 15 0 0 1 0 Jeff Treadway arb -305.57
14 940 0.259 0.358 49 91 14 3 11 54 54 59 5 17 0 0 1 0 Jeff Blauser arb -627.57
15 500 0.249 0.296 36 88 9 2 0 27 22 63 3 18 0 0 1 0 Rafael Belliard arb -1067.57
16 370 0.188 0.243 13 30 7 0 5 14 11 42 1 8 0 0 1 0 Damon Berryhill arb -1197.57
17 2833 0.256 0.346 71 136 36 0 28 91 73 107 12 2 0 0 1 0 Paul O'Neill arb 1265.43
18 2750 0.301 0.354 91 175 35 3 26 88 44 79 19 12 0 0 1 0 Chris Sabo arb 1182.43
19 1550 0.281 0.342 66 119 13 3 3 32 37 71 26 10 0 0 1 0 Bip Roberts arb -17.57
20 1300 0.234 0.301 13 36 5 0 6 19 16 39 0 6 0 0 1 0 Dave Martinez arb -267.57
21 1000 0.260 0.323 36 65 10 0 11 39 23 46 11 5 0 0 1 1 Geronimo Berroa arb -567.57
22 1500 0.253 0.312 65 145 30 3 13 80 46 85 4 23 0 0 1 0 Ken Caminiti arb -67.57
23 1458 0.295 0.358 79 161 23 4 4 46 53 71 19 11 0 0 1 0 Craig Biggio arb -109.57
24 1210 0.285 0.331 84 170 28 10 8 54 42 65 34 5 0 0 1 0 Steve Finley arb -357.57
25 587 0.278 0.355 24 60 11 2 2 20 25 24 1 4 0 0 1 0 Mike Sharperson arb -980.57
26 3300 0.267 0.296 60 155 22 3 17 87 23 114 8 14 0 0 1 1 Benito Santiago arb 1732.43
27 2100 0.272 0.337 81 162 27 5 4 38 55 74 23 20 0 0 1 0 Tony Fernandez arb 532.43
28 805 0.262 0.315 51 94 12 1 21 49 27 66 5 2 0 0 1 0 Darrin Jackson arb -762.57
29 725 0.194 0.277 25 34 12 2 2 22 19 15 5 8 0 0 1 0 Gary Sheffield arb -842.57
30 125 0.269 0.345 4 7 2 1 0 5 3 4 0 0 0 0 1 1 Dann Bilardello arb -1442.57
31 2000 0.268 0.310 72 158 24 5 34 98 33 128 5 16 0 0 1 0 Matt Williams arb 432.43
32 1533 0.221 0.283 23 51 8 4 1 12 20 33 3 11 0 0 1 0 Jose Uribe arb -34.57
33 850 0.238 0.273 31 104 16 2 5 41 18 61 3 0 0 0 1 0 Chris James arb -717.57
34 1200 0.263 0.373 57 127 17 2 16 70 84 108 0 11 0 0 1 0 Randy Milligan arb -367.57
35 730 0.216 0.253 24 62 11 1 0 14 15 31 0 7 0 0 1 0 Billy Ripken arb -837.57
36 3050 0.300 0.350 76 163 26 6 9 83 43 35 15 3 0 0 1 0 Mike Greenwell arb 1482.43
37 1650 0.262 0.312 45 116 25 3 4 41 26 55 11 5 0 0 1 0 Billy Hatcher arb 82.43
38 1600 0.283 0.349 87 175 42 2 5 60 60 53 6 14 0 0 1 1 Jody Reed arb 32.43
39 1075 0.258 0.318 64 107 22 3 8 40 35 86 4 24 0 0 1 0 Luis Rivera arb -492.57
40 950 0.262 0.307 30 111 13 2 0 31 26 27 5 12 0 0 1 0 Felix Fermin arb -617.57
41 2530 0.289 0.319 57 146 19 4 5 68 26 33 5 4 0 0 1 0 B.J. Surhoff arb 962.43
42 2150 0.267 0.333 68 130 22 2 20 69 45 77 32 4 0 0 1 0 Roberto Kelly arb 582.43
43 1300 0.285 0.321 67 140 23 2 19 80 26 40 0 3 0 0 1 0 Mel Hall arb -267.57
44 2983 0.295 0.354 88 188 41 11 9 69 57 86 53 15 0 0 1 0 Roberto Alomar arb 1415.43
45 1000 0.244 0.271 22 71 17 0 5 36 11 45 0 4 0 0 1 0 Pat Borders arb -567.57
46 1000 0.234 0.274 41 104 18 3 0 29 24 107 7 19 0 0 1 0 Manuel Lee arb -567.57
The SAS System 13:29 Friday, October 25, 2002 246
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
47 1650 0.296 0.352 92 179 28 8 2 50 52 74 48 5 0 0 1 1 Luis Polonia arb 82.43
48 1900 0.273 0.284 52 143 20 3 3 49 11 38 21 21 0 0 1 0 Ozzie Guillen arb 332.43
49 740 0.284 0.367 92 172 25 1 23 100 80 67 2 18 0 0 1 0 Robin Ventura arb -827.57
50 650 0.246 0.310 25 41 13 0 5 22 15 42 0 4 0 0 1 0 Ron Karkovice arb -917.57
51 109 0.225 0.333 71 8 16 4 0 3 14 12 25 0 0 0 1 0 Bo Jackson arb -1458.57
52 1150 0.272 0.338 59 132 19 2 9 62 47 38 26 17 0 0 1 0 Gregg Jeffries arb -417.57
53 740 0.277 0.330 34 74 18 2 13 41 17 52 1 3 0 0 1 0 Mike Macfarlane arb -827.57
54 425 0.252 0.301 15 35 5 1 5 22 10 23 1 0 0 0 1 0 Chris Gwynn arb -1142.57
55 1933 0.265 0.310 52 108 23 3 8 42 26 72 11 9 0 0 1 0 Greg Gagne arb 365.43
56 1075 0.310 0.363 79 137 27 8 18 74 34 79 13 7 0 0 1 0 Shane Mack arb -492.57
57 950 0.286 0.361 34 73 14 1 2 19 30 21 2 3 0 0 1 0 Gene Larkin arb -617.57
58 5000 0.307 0.357 110 203 44 5 25 116 56 91 16 7 0 0 1 1 Ruben Sierra arb 3432.43
59 2050 0.274 0.312 50 125 31 1 6 67 22 70 2 15 0 0 1 0 Terry Steinbach arb 482.43
60 760 0.226 0.286 15 30 8 1 0 13 12 14 0 5 0 0 1 0 Walt Weiss arb -807.57
61 2167 0.254 0.332 95 160 34 6 3 57 72 63 28 18 0 0 1 0 Harold Reynolds arb 599.43
62 2050 0.327 0.399 76 179 42 1 22 100 71 82 18 4 0 0 1 0 Ken Griffey arb 482.43
63 1445 0.244 0.337 64 99 14 4 27 77 53 117 0 5 0 0 1 0 Jay Buhner arb -122.57
64 875 0.305 0.347 35 54 6 2 6 23 10 27 16 2 0 0 1 0 Henry Cotto arb -692.57
65 3850 0.322 0.389 115 203 49 3 26 88 68 72 4 12 0 0 1 1 Rafael Palmeiro arb 2282.43
66 3300 0.272 0.302 69 153 21 4 31 104 22 80 4 3 1 0 0 0 Andre Dawson free 1191.06
67 2600 0.269 0.335 58 111 17 2 18 66 39 69 0 3 1 1 0 0 Steve Buchele free 491.06
68 2500 0.249 0.337 54 115 15 1 17 73 63 116 6 5 1 0 0 0 Kal Daniels free 391.06
69 2175 0.291 0.379 104 170 32 2 26 100 87 89 22 4 1 0 0 0 Ryne Sandberg free 66.06
70 600 0.258 0.370 34 86 14 1 14 38 15 45 0 10 1 0 0 0 Luis Salazar free -1508.94
71 2600 0.300 0.368 69 141 22 3 19 75 53 64 31 7 1 0 0 0 Ivan Calderon free 491.06
72 1907 0.225 0.292 60 130 22 1 13 73 50 100 2 14 1 0 0 0 Tim Wallach free -201.94
73 990 0.290 0.349 59 141 30 2 16 64 42 102 14 6 1 0 0 0 Larry Walker free -1118.94
74 925 0.246 0.323 22 81 14 0 6 26 22 26 2 5 1 0 0 0 Gary Carter free -1183.94
75 6100 0.302 0.391 102 174 44 6 18 100 90 67 2 15 1 1 0 0 Bobby Bonilla free 3991.06
76 4125 0.260 0.321 69 150 23 1 19 96 55 74 10 7 1 1 0 0 Eddie Murray free 2016.06
77 3213 0.255 0.347 45 71 7 5 1 17 39 47 37 3 1 0 0 0 Vince Coleman free 1104.06
78 2319 0.259 0.349 108 146 34 4 38 117 78 120 30 31 1 0 0 0 Howard Johnson free 210.06
79 2000 0.223 0.307 43 84 10 4 10 40 36 56 7 4 1 0 0 0 Kevin Bass free -108.94
80 1600 0.225 0.310 44 96 9 3 0 31 50 69 8 15 1 1 0 0 Dick Schofield free -508.94
81 1394 0.258 0.381 58 108 23 0 4 51 83 50 1 5 1 0 0 0 Dave Magadan free -714.94
82 935 0.275 0.351 40 70 16 4 4 21 30 42 15 3 1 1 0 0 Daryl Boston free -1173.94
83 850 0.327 0.424 60 141 14 3 0 54 75 38 4 20 1 1 0 0 Willie Randolph free -1258.94
84 2500 0.252 0.309 66 137 33 1 28 81 48 93 1 5 1 0 0 0 Dale Murphy free 391.06
85 2350 0.294 0.367 84 158 27 6 21 92 67 100 7 3 1 0 0 0 John Kruk free 241.06
86 2317 0.297 0.391 48 73 13 5 3 12 37 20 24 4 1 0 0 0 Lenny Dykstra free 208.06
87 2000 0.258 0.288 46 86 7 4 12 40 12 57 5 9 1 1 0 0 Mariano Duncan free -108.94
88 715 0.205 0.268 21 36 5 3 1 11 16 36 7 3 1 0 0 0 Stan Javier free -1393.94
89 650 0.243 0.344 20 45 12 0 0 15 30 30 3 4 1 0 0 0 Wally Backman free -1458.94
90 4450 0.265 0.355 87 130 24 7 17 83 71 85 10 1 1 0 0 0 Andy Van Slyke free 2341.06
91 1850 0.289 0.351 25 97 11 2 3 41 33 27 2 1 1 1 0 0 Mike LaValliere free -258.94
92 1192 0.295 0.363 19 65 17 1 1 29 21 32 1 5 1 0 0 0 Don Slaught free -916.94
The SAS System 13:29 Friday, October 25, 2002 247
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
93 825 0.246 0.324 45 62 12 2 7 24 28 39 17 6 1 0 0 0 Gary Redus free -1283.94
94 2425 0.272 0.326 41 116 12 1 8 70 37 46 4 16 1 1 0 0 Pedro Guerrero free 316.06
95 2367 0.219 0.268 34 82 13 2 9 33 23 86 5 9 1 0 0 0 Andres Galarraga free 258.06
96 2050 0.240 0.357 37 88 11 4 1 26 67 48 1 9 1 0 0 0 Jose Guillen free -58.94
97 2000 0.285 0.380 96 157 30 3 3 50 83 36 35 8 1 0 0 0 Ozzie Smith free -108.94
98 1617 0.307 0.368 55 100 16 5 6 34 32 53 16 2 1 0 0 0 Milt Thompson free -491.94
99 1167 0.240 0.300 29 58 8 4 6 36 22 34 15 5 1 0 0 0 Gerald Perry free -941.94
100 3150 0.319 0.363 94 187 34 8 22 86 43 70 10 24 1 0 0 0 Terry Pendleton free 1041.06
101 2785 0.297 0.371 81 119 10 1 0 26 47 40 72 3 1 1 0 0 Otis Nixon free 676.06
102 2400 0.253 0.313 32 67 12 0 11 45 25 31 0 3 1 0 0 0 Sid Bream free 291.06
103 1750 0.275 0.377 58 97 19 1 7 44 50 64 9 5 1 0 0 0 Lonnie Smith free -358.94
104 4350 0.302 0.378 88 140 27 4 20 69 55 64 24 15 1 0 0 0 Barry Larkin free 2241.06
105 2833 0.280 0.359 51 101 12 2 6 35 46 39 5 7 1 0 0 0 Bill Doran free 724.06
106 800 0.214 0.290 38 72 12 1 11 38 36 92 1 3 1 1 0 0 Pete Incaviglia free -1308.94
107 4050 0.265 0.361 86 134 22 4 28 99 75 125 10 5 1 0 0 0 Darryl Strawberry free 1941.06
108 3600 0.235 0.353 39 67 10 0 11 33 48 92 14 3 1 0 0 0 Eric Davis free 1491.06
109 3333 0.296 0.401 112 182 13 5 2 38 108 79 38 0 1 0 0 0 Brett Butler free 1224.06
110 2183 0.264 0.353 39 91 16 2 8 40 47 32 4 7 1 0 0 0 Mike Scioscia free 74.06
111 1150 0.294 0.338 29 86 15 3 2 40 17 46 2 3 1 0 0 0 Todd Benzinger free -958.94
112 840 0.287 0.349 59 123 16 1 3 38 37 32 12 20 1 0 0 0 Lenny Harris free -1268.94
113 400 0.222 0.296 21 38 8 5 2 19 18 52 0 2 1 0 0 0 Mitch Webster free -1708.94
114 350 0.248 0.286 24 56 5 2 2 13 12 35 2 11 1 1 0 0 Dave Anderson free -1758.94
115 4075 0.278 0.396 84 147 19 1 31 106 105 135 4 14 1 0 0 0 Fred McGriff free 1966.06
116 2387 0.317 0.355 69 158 27 11 4 62 34 19 8 3 1 0 0 0 Tony Gwynn free 278.06
117 1750 0.265 0.322 44 102 17 1 6 51 33 56 3 18 1 1 0 0 Kurt Stillwell free -358.94
118 687 0.217 0.319 41 74 16 0 12 44 51 77 9 9 1 1 0 0 Tim Teufel free -1421.94
119 4275 0.301 0.359 84 170 32 7 29 116 51 91 4 4 1 0 0 0 Will Clark free 2166.06
120 3563 0.312 0.357 67 155 30 3 4 43 34 74 17 6 1 0 0 0 Willie McGee free 1454.06
121 1600 0.262 0.352 74 129 24 5 19 48 63 95 14 11 1 0 0 0 Robby Thompson free -508.94
122 940 0.175 0.216 14 29 4 1 3 17 9 60 0 3 1 0 0 0 Corey Snyder free -1168.94
123 3415 0.227 0.307 29 40 9 1 10 28 16 29 4 8 1 1 0 0 Glenn Davis free 1306.06
124 2100 0.323 0.374 99 210 46 5 34 114 53 46 6 11 1 0 0 0 Cal Ripken free -8.94
125 1300 0.278 0.321 57 135 22 1 5 43 28 45 6 1 1 0 0 0 Joe Orsulak free -808.94
126 1025 0.260 0.313 82 158 27 10 19 59 47 115 16 3 1 0 0 0 Mike Devereaux free -1083.94
127 2900 0.249 0.374 75 120 18 1 26 87 96 133 0 0 1 0 0 0 Jack Clark free 791.06
128 2850 0.229 0.303 54 105 24 1 16 70 49 72 1 3 1 0 0 0 Tom Brunansky free 741.06
129 2700 0.332 0.421 93 181 42 2 8 51 89 32 1 12 1 0 0 0 Wade Boggs free 591.06
130 2400 0.231 0.291 45 107 23 2 5 48 37 53 8 5 1 0 0 0 Tony Pena free 291.06
131 2300 0.251 0.314 56 119 33 3 14 56 39 81 6 2 1 0 0 0 Ellis Burks free 191.06
132 550 0.225 0.272 17 38 6 1 1 4 11 40 4 5 1 1 0 0 Herm Winningham free -1558.94
133 550 0.224 0.274 28 94 21 1 1 44 27 54 2 7 1 1 0 0 Brook Jacoby free -1558.94
134 300 0.209 0.293 9 28 5 1 0 11 15 12 0 1 1 1 0 0 Junior Ortiz free -1808.94
135 4500 0.261 0.347 102 163 25 0 44 133 78 151 0 8 1 0 0 0 Cecil Fielder free 2391.06
136 3358 0.263 0.387 85 132 17 2 31 89 101 131 3 6 1 0 0 0 Mickey Tettleton free 1249.06
137 2400 0.248 0.320 57 93 20 0 9 55 37 39 11 9 1 0 0 0 Alan Trammell free 291.06
138 2200 0.279 0.391 94 131 26 2 23 78 90 45 4 4 1 0 0 0 Lou Whitaker free 91.06
The SAS System 13:29 Friday, October 25, 2002 248
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
139 2017 0.179 0.314 64 60 14 2 25 64 89 175 1 7 1 0 0 0 Rob Deer free -91.94
140 1567 0.284 0.371 87 160 28 4 17 72 79 95 10 8 1 0 0 0 Tony Phillips free -541.94
141 1050 0.247 0.306 65 114 14 9 6 52 36 60 15 3 1 1 0 0 Dan Gladden free -1058.94
142 375 0.237 0.351 23 46 10 1 7 29 35 40 1 1 1 1 0 0 Dave Bergman free -1733.94
143 355 0.260 0.293 18 66 6 0 4 21 12 26 2 3 1 0 0 0 Mark Carreon free -1753.94
144 109 0.216 0.341 37 61 7 5 0 19 54 91 29 6 1 0 0 0 Gary Pettis free -1999.94
145 3453 0.325 0.399 133 216 32 13 17 75 77 62 19 6 1 0 0 0 Paul Molitor free 1344.06
146 3200 0.260 0.332 66 131 20 4 10 77 54 79 6 2 1 0 0 0 Robin Yount free 1091.06
147 2167 0.213 0.282 48 77 16 2 11 38 35 71 13 9 1 0 0 0 Franklin Stubbs free 58.06
148 1150 0.286 0.320 63 149 27 4 2 47 27 34 4 12 1 1 0 0 Jim Gantner free -958.94
149 300 0.206 0.262 14 51 18 1 1 28 17 26 0 3 1 1 0 0 Scott Fletcher free -1808.94
150 284 0.265 0.350 28 62 11 3 1 25 29 21 4 11 1 0 0 0 Kevin Seitzer free -1824.94
151 5300 0.316 0.397 78 153 35 3 31 100 65 121 6 7 1 1 0 0 Danny Tartabull free 3191.06
152 3620 0.288 0.339 64 169 35 0 9 68 46 42 2 5 1 0 0 0 Don Mattingly free 1511.06
153 2500 0.268 0.308 52 122 20 0 24 77 25 49 3 6 1 0 0 0 Matt Nokes free 391.06
154 2167 0.225 0.312 37 64 12 0 17 48 36 80 1 0 1 0 0 0 Jesse Barfield free 58.06
155 1950 0.247 0.343 67 119 15 4 12 49 67 84 6 12 1 1 0 0 Mike Gallego free -158.94
156 3742 0.273 0.330 89 174 42 3 33 108 49 112 20 8 1 0 0 0 Joe Carter free 1633.06
157 3633 0.252 0.308 58 108 18 2 20 65 31 70 12 13 1 0 0 0 Kelly Griffin free 1524.06
158 2383 0.282 0.342 110 181 40 10 17 60 55 135 33 1 1 0 0 0 Devon White free 274.06
159 2300 0.262 0.326 75 149 27 4 28 86 56 109 7 2 1 1 0 0 Dave Winfield free 191.06
160 1375 0.250 0.342 37 72 15 0 12 48 36 76 4 2 1 0 0 0 Candy Maldonado free -733.94
161 900 0.216 0.318 20 40 5 1 1 21 29 21 0 3 1 0 0 0 Pat Tabler free -1208.94
162 775 0.250 0.364 27 60 12 1 2 24 44 44 0 0 1 0 0 0 Rance Mulliniks free -1333.94
163 600 0.243 0.286 27 85 6 2 0 27 22 49 5 22 1 1 0 0 Alfredo Griffin free -1508.94
164 2700 0.246 0.293 58 144 22 1 18 66 33 104 5 17 1 0 0 0 Gary Gaetti free 591.06
165 2317 0.238 0.322 48 85 11 1 16 50 44 62 3 5 1 0 0 0 Hubie Brooks free 208.06
166 3650 0.285 0.323 63 159 27 0 25 86 32 62 2 10 1 0 0 0 George Bell free 1541.06
167 3575 0.304 0.345 85 198 38 2 10 56 41 38 31 10 1 0 0 0 Steve Sax free 1466.06
168 3500 0.268 0.359 102 163 20 6 5 50 83 68 51 3 1 0 0 0 Tim Raines free 1391.06
169 2500 0.259 0.358 71 106 22 5 18 66 62 86 0 6 1 1 0 0 Dan Pasqua free 391.06
170 1350 0.241 0.299 42 111 25 0 18 74 32 86 1 6 1 1 0 0 Carlton Fisk free -758.94
171 4200 0.301 0.360 79 166 34 3 21 96 52 66 2 8 1 1 0 0 Wally Joyner free 2091.06
172 3417 0.259 0.322 65 135 32 1 16 74 49 46 6 2 1 0 0 0 Kevin McReynolds free 1308.06
173 3100 0.255 0.327 77 129 40 2 10 61 58 75 2 1 1 0 0 0 George Brett free 991.06
174 1650 0.301 0.333 47 113 22 3 2 47 20 35 5 5 1 1 0 0 Jim Eisenreich free -458.94
175 900 0.250 0.279 11 57 10 0 1 23 11 46 0 1 1 0 0 0 Bob Melvin free -1208.94
176 400 0.188 0.243 20 36 9 1 2 18 15 40 2 2 1 1 0 0 Curtis Wilkerson free -1708.94
177 109 0.271 0.328 74 161 22 6 12 58 49 133 23 17 1 1 0 0 Juan Samuel free -1999.94
178 3100 0.284 0.373 72 131 20 1 20 89 67 48 4 8 1 0 0 0 Kent Hrbek free 991.06
179 2992 0.319 0.352 92 195 29 6 15 89 31 78 11 6 1 0 0 0 Kirby Puckett free 883.06
180 2800 0.277 0.385 84 148 34 1 29 93 95 117 5 0 1 0 0 0 Chili Davis free 691.06
181 2500 0.311 0.336 54 137 28 1 10 69 14 22 1 8 1 1 0 0 Brian Harper free 391.06
182 1200 0.279 0.322 36 102 20 0 6 36 21 55 1 11 1 1 0 0 Mike Pagliarulo free -908.94
183 3250 0.268 0.400 105 126 17 1 18 57 96 73 58 8 1 0 0 0 Rickey Henderson free 1141.06
184 2825 0.201 0.330 62 97 22 0 22 75 93 116 2 4 1 0 0 0 Mark McGwire free 716.06
The SAS System 13:29 Friday, October 25, 2002 249
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
185 2600 0.276 0.346 86 158 33 0 25 85 58 113 6 1 1 0 0 0 Dave Henderson free 491.06
186 1583 0.295 0.383 76 144 25 1 20 90 72 67 0 1 1 0 0 0 Harold Baines free -525.94
187 1150 0.063 0.063 0 1 0 0 0 1 0 2 0 0 1 1 0 0 Carney Lansford free -958.94
188 1100 0.238 0.290 38 70 14 4 0 28 18 43 20 3 1 0 0 0 Willie Wilson free -1008.94
189 525 0.261 0.321 16 53 4 0 1 17 16 28 0 6 1 0 0 0 Jamie Quirk free -1583.94
190 500 0.249 0.385 32 51 10 1 1 20 47 25 2 3 1 1 0 0 Randy Ready free -1608.94
191 3750 0.256 0.338 52 95 13 1 27 69 43 57 2 6 1 0 0 0 Kevin Mitchell free 1641.06
192 2188 0.248 0.300 58 139 29 3 17 88 44 61 0 5 1 0 0 0 Pete O'Brien free 79.06
193 2167 0.194 0.286 38 63 8 1 8 32 34 49 0 6 1 0 0 0 Dave Valle free 58.06
194 109 0.216 0.285 38 87 12 0 19 51 35 117 0 2 1 0 0 0 Lance Parrish free -1999.94
195 4300 0.266 0.359 115 152 32 1 44 122 78 152 26 9 1 0 0 0 Jose Canseco free 2191.06
196 2387 0.341 0.408 108 201 27 3 15 78 65 78 36 14 1 0 0 0 Julio Franco free 278.06
197 950 0.278 0.377 76 113 17 2 17 49 58 70 1 0 1 1 0 0 Brian Downing free -1158.94
198 675 0.271 0.339 21 54 8 1 2 20 21 25 2 11 1 1 0 0 Geno Petralli free -1433.94
199 600 0.252 0.283 44 136 18 4 9 44 25 84 11 21 1 1 0 0 Dickie Thon free -1508.94
200 460 0.228 0.279 16 38 7 2 3 21 11 32 2 3 0 0 0 0 Dwight Smith none 197.22
201 240 0.250 0.327 40 61 11 0 1 18 24 26 14 2 0 0 0 0 Doug Dascenzo none -22.78
202 200 0.203 0.240 39 64 10 1 10 33 14 96 13 6 0 0 0 0 Sammy Sosa none -62.78
203 177 0.262 0.283 7 38 5 0 0 10 5 18 2 7 0 0 0 0 Jose Vizcaino none -85.78
204 140 0.222 0.307 21 45 9 0 6 22 19 56 3 3 0 0 0 0 Rick Wilkins none -122.78
205 117 0.227 0.280 4 5 2 0 1 3 2 1 0 0 0 0 0 0 Derrick May none -145.78
206 115 0.261 0.370 1 6 0 0 0 2 4 3 0 0 0 0 0 0 Rey Sanchez none -147.78
207 365 0.208 0.265 12 35 11 1 0 15 14 30 2 6 0 0 0 0 Tom Foley none 102.22
208 302 0.238 0.347 83 134 15 4 10 51 95 151 56 27 0 0 0 0 Delino DeShields none 39.22
209 300 0.267 0.310 73 149 23 9 6 39 34 89 76 6 0 0 0 0 Marquis Grissom none 37.22
210 129 0.353 0.435 16 48 12 2 2 18 20 22 0 5 0 0 0 0 Bret Barberie none -133.78
211 111 0.213 0.222 4 13 4 1 1 8 1 18 0 0 0 0 0 0 John VanderWal none -151.78
212 629 0.293 0.355 32 79 17 0 1 30 24 43 2 0 0 0 0 0 Dave Gallagher none 366.22
213 275 0.257 0.315 51 96 10 1 6 34 33 57 13 8 0 0 0 0 Chico Walker none 12.22
214 120 0.225 0.330 7 20 2 0 0 5 14 19 1 2 0 0 0 0 Chris Donnels none -142.78
215 260 0.337 0.413 13 32 5 0 0 12 13 14 0 0 0 0 0 0 Jim Lindeman none -2.78
216 250 0.228 0.238 12 36 4 1 1 11 2 26 0 2 0 0 0 0 Steve Lake none -12.78
217 200 0.240 0.300 51 92 16 3 13 50 31 73 9 3 0 0 0 0 Wes Chamberlain none -62.78
218 180 0.298 0.378 18 45 10 2 6 21 17 26 1 8 0 0 0 0 Dave Hollins none -82.78
219 180 0.249 0.313 38 81 11 4 1 20 29 45 13 6 0 0 0 0 Mickey Morandini none -82.78
220 525 0.288 0.366 24 47 7 0 7 24 18 23 2 3 0 0 0 0 Lloyd McClendon none 262.22
221 367 0.273 0.344 23 51 11 2 4 23 19 34 9 1 0 0 0 0 Gary Varsho none 104.22
222 325 0.239 0.328 16 26 1 1 4 18 14 15 3 2 0 0 0 0 Jeff King none 62.22
223 320 0.244 0.281 7 20 4 0 1 11 5 17 4 2 0 0 0 0 Cecil Espy none 57.22
224 150 0.275 0.373 83 113 17 2 10 50 64 81 8 12 0 0 0 0 Orlando Merced none -112.78
225 113 0.340 0.381 15 36 7 0 0 7 7 17 3 6 0 0 0 0 John Wehner none -149.78
226 113 0.250 0.280 2 6 0 2 0 1 1 8 0 1 0 0 0 0 Carlos Garcia none -149.78
227 400 0.227 0.260 21 47 10 2 1 15 10 29 12 2 0 0 0 0 Rex Hudler none 137.22
228 315 0.305 0.360 69 173 40 6 8 77 50 113 20 3 0 0 0 0 Felix Jose none 52.22
229 315 0.280 0.353 76 158 36 3 11 81 62 94 17 25 0 0 0 0 Todd Zeile none 52.22
230 230 0.251 0.301 83 142 23 15 9 69 41 114 44 6 0 0 0 0 Ray Lankford none -32.78
The SAS System 13:29 Friday, October 25, 2002 250
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
231 135 0.216 0.316 28 58 7 2 5 28 39 33 14 1 0 0 0 0 Bernard Gilkey none -127.783
232 130 0.243 0.322 38 45 8 3 5 17 18 45 15 6 0 0 0 0 Geronimo Pena none -132.783
233 555 0.275 0.377 67 109 25 1 21 87 65 81 8 7 0 0 0 0 David Justice none 292.217
234 350 0.241 0.316 46 99 25 0 6 44 44 48 1 4 0 0 0 0 Greg Olson none 87.217
235 148 0.242 0.284 7 23 6 0 4 23 6 20 1 3 0 0 0 0 Francisco Cabrera none -114.783
236 146 0.251 0.296 32 68 16 1 12 50 17 48 0 8 0 0 0 0 Brian Hunter none -116.783
237 750 0.267 0.321 20 72 15 2 3 31 23 38 0 5 0 0 0 0 Jeff Reed none 487.217
238 430 0.318 0.374 72 152 33 1 14 59 46 61 10 9 0 0 0 0 Hal Morris none 167.217
239 260 0.216 0.265 21 58 11 0 11 41 18 53 0 11 0 0 0 0 Joe Oliver none -2.783
240 120 0.286 0.303 11 18 1 0 0 3 1 15 1 2 0 0 0 0 Freddie Benavides none -142.783
241 935 0.262 0.319 44 121 20 7 4 50 40 49 9 10 0 0 0 0 Casey Candaele none 672.217
242 395 0.218 0.327 26 31 3 1 1 11 24 17 16 0 0 0 0 0 Gerald Young none 132.217
243 350 0.294 0.387 79 163 26 4 15 82 75 116 7 12 0 0 0 0 Jeff Bagwell none 87.217
244 285 0.254 0.320 51 120 28 9 13 69 40 101 10 5 0 0 0 0 Luis Gonzalez none 22.217
245 139 0.243 0.270 27 61 13 2 9 36 9 74 4 18 0 0 0 0 Andujar Cedeno none -123.783
246 133 0.153 0.227 11 18 6 0 1 7 12 41 1 1 0 0 0 0 Eric Anthony none -129.783
247 135 0.268 0.293 3 15 4 0 1 5 2 12 1 0 0 0 0 0 Dave Hansen none -127.783
248 135 0.214 0.250 1 3 1 0 0 1 0 5 1 1 0 0 0 0 Carlos Hernandez none -127.783
249 135 0.195 0.345 10 22 2 0 0 3 25 32 3 10 0 0 0 0 Jose Offerman none -127.783
250 200 0.228 0.295 26 84 16 0 10 47 31 90 2 2 0 0 0 0 Jerald Clark none -62.783
251 130 0.286 0.444 0 2 0 0 0 0 2 3 0 0 0 0 0 0 Phil Stephenson none -132.783
252 120 0.246 0.267 5 14 2 0 0 9 1 9 2 2 0 0 0 0 Oscar Azocar none -142.783
253 117 0.275 0.298 6 25 3 0 1 6 2 14 0 7 0 0 0 0 Craig Shipley none -145.783
254 114 0.243 0.308 13 26 7 2 2 8 9 27 1 1 0 0 0 0 Dan Walters none -148.783
255 650 0.264 0.325 51 92 10 6 0 18 30 31 21 4 0 0 0 0 Mike Felder none 387.217
256 360 0.225 0.271 16 40 9 0 0 19 9 22 1 4 0 0 0 0 Kirt Manwaring none 97.217
257 150 0.123 0.188 12 13 3 0 2 8 7 26 3 3 0 0 0 0 Mike Benjamin none -112.783
258 145 0.246 0.358 41 55 5 3 1 15 36 30 13 0 0 0 0 0 Darren Lewis none -117.783
259 140 0.240 0.306 14 31 7 1 2 14 12 25 0 0 0 0 0 0 Mark Leonard none -122.783
260 109 0.115 0.148 0 3 1 0 0 2 1 6 0 3 0 0 0 0 Royce Clayton none -153.783
261 109 0.120 0.185 0 3 0 0 0 1 2 11 0 1 0 0 0 0 Ted Wood none -153.783
262 687 0.233 0.326 45 74 16 0 23 61 41 99 0 0 0 0 0 0 Sam Horn none 424.217
263 380 0.204 0.255 29 42 9 0 7 18 13 49 0 4 0 0 0 0 Tim Hulett none 117.217
264 365 0.230 0.336 40 59 12 3 2 27 36 44 12 3 0 0 0 0 Brady Anderson none 102.217
265 175 0.243 0.304 36 83 15 0 11 31 29 61 0 1 0 0 0 0 Chris Hoiles none -87.783
266 150 0.233 0.302 40 91 17 2 16 45 40 82 1 7 0 0 0 0 Leo Gomez none -112.783
267 150 0.278 0.316 15 59 7 0 2 22 12 19 1 3 0 0 0 0 David Segui none -112.783
268 140 0.269 0.303 32 58 12 1 13 33 11 51 1 2 0 0 0 0 Chito Martinez none -122.783
269 350 0.263 0.271 10 30 8 0 0 9 1 16 0 3 0 0 0 0 John Marzano none 87.217
270 340 0.295 0.375 69 141 21 1 11 71 61 66 1 9 0 0 0 0 Carlos Quintana none 77.217
271 155 0.260 0.339 21 57 12 0 4 32 26 43 2 6 0 0 0 0 Mo Vaughn none -107.783
272 145 0.457 0.486 6 16 4 2 0 7 2 2 0 2 0 0 0 0 Scott Cooper none -117.783
273 700 0.243 0.279 23 69 14 0 1 24 14 67 0 5 0 0 0 0 Joel Skinner none 437.217
274 525 0.217 0.264 10 40 9 0 0 7 8 24 0 4 0 0 0 0 Sandy Alomar none 262.217
275 525 0.288 0.346 80 171 28 2 11 69 48 74 3 27 0 0 0 0 Carlos Baerga none 262.217
276 333 0.243 0.297 46 99 18 7 9 45 30 85 4 7 0 0 0 0 Mark Whiten none 70.217
The SAS System 13:29 Friday, October 25, 2002 251
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
277 325 0.258 0.324 29 57 8 2 8 25 23 54 6 3 0 0 0 0 Glenallen Hill none 62.217
278 200 0.284 0.310 22 73 14 0 5 30 10 43 3 8 0 0 0 0 Carlos Martinez none -62.783
279 175 0.282 0.323 60 130 31 2 26 95 25 99 3 9 0 0 0 0 Albert Belle none -87.783
280 158 0.249 0.309 30 70 12 3 4 22 24 57 10 1 0 0 0 0 Thomas Howard none -104.783
281 145 0.264 0.293 29 83 15 1 0 30 15 45 2 9 0 0 0 0 Mark Lewis none -117.783
282 300 0.259 0.309 65 144 36 3 21 91 40 149 12 23 0 0 0 0 Travis Fryman none 37.217
283 230 0.257 0.335 77 122 15 7 3 33 52 92 41 6 0 0 0 0 Milt Cuyler none -32.783
284 150 0.289 0.325 29 46 13 2 5 17 9 24 10 2 0 0 0 0 Skeeter Barnes none -112.783
285 120 0.291 0.341 19 37 5 0 2 11 10 25 2 2 0 0 0 0 Scott Livingstone none -142.783
286 750 0.283 0.337 71 117 13 6 8 54 34 55 14 17 0 0 0 0 Bill Spiers none 487.217
287 500 0.244 0.319 81 132 24 5 27 98 62 125 2 2 0 0 0 0 Greg Vaughn none 237.217
288 395 0.311 0.361 64 125 15 6 1 57 33 38 16 1 0 0 0 0 Darryl Hamilton none 132.217
289 230 0.238 0.272 53 106 18 3 15 59 22 107 14 7 0 0 0 0 Dante Bichette none -32.783
290 109 0.364 0.364 2 4 1 0 1 1 0 4 0 0 0 0 0 0 Tim McIntosh none -153.783
291 360 0.245 0.322 19 45 11 1 1 15 18 43 3 15 0 0 0 0 Randy Velarde none 97.217
292 280 0.230 0.257 34 106 23 1 12 53 16 75 3 15 0 0 0 0 Charlie Hayes none 17.217
293 255 0.220 0.333 69 110 14 1 23 63 83 128 5 6 0 0 0 0 Kevin Maas none -7.783
294 147 0.242 0.288 35 72 12 4 3 23 15 52 12 18 0 0 0 0 Pat Kelly none -115.783
295 125 0.238 0.336 43 76 19 4 3 34 48 57 10 5 0 0 0 0 Bernie Williams none -137.783
296 109 0.308 0.310 4 8 1 0 0 3 1 3 0 0 0 0 0 0 John Ramos none -153.783
297 387 0.256 0.353 64 116 30 1 17 68 68 84 0 5 0 0 0 0 John Olerud none 124.217
298 117 0.275 0.361 17 44 7 0 4 20 19 43 0 14 0 0 0 0 Ed Sprague none -145.783
299 640 0.263 0.321 32 65 10 2 2 26 11 55 7 3 0 0 0 0 Junior Felix none 377.217
300 190 0.258 0.295 38 94 14 1 3 20 14 26 4 11 0 0 0 0 Luis Sojo none -72.783
301 170 0.200 0.258 11 23 7 0 1 13 8 34 1 3 0 0 0 0 Ron Tingley none -92.783
302 135 0.211 0.274 5 12 2 0 0 3 3 2 0 4 0 0 0 0 Gary DiSarcina none -127.783
303 130 0.203 0.313 7 14 4 0 0 3 10 17 0 1 0 0 0 0 John Orton none -132.783
304 130 0.293 0.354 8 17 7 0 0 9 6 12 1 1 0 0 0 0 Lee Stevens none -132.783
305 620 0.318 0.453 104 178 31 2 32 109 138 112 1 2 0 0 0 0 Frank Thomas none 357.217
306 565 0.274 0.304 72 161 14 13 0 49 26 58 26 2 0 0 0 0 Lance Johnson none 302.217
307 235 0.241 0.313 37 55 2 3 0 18 20 21 11 10 0 0 0 0 Joey Cora none -27.783
308 225 0.165 0.218 15 19 4 1 1 5 7 25 0 0 0 0 0 0 Shawn Abner none -37.783
309 200 0.281 0.386 37 63 16 3 6 31 38 40 1 10 0 0 0 0 Craig Grebeck none -62.783
310 145 0.251 0.361 42 61 10 2 3 25 39 48 14 2 0 0 0 0 Mike Huff none -117.783
311 120 0.217 0.250 4 5 0 0 0 0 1 7 1 1 0 0 0 0 Shawn Jeter none -142.783
312 575 0.280 0.336 41 77 22 1 4 23 23 44 14 10 0 0 0 0 Keith Miller none 312.217
313 287 0.277 0.320 24 51 9 0 2 13 11 42 15 4 0 0 0 0 Gary Thurman none 24.217
314 275 0.261 0.289 86 164 28 9 8 64 24 99 20 3 0 0 0 0 Brian McRae none 12.217
315 183 0.217 0.283 45 80 16 4 5 34 30 75 17 16 0 0 0 0 Terry Shumpert none -79.783
316 170 0.251 0.315 22 58 8 0 3 31 23 42 2 6 0 0 0 0 Brent Mayne none -92.783
317 153 0.216 0.267 20 51 7 0 1 17 16 45 3 12 0 0 0 0 David Howard none -109.783
318 450 0.303 0.401 21 50 10 1 6 23 24 25 0 2 0 0 0 0 Randy Bush none 187.217
319 360 0.281 0.351 78 159 24 6 1 50 59 40 25 18 0 0 0 0 Chuck Knoblauch none 97.217
320 175 0.286 0.378 35 57 7 2 5 20 30 35 5 7 0 0 0 0 Scott Leius none -87.783
321 155 0.283 0.327 15 39 7 1 7 26 9 31 3 1 0 0 0 0 Pedro Munoz none -107.783
322 205 0.249 0.336 33 46 8 0 3 21 23 42 12 3 0 0 0 0 Lance Blankenship none -57.783
The SAS System 13:29 Friday, October 25, 2002 252
S
T r
A e
O X X X X X X X T s
b X X X X X X X X X 1 1 1 1 1 1 1 I U i
s Y 1 2 3 4 5 6 7 8 9 0 1 2 3 4 5 6 D S d
323 185 0.238 0.289 21 56 5 1 0 21 14 37 3 11 0 0 0 0 Mike Bordick none -77.783
324 115 0.235 0.268 9 16 5 0 2 4 3 11 3 1 0 0 0 0 Scott Brosius none -147.783
325 560 0.307 0.405 98 167 35 1 14 52 84 72 0 15 0 0 0 0 Edgar Martinez none 297.217
326 360 0.230 0.302 42 98 16 4 1 41 45 37 7 13 0 0 0 0 Omar Vizquel none 97.217
327 162 0.247 0.286 16 44 13 0 2 22 9 38 0 7 0 0 0 0 Dave Cochrane none -100.783
328 133 0.205 0.272 11 23 2 0 4 9 11 24 0 2 0 0 0 0 Tino Martinez none -129.783
329 287 0.264 0.321 78 144 34 1 27 102 42 118 4 6 0 0 0 0 Juan Gonzalez none 24.217
330 230 0.269 0.332 46 106 22 0 20 69 33 93 0 6 0 0 0 0 Kevin Reimer none -32.783
331 215 0.194 0.270 8 28 3 2 1 11 16 23 1 1 0 0 0 0 Jack Daugherty none -47.783
332 183 0.213 0.312 36 57 8 3 2 26 39 32 8 15 0 0 0 0 Jeff Huson none -79.783
333 170 0.111 0.138 3 3 0 0 0 1 1 7 0 0 0 0 0 0 John Russell none -92.783
334 160 0.264 0.318 24 48 7 0 1 22 15 18 0 7 0 0 0 0 Mario Diaz none -102.783
335 142 0.187 0.281 38 50 9 2 15 37 32 98 0 9 0 0 0 0 Dean Palmer none -120.783
336 140 0.264 0.270 24 74 16 0 3 27 5 42 0 10 0 0 0 0 Ivan Rodriguez none -122.783
337 109 0.258 0.395 6 8 1 0 1 6 7 11 0 0 0 0 0 0 Monty Fariss none -153.783
/* Nonparametric: Kruskal-Wallis */
PROC NPAR1WAY DATA=salary1 WILCOXON;
CLASS STATUS;
VAR Y;
* EXACT WILCOXON;
RUN;
RESULTS
The SAS System 13:29 Friday, October 25, 2002 253
The NPAR1WAY Procedure
Wilcoxon Scores (Rank Sums) for Variable Y
Classified by Variable STATUS
Sum of Expected Std Dev Mean
STATUS N Scores Under H0 Under H0 Score
ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ
arb 65 13971.00 10985.0 705.657420 214.938462
free 134 32252.50 22646.0 875.292486 240.690299
none 138 10729.50 23322.0 879.465613 77.750000
Average scores were used for ties.
Kruskal-Wallis Test
Chi-Square 208.0733
DF 2
Pr > Chi-Square <.0001
/* Multiple Comparison - Tukey's Method */
PROC GLM DATA=salary1;
CLASS STATUS;
Model Y = STATUS;
Means STATUS / Tukey;
Means STATUS / t cldiff alpha = 0.05;
Means STATUS / tukey cldiff alpha = 0.05;
RUN;
RESULTS
The SAS System 13:29 Friday,
October 25, 2002 259
The GLM Procedure
Class Level Information
Class Levels Values
STATUS 3 arb free none
Number of observations 337
The SAS System 13:29 Friday, October 25, 2002 260
The GLM Procedure
Dependent Variable: Y Salary
Sum of
Source DF Squares Mean Square F Value Pr > F
Model 2 239911393.0 119955696.5 144.78 <.0001
Error 334 276733296.9 828542.8
Corrected Total 336 516644690.0
R-Square Coeff Var Root MSE Y Mean
0.464364 72.90530 910.2433 1248.528
Source DF Type I SS Mean Square F Value Pr > F
STATUS 2 239911393.0 119955696.5 144.78 <.0001
Source DF Type III SS Mean Square F Value Pr > F
STATUS 2 239911393.0 119955696.5 144.78 <.0001
The SAS System 13:29 Friday, October 25, 2002 261
The GLM Procedure
Tukey's Studentized Range (HSD) Test for Y
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 334
Error Mean Square 828542.8
Critical Value of Studentized Range 3.32936
Comparisons significant at the 0.05 level are indicated by ***.
Difference
STATUS Between Simultaneous 95%
Comparison Means Confidence Limits
free - arb 541.4 217.5 865.3 ***
free - none 1846.2 1586.3 2106.1 ***
arb - free -541.4 -865.3 -217.5 ***
arb - none 1304.8 982.4 1627.2 ***
none - free -1846.2 -2106.1 -1586.3 ***
none - arb -1304.8 -1627.2 -982.4 ***
The SAS System 13:29 Friday, October 25, 2002 262
The GLM Procedure
t Tests (LSD) for Y
NOTE: This test controls the Type I comparisonwise error rate, not the experimentwise error
rate.
Alpha 0.05
Error Degrees of Freedom 334
Error Mean Square 828542.8
Critical Value of t 1.96709
Comparisons significant at the 0.05 level are indicated by ***.
Difference
STATUS Between 95% Confidence
Comparison Means Limits
free - arb 541.4 270.7 812.0 ***
free - none 1846.2 1629.0 2063.3 ***
arb - free -541.4 -812.0 -270.7 ***
arb - none 1304.8 1035.4 1574.1 ***
none - free -1846.2 -2063.3 -1629.0 ***
none - arb -1304.8 -1574.1 -1035.4 ***
The SAS System 13:29 Friday, October 25, 2002 263
The GLM Procedure
Tukey's Studentized Range (HSD) Test for Y
NOTE: This test controls the Type I experimentwise error rate.
Alpha 0.05
Error Degrees of Freedom 334
Error Mean Square 828542.8
Critical Value of Studentized Range 3.32936
Comparisons significant at the 0.05 level are indicated by ***.
Difference
STATUS Between Simultaneous 95%
Comparison Means Confidence Limits
free - arb 541.4 217.5 865.3 ***
free - none 1846.2 1586.3 2106.1 ***
arb - free -541.4 -865.3 -217.5 ***
arb - none 1304.8 982.4 1627.2 ***
none - free -1846.2 -2106.1 -1586.3 ***
none - arb -1304.8 -1627.2 -982.4 ***
/* An Example of Insiginificant Differences */
/*Does not seem to work*/
/*Is it necessary Free?*/
PROC GLM DATA=salary1;
CLASS STATUS;
Model Free = STATUS;
Means STATUS / Tukey;
RUN;