The SAS System 147 16:32 Thursday, December 13, 2001 CONTENTS PROCEDURE Data Set Name: WORK.GRADEPOP Observations: 193 Member Type: DATA Variables: 12 Engine: V612 Indexes: 0 Created: 17:10 Thursday, December 13, 2001 Observation Length: 142 Last Modified: 17:10 Thursday, December 13, 2001 Deleted Observations: 0 Protection: Compressed: NO Data Set Type: Sorted: NO Label: -----Engine/Host Dependent Information----- Data Set Page Size: 8192 Number of Data Set Pages: 4 File Format: 607 First Data Page: 1 Max Obs per Page: 57 Obs in First Data Page: 44 -----Alphabetic List of Variables and Attributes----- # Variable Type Len Pos Informat ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 2 CARDNUM Char 4 16 $4. 11 GROWTH Num 8 126 5 N1 Num 8 78 8 N2 Num 8 102 3 PLAYERNM Char 50 20 $50. 1 PRINTER Char 16 0 $16. 7 SIGMA1 Num 8 94 10 SIGMA2 Num 8 118 12 VINTAGE Num 8 134 6 XBAR1 Num 8 86 9 XBAR2 Num 8 110 4 YEAR Num 8 70 The SAS System 148 16:32 Thursday, December 13, 2001 Cumulative Cumulative VINTAGE Frequency Percent Frequency Percent ƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒƒ 0 31 16.1 31 16.1 1 162 83.9 193 100.0 The SAS System 149 16:32 Thursday, December 13, 2001 OBS PLAYERNM _TYPE_ _FREQ_ SUM_N1 SUM_N2 1 Carl Yastrzemski 1 1 100 490 2 Joey Belle 1 1 100 6053 3 Jim Bunning 1 1 102 316 4 Joe DiMaggio 1 1 102 427 5 Jonny Bench 1 1 104 442 6 Fred Mcgriff 1 1 106 1019 7 Mantle Blasts 1 1 106 518 8 Ty Cobb 1 1 107 415 9 Series Batting 1 1 108 669 10 Catfish Hunter 1 1 110 450 11 Rollie Fingers 1 1 112 421 12 Pete Rose 1 1 114 531 13 Juan Gonzalez 1 1 116 7088 14 AL Bombers 1 1 120 509 15 Lou Brock 1 1 120 469 16 Satchel Paige 1 1 124 536 17 Billy Williams 1 1 128 493 18 Pee Wee Reese 1 1 128 409 19 Rookie Outfielder 1 1 131 588 20 Rod Carew 1 1 133 556 21 Chipper Jones 1 1 137 4355 22 Roberto Alomar 1 1 138 1950 23 Juan Marichal 1 1 140 470 24 Willie McCovey 1 1 140 586 25 Willie Stargell 1 1 141 444 26 Mike Schmidt 1 1 142 576 27 Rocco Colavito 1 1 143 503 28 Sandy Kaufax 1 1 150 697 29 Alex Rodriguez 1 1 155 10365 30 Dodgers' Sluggers 1 1 155 573 31 Jim Palmer 1 1 162 577 32 Super Stars 1 1 163 593 33 Rival All Stars 1 1 169 761 34 Yankees Power Hit 1 1 182 777 35 Bob Gibson 1 1 183 641 36 Carlton Fisk 1 1 191 1026 37 Harmon Killebrew 1 1 193 851 38 Joe Carter 1 1 196 659 39 Wade Boggs 1 1 213 4519 40 Manager's Dream 1 2 221 954 41 Tom Seaver 1 1 223 722 42 Don Mattingly 1 1 225 1651 43 Yogi Berra 1 2 230 966 44 Don Drysdale 1 2 236 926 45 Ozzie Smith 1 1 243 1694 46 Carl Yasztremski 1 1 250 1091 47 Reds Rookie Stars J. Bench 1 1 259 1348 48 Duke Snider 1 2 263 1058 49 Rookie Stars Ro P.Rose 1 1 265 1061 50 Rookie Shortstops 1 1 269 1571 51 Brooks Robinson 1 2 270 1075 52 Henry Aaron 1 1 280 1068 53 Reggie Jackson 1 1 281 1121 54 Barry Bonds 1 1 283 13148 55 Kirby Puckett 1 1 287 1320 56 Dave Winfield 1 1 293 1354 57 Frank Robinson 1 2 293 1168 58 Ryne Sandberg 1 1 295 3444 The SAS System 150 16:32 Thursday, December 13, 2001 OBS PLAYERNM _TYPE_ _FREQ_ SUM_N1 SUM_N2 59 Roger Clemens 1 1 312 1999 60 Roger Maris 1 2 319 1421 61 Rookie Third Base Schmidt 1 1 343 1293 62 Roy Campanella 1 3 343 1279 63 Rickey Henderson 1 1 358 4061 64 Ernie Banks 1 3 367 1695 65 Cards Rookie Star Carlton 1 1 373 1288 66 Al Kaline 1 3 415 1631 67 Mike Piazza 1 2 468 9421 68 Eddie Murray 1 1 505 2193 69 Jackie Robinson 1 3 537 2473 70 Robin Yount 1 3 608 2614 71 George Brett 1 2 618 2517 72 Stan Musial 1 5 685 2514 73 Greg Maddux 1 3 821 28130 74 Ted Williams 1 7 1007 4827 75 Tony Gwynn 1 4 1198 20949 76 Hank Aaron 1 9 1324 5666 77 Sandy Koufax 1 9 1492 6404 78 Willie Mays 1 12 1680 7264 79 Orioles Future ST. 1 1 1728 11308 80 Roberto Clemente 1 10 1918 8462 81 Cal Ripken Jr. 1 4 2037 12363 82 Ken Griffey Jr. 1 2 2153 48304 83 Nolan Ryan 1 10 2258 10804 84 Mickey Mantle 1 27 6412 27098 85 0 193 40609 318040 The SAS System 151 16:32 Thursday, December 13, 2001 OBS PLAYERNM _TYPE_ _FREQ_ SUM_N1 SUM_N2 1 Jim Bunning 1 1 102 316 2 Pee Wee Reese 1 1 128 409 3 Ty Cobb 1 1 107 415 4 Rollie Fingers 1 1 112 421 5 Joe DiMaggio 1 1 102 427 6 Jonny Bench 1 1 104 442 7 Willie Stargell 1 1 141 444 8 Catfish Hunter 1 1 110 450 9 Lou Brock 1 1 120 469 10 Juan Marichal 1 1 140 470 11 Carl Yastrzemski 1 1 100 490 12 Billy Williams 1 1 128 493 13 Rocco Colavito 1 1 143 503 14 AL Bombers 1 1 120 509 15 Mantle Blasts 1 1 106 518 16 Pete Rose 1 1 114 531 17 Satchel Paige 1 1 124 536 18 Rod Carew 1 1 133 556 19 Dodgers' Sluggers 1 1 155 573 20 Mike Schmidt 1 1 142 576 21 Jim Palmer 1 1 162 577 22 Willie McCovey 1 1 140 586 23 Rookie Outfielder 1 1 131 588 24 Super Stars 1 1 163 593 25 Bob Gibson 1 1 183 641 26 Joe Carter 1 1 196 659 27 Series Batting 1 1 108 669 28 Sandy Kaufax 1 1 150 697 29 Tom Seaver 1 1 223 722 30 Rival All Stars 1 1 169 761 31 Yankees Power Hit 1 1 182 777 32 Harmon Killebrew 1 1 193 851 33 Don Drysdale 1 2 236 926 34 Manager's Dream 1 2 221 954 35 Yogi Berra 1 2 230 966 36 Fred Mcgriff 1 1 106 1019 37 Carlton Fisk 1 1 191 1026 38 Duke Snider 1 2 263 1058 39 Rookie Stars Ro P.Rose 1 1 265 1061 40 Henry Aaron 1 1 280 1068 41 Brooks Robinson 1 2 270 1075 42 Carl Yasztremski 1 1 250 1091 43 Reggie Jackson 1 1 281 1121 44 Frank Robinson 1 2 293 1168 45 Roy Campanella 1 3 343 1279 46 Cards Rookie Star Carlton 1 1 373 1288 47 Rookie Third Base Schmidt 1 1 343 1293 48 Kirby Puckett 1 1 287 1320 49 Reds Rookie Stars J. Bench 1 1 259 1348 50 Dave Winfield 1 1 293 1354 51 Roger Maris 1 2 319 1421 52 Rookie Shortstops 1 1 269 1571 53 Al Kaline 1 3 415 1631 54 Don Mattingly 1 1 225 1651 55 Ozzie Smith 1 1 243 1694 56 Ernie Banks 1 3 367 1695 57 Roberto Alomar 1 1 138 1950 58 Roger Clemens 1 1 312 1999 The SAS System 152 16:32 Thursday, December 13, 2001 OBS PLAYERNM _TYPE_ _FREQ_ SUM_N1 SUM_N2 59 Eddie Murray 1 1 505 2193 60 Jackie Robinson 1 3 537 2473 61 Stan Musial 1 5 685 2514 62 George Brett 1 2 618 2517 63 Robin Yount 1 3 608 2614 64 Ryne Sandberg 1 1 295 3444 65 Rickey Henderson 1 1 358 4061 66 Chipper Jones 1 1 137 4355 67 Wade Boggs 1 1 213 4519 68 Ted Williams 1 7 1007 4827 69 Hank Aaron 1 9 1324 5666 70 Joey Belle 1 1 100 6053 71 Sandy Koufax 1 9 1492 6404 72 Juan Gonzalez 1 1 116 7088 73 Willie Mays 1 12 1680 7264 74 Roberto Clemente 1 10 1918 8462 75 Mike Piazza 1 2 468 9421 76 Alex Rodriguez 1 1 155 10365 77 Nolan Ryan 1 10 2258 10804 78 Orioles Future ST. 1 1 1728 11308 79 Cal Ripken Jr. 1 4 2037 12363 80 Barry Bonds 1 1 283 13148 81 Tony Gwynn 1 4 1198 20949 82 Mickey Mantle 1 27 6412 27098 83 Greg Maddux 1 3 821 28130 84 Ken Griffey Jr. 1 2 2153 48304 85 0 193 40609 318040 The SAS System 153 16:32 Thursday, December 13, 2001 VINTAGE N Obs Variable N Mean Std Dev Minimum ---------------------------------------------------------------------------- 0 31 AVGTEST 31 5.7552249 5.5071725 -5.4087128 REJECT 31 0.9032258 0.3005372 0 1 162 AVGTEST 162 4.8699136 1.8931009 -0.4474697 REJECT 162 0.9753086 0.1556640 0 ---------------------------------------------------------------------------- VINTAGE N Obs Variable Maximum ------------------------------------------- 0 31 AVGTEST 24.2844728 REJECT 1.0000000 1 162 AVGTEST 11.8463959 REJECT 1.0000000 ------------------------------------------- The SAS System 154 16:32 Thursday, December 13, 2001 General Linear Models Procedure Class Level Information Class Levels Values RACEAGE 4 modern + non- modern + whit vintage+non-w vintage+white Number of observations in data set = 193 NOTE: Due to missing values, only 168 observations can be used in this analysis. The SAS System 155 16:32 Thursday, December 13, 2001 General Linear Models Procedure Dependent Variable: GROWTH Sum of Mean Source DF Squares Square F Value Pr > F Model 3 6782.1864633 2260.7288211 39.13 0.0001 Error 164 9475.0926580 57.7749552 Corrected Total 167 16257.2791212 R-Square C.V. Root MSE GROWTH Mean 0.417178 122.2887 7.6009838 6.2156063 Source DF Type I SS Mean Square F Value Pr > F RACEAGE 3 6782.1864633 2260.7288211 39.13 0.0001 Source DF Type III SS Mean Square F Value Pr > F RACEAGE 3 6782.1864633 2260.7288211 39.13 0.0001 The SAS System 156 16:32 Thursday, December 13, 2001 General Linear Models Procedure Waller-Duncan K-ratio T test for variable: GROWTH NOTE: This test minimizes the Bayes risk under additive loss and certain other assumptions. Kratio= 100 df= 164 MSE= 57.77496 F= 39.12991 Critical Value of T= 1.75996 Minimum Significant Difference= 3.9393 WARNING: Cell sizes are not equal. Harmonic Mean of cell sizes= 23.06403 Means with the same letter are not significantly different. Waller Grouping Mean N RACEAGE A 20.791 19 modern + non- A A 18.062 11 modern + whit B 3.319 57 vintage+non-w B B 3.227 81 vintage+white The SAS System 157 16:32 Thursday, December 13, 2001 General Linear Models Procedure T tests (LSD) for variable: GROWTH NOTE: This test controls the type I comparisonwise error rate not the experimentwise error rate. Alpha= 0.05 Confidence= 0.95 df= 164 MSE= 57.77496 Critical Value of T= 1.97453 Comparisons significant at the 0.05 level are indicated by '***'. Lower Difference Upper RACEAGE Confidence Between Confidence Comparison Limit Means Limit modern + non- - modern + whit -2.957 2.729 8.415 modern + non- - vintage+non-w 13.497 17.472 21.448 *** modern + non- - vintage+white 13.739 17.564 21.390 *** modern + whit - modern + non- -8.415 -2.729 2.957 modern + whit - vintage+non-w 9.801 14.743 19.686 *** modern + whit - vintage+white 10.013 14.835 19.658 *** vintage+non-w - modern + non- -21.448 -17.472 -13.497 *** vintage+non-w - modern + whit -19.686 -14.743 -9.801 *** vintage+non-w - vintage+white -2.503 0.092 2.687 vintage+white - modern + non- -21.390 -17.564 -13.739 *** vintage+white - modern + whit -19.658 -14.835 -10.013 *** vintage+white - vintage+non-w -2.687 -0.092 2.503 The SAS System 158 16:32 Thursday, December 13, 2001 Model: MODEL1 Dependent Variable: GROWTH Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 300.33870 300.33870 3.124 0.0790 Error 166 15956.94042 96.12615 C Total 167 16257.27912 Root MSE 9.80439 R-square 0.0185 Dep Mean 6.21561 Adj R-sq 0.0126 C.V. 157.73834 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 7.686693 1.12464115 6.835 0.0001 RACE 1 -2.686331 1.51975891 -1.768 0.0790 The SAS System 159 16:32 Thursday, December 13, 2001 Model: MODEL1 Dependent Variable: GROWTH Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 2 6742.08699 3371.04350 58.456 0.0001 Error 165 9515.19213 57.66783 C Total 167 16257.27912 Root MSE 7.59393 R-square 0.4147 Dep Mean 6.21561 Adj R-sq 0.4076 C.V. 122.17527 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 19.990751 1.45398069 13.749 0.0001 RACE 1 -0.546495 1.19440476 -0.458 0.6479 VINTAGE 1 -16.405412 1.55221568 -10.569 0.0001 The SAS System 160 16:32 Thursday, December 13, 2001 ---------------------------------- VINTAGE=0 ----------------------------------- Model: MODEL1 Dependent Variable: GROWTH Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 51.88894 51.88894 0.154 0.6973 Error 28 9408.65869 336.02352 C Total 29 9460.54763 Root MSE 18.33094 R-square 0.0055 Dep Mean 19.79037 Adj R-sq -0.0300 C.V. 92.62558 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 20.791052 4.20540708 4.944 0.0001 RACE 1 -2.729134 6.94500121 -0.393 0.6973 The SAS System 161 16:32 Thursday, December 13, 2001 ---------------------------------- VINTAGE=1 ----------------------------------- Model: MODEL1 Dependent Variable: GROWTH Analysis of Variance Sum of Mean Source DF Squares Square F Value Prob>F Model 1 0.28320 0.28320 0.580 0.4477 Error 136 66.43397 0.48849 C Total 137 66.71716 Root MSE 0.69892 R-square 0.0042 Dep Mean 3.26457 Adj R-sq -0.0031 C.V. 21.40916 Parameter Estimates Parameter Standard T for H0: Variable DF Estimate Error Parameter=0 Prob > |T| INTERCEP 1 3.318573 0.09257383 35.848 0.0001 RACE 1 -0.092003 0.12083291 -0.761 0.4477