OFP CI THE APPLICATION OF KRIGING IN THE STATISTICAL ANALYSIS OF ANTHROPOMETRIC DATA VOLUME II THESIS Michael Grant Captain, USAF AFIT/G OR/ENY/ ENS /90M-8 DTIC ELECTE DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY S AP119D AIR FORCE INSTITUTE OF TECHNOLOGY I., 1 Wright-Patterson Air Force Base, Ohio 90 04 13 190 B
SECURITY CLASSIFICATION OF THIS PAGE REPORT DOCUMENTATION PAGE Form OMF Approved No. 0p04r018e la. REPORT SECURI1,Y CLASSIFICATION lb. RESTRICTIVE MARKINGS UNCLASSIFIED............... "za. SECURITY CLASSIFICATIUN AUTHORITY 3 DISTRIBUTION/AVAILABILITY OF REPORT Approved for pu-ilic release: 2b. DECLASSIFICATION/DOWNGRADING SCHEDULE distribution unlimited 4. PERFORMING ORGANIZATION REPORT NUMBER(S) 5 MONITORING ORGANIZATION REPORT NUMBER(S) AFIT/GOR/ENY/ENS/9OM-8 6a. NAME OF PERFORMING ORGANIZATION 6b. OFFICE SYMBOL 7a. NAME-aF MONITORING ORGANIZATION School of Engineering A I Pfl fcfl') 6c. ADDRESS (City, State, and ZIPCode) / 7b. ADDRESS (City, State, and ZIP Code) 8a. NAME OF FUNDING /SPONSORING 8b. OFFICE SYMBOL 9. PROCUREMENT INSTRUMENT IDENTIFICATION NUMBER ORGANIZATION (If applicable) AAMRL HEG 8c. ADDRESS (City, State, and ZIP Code) '0. SOURCE OF FUNDING NUMBERS AAMPL/HEG PROGRA.M PROJECT TASK WORK UNIT ELEMENT NO. NO. NO. ACCESSION NO. WPAFB, OH 45433 11. TITLE (Include Security Classification) THE APPLICATION OF KRIGING IN THE STATISTICAL ANALYSIS OF ANTHROPOMETRIC DATA 12 PERSONAL AUTHOR(S) Michael Grant, B.S., M.S., Capt, USAF 13a. TYPE OF REPORT 113b. T:ME COVERED 114. DATE OF REPORT (Year, Month, Day) 15. PAGE COUNT MS Thesis FROM TO 430 16. SUPPLEMENTARY NOTATION 17..Z COSATI CODES 18.-3UBJECT TERMS (Continue on reverse if necessary and identify by block number) -FIELD GROUP SU'BGROUP ->Kriging." Bayesian Statistics- Morphometricz' 12 03 Geostatistics' Multivariate Analysis_,-) I ' 19. ABSTRACT (Continue on reverse if necessary and identify by block numberl Thesis Advisors: David G. Robinson Assistant Professor Department of Aeronautics and Astronautics Kenneth W. Bauer Assistant Professor Department of Operational Sciences 20. DISTRIBUTION/AVAILABILITY OF ABSTRACT 21. ABSTRACT SECURITY CLASSIFICATION S UNCLASSIFIED/UNLIMITED 0 SAME AS RPT El DTiC USERS UNCLASSIFIED 22a. NAME OF RESPONSIBLE INDIVIDUAL 22b. TELEPHONE (Include Area Code) 122C. OFFICE SYMBOL David G. Robinson, Asst. Professor (513) 255-2362 AFIT/ENY DD Form 1473, JUN 86 Previous editions ate obsolete. SECURITY CLASSIFICATION C'( THIS PAGE
--- UNCLASSIFIED---- - Quality flight equipment is essential to flight crew safety and performance. Oxygen masks, night-vision goggles, and other apparatus must fit crew members comfortably and with complete functional precision. A problem currently facing the Air Force is the inconsistent quality of flight equipment. As new equipment is developed to improve crew members' performance, the requirement for design engineers-to accurately account for the shape arid variability of facial features becomes more critical. This thesis develops the application of kriging in the statistical analysis of anthropometric data to support improvements in the design of flight equipment. Specifically, the geostatistical estimation technique of kriging is used to estimate the facial surfaces which influence the designs of flight apparatus. These surfaces account for the shape of the facial features and minimize the variance between individuals. A Kalman filter is developed to update and aggregate the kriged surfaces. As a proof of concept study, the techniques are demonstrated using data to support the design of the night-vision goggles currently under development. To further enhance the surface estimates, a multivariate analysis is performed to identify the factors which account for the majority of the variability between faces and to group the faces into homogenous clusters. ;- / r._- 7, /7
AFIT/GOR/ENY/ENS/90M-8 THE APPLICATION OF KRIGING IN THE STATISTICAL ANALYSIS OF ANTHROPOMETRIC DATA VOLUME II THESIS Presented to the Faculty of the School of Engineering of the Air Force Institute of Technology Air University In Partial Fulfi!lment of the Requirements for the Degree of Master of Science in Operations Research LAOOO9SODlon DTIC T.AB0 w M ichael Grant, B.S., M.S. Uni.ounOd 0 Captain, USAF March 1990 By... - Dit tr ibut ion/l AvallabilitY Codes Avail and/or Approved for public release; distribution unlimited
Appendix A. Subjects This appendix provides a graphical representation of the facial data used for this research effort. The first 25 subjects were included in the trend analysis and the final variogram analysis. The next five subjects were used in the kriging and updating analysis. Following these subjects are a group of five faces which were used only in the trend analysis. The last two faces were considered for the analysis but discarded because of inherent shortfalls in the data. A-1
200 150 *~~0 Subject 09 A-2
20o 1go b, M Subject 10 A-3
5O Subject 60 A-4
-00 160 too 50 Subject 68 A-5
200 i5o 50 0 Subject 114 A-6
200 560 50 Subject 116 A-7
2000 oo 150 go- Subject 118 A-8
100 f50 Subject 122 A-9
g00 160 5O Subject 130 A-10
200 150 100 Subject 133 A-11
200 10o t50. Subject 136 A-12
oo 150 O0! Subject 140 A-13
200 too- 50 Subject 142 A-1.4
00 f50 10 Subject 153 A-15
200 z5o 50O Subject 154 A-16
200 600 f5o *~, 0 Subject 155 A-17
200-150. 1 00.~~ 0 Subject 159 A-18
2Oo 150, SfO0 50 Subject 160 A-19
goo 15o too Subject 161 A-20
z0' O60 100 Subject 167 A-21
100 O0 Subject 171 A-22
200 16O g~o Subject 173 A-23
too 150 Subject 176 A-24
"20o go0 100 go- Subject 183 A-25
ZOO= 160 f~o 0 Subject 185 A-26
200 15o 50 Subject 112 A-27
200 150 Subject 141 A-28
200 150 '00. go. 600 Subject 152 A-29
20o 50 Subject 156 A-30
Ooo.50 Subject 199 A-31
$00 t5o too- 50 Subject 01 A-32
200 150 50 Subject 07 A-33
too 50 50 0 Subject 12 A-34
200 160 50.] Subject 89 A-35
200. Subject 150 A-36
160,r 400 Subject 33 A-37
200 160 Subject 151 A-38
Append c B. Residual Plots This appendix includes the residual plots obtained by differencing the subject data with the trend data. The first 25 residual data sets where used to determine the overall variogram and were used in the kriging and updating analysis. The next five data sets were excluded from the overall variogram analysis, the kriging analysis, and the updating analysis because the variograms were not consistent with the set of 25. These five data sets were included in the trend. The final seven data sets were considered for the kriging and updating procedures. However, only the first five sets followed the standard variogram pattern and were used for kriging and updating the surface estimates. B-1
20 io ~0 0) Subject 09 Residuals B-2
90' f 0 -to Subject 10 Residuals B-3
,jo 10 0 to Subject 60 Residuals B-4
ý0 10 00( 0o Subject 68 Residuals B-5
g0 0) Subject 114 Residuals B-6
20-10 Subject 116 Residuals B-7
20,.10 0 00 Subject 118 Residuals B-8
2 0 ~0 10 Uo...0 Subject 122 Residuals B-9
20 10 /0 lip Subject 130 Residuals B-10
20-10 Subject 133 Residuals B-11
c "10 -~0 Subject 136 Residuals B-12
20 10.0 Subject 140 Residuals B-13
20 20 d ~o Subject 142 Residuals B-14
U, 0 o) /10 Subject 153 Residuals B-15
20..10 ili Subject 154 Residuals B- 16
f. m 20 Cm to co 100 Subject 155 Residuals B-17
go 10 ~0 go Subject 159 Residuals
10 ~0,-.g Subject 160 Residuals B-19
20 10.10 Subject 161 Residuals B-20
20 t0 Subject 167 Residuals
o0 t0,10 --- I Subject 171 Residuals
go 80 0 Subject 173 Residuals B-23
20 10 Subject 176 Residuals B-24
'_ 0 20 CO ~0 '70_ :S h Subject 183 Residuals B-25
20 1o -.10 r 00 Subject 185 Residuals B-26
20.1ý0 Subject 01 Residuals B-27
10 co 110 Subject 07 Residuals B-28
20 'fo 0).. lip Subject 12 Residuals B-29
t0 go '90O Subject 89 Residuals B-30
20- ~0 U, 0 Subject 150 Residuals B-31
20 10 S10 Subject 112 Residuals B-32
1*o 20 PP Subject 141 Residuals B-33
go- Subject 152 Residuals B-34
go -- 10" 0.10 Subject 156 Residuals B-35
g0 10 20 Subject 199 Residuals B-36
20 'go 400 Subject 33 Residuals B-37
to,, 20.. 0.5 Subject 151 Residuals B-38
Appendix C. Variograms This appendix provides the variograms corresponding to each of the residual data sets in the previous appendix. Each plot displays a set of four variograrns (one for each direction for the individual) and the overall variogram. C-1
10'-I Subject 09 -Esf,.mated 6-4.-.- --..".,.. 0 2 4 6 8 h (disto.?,ce) Subject 09 Variograms 6r Subject 10 -Estimated 2-0 0.2 4 _ 6 h (distance) Subject 10 variogrrms C-2
to -0u j.ct 60 8 - Estimatied 6 4 4....... i, 0 2 4 6 8 h (distance) Subject 60 Variograms -,Subject 68 -Estimated 0 2 4 6 8 h (distance) Subject 68 Variograms C-3
10 Subject 114 8 8Estimated 6 4 0 2 4 3 8 h (distance) Subject 114 Variograms Subject 116 - stima Ztd h (distance) Subject 116 Variograms 6 8 C-4
10. 8 O-Subject 118 -Estimated 6-4 2 0 2 4 6 8 h (distance) Subject 118 Variograms 10-8 ""-[ Subject 122 -- Estimated 6 4 S... 0 2 4 6 8 h (distance) Svtbject 122 Variograms C-5
W0 $ubject 130 8 Es~imated 6 0 2 4 6 8 h (distance) Subject 130 Variograms 10. Eabject 133 SEstimaryted.- 4 - - 2 -- L 0 2 4 6 8 h (dilstance) Subject 133 Variograrns C-6
10, 10 Subject 136 8 Estimated 4 0 0 2 4 6 8 h (distance) Subject 136 Variograms 10[.' $ubject 140 - EsUmnAted 6-4... - "-- - r 2 0 2 4 6 8 h (distance) Subject 140 Variograms C-7
10....... 1-S- ubject 142 8 Estimated 6. 4 0..... 0,8 4 6 8 h (distance) Subject 142 Variograms 10 -" " " ' ".... - - - - 1-SI ubject 15? Estimated 4 2 0 0 2 4 6.. h (distance) Subject 153 Variograms C-8
10 Subject 154 8Estimated 6 2 0 2 4 6 8 h (distance) Subject 154 Variograms "S'- Subject 165 E- stimated 6-4- 2 0 2 4 6 8 h (distance) Subject 155 Variograms C-9
10 -Ubject 159 8 - Estimated 6 4 2 0 0 2 4 6 8 h (distance) Subject 159 Variograms 10.! - 5-' Subject 160 b 8 Estir,v't, d 4 2 0, I, 0 2 4 6 8 h (distance) Subject 160 Variograms C-10
10 _uuject 161 a' Estimated 8 A-mGU 6-4 0 2 4 6 8 h (distance) Subject 161 Variograms i 0 8 Subject 167 SEstimated 0 2 4 6 a h (distance) Subject 167 Variograms C-11
10. 8 Subject 171 8- Estimated 6-2 0 2 4 6 8 h (distance) Subject 171 Variograms 10. I I. S--': ubject 173 8 Estimated 4 0 2 4 6 8 h (distance) Subject 173 Variograms C-12
10, 8 1-0- 1bject u 176 Esftmated 6- --...-- " /',...".% 4 2 0-~ 0 2 4 6 8 h (distance) Subject 176 Variograms 10 ] 8 ' Estimated 6 ----..7,' ' -. 4 // o.'" 2 /,,/......... 0 0 2 4 6 8 h (distance) Subject 183 Variograrns C-13
Subject 185 8 E- Estimated 4.- 0 0 2 4 6 8 h (distance) Subject 185 Variograms 20. Subject 01 Estimated 15 0 -............. 0 2 4 6 8 h (distance) Subject 01 Variograms C- 14
2 0 :subject 0?7_ 75 -EsiatemLd oo....o 10 "'"" """ -" 0 2 4 6 8 h (distance) Subject 07 Variograms 2 0 i ' ' " " ' ' " ' ' ' '.. -Subject 12 Estimnced ''" I, 10" 5 9./.. 0 2 4 6 8 ft (cdis (mce) C-1 Subject 12 Va~riograms C-15
S'uh'jec, t 89 -Es~rtimted ~10~ 5 -,- o. 0 2 4 6 8 h, (distance) Subject 89 Variograms 20 - Subject 150 SEstimated 15 5..;... 0 ~- 0 2 4 6 8 h (distance) Subject 150 Variograms C-16
10~ 10.Subject 112 - Estimated 6-2- 0 1...... i. 0 2 4 6 8 h (distance) Subject 112 Variograms 10. 1;*,ubjuct 141 8- -Estimated 0 0 2 4 6 8 h (distance) Subject 141 Variograms C-17
10 8 0.Subject 152 - Estimated 6-, 4-- 0 0 2 4 6 8 h (distanmce) Subject 152 Variograms 4f 8- [ - 10. --- Subject 156 Estimated 0 2 4 6 8 h (distance) Subject 156 Variograms G-18
10 Subject f99 Estimated 6 2-- 0 2.4 6 8 h (&dstance) Subject 199 Variograms Subject 33 - Estimated 5-0 2 4 6 9 h (distance) Subject 33 Variograms C-19
20 "-Subject 157 -Estimated 15,% 0 0 2 4 6 8 h (distance) Subject 151 Variograms C-20
Appeadix D. Kriging Analysis Figures Kriged Residual Plots This section includes the kriged residual plots for the 30 data sets used in kriging and updating procedures. D-1
0o 10 'to Sb00 Subject 09 Kriged Residuals
10 b I I Subject 10 Kriged Residuals D-3
10 8t0 Subject 60 Kriged Residuals D-4
go /0 40 Subject 68 Kriged Residuals D-5
20 ~0.10 Subject 114 Kriged Residuals D-6
0 10 '20 Subject 116 Kriged Residuals D-7
I, /101 Subject 118 Kriged Residuals D-8
10 ~0 Subject 122 Kriged Residuals D-9
101 20 10 Subject 130 Kriged Residuals D-10
290 ~0 Q~Q Subject 133 Kriged Residuals D-11
20 0.10 Subject 1.36 Kriged Residuals D-12
20 b10 Subject 140 Kriged Residuals D-13
.,90 10,1 0 Subject 142 Kriged Residuals D-14
20 t0.0 Subject 153 Kriged Residuals D.15
20 10 Subject 154 Kriged Residuals i! i I i-i6
ýo 10 U Subject 155 Kriged Residuals D-17
20 joý i0 'I,1 -I-- ý-i Subject 159 Kriged Residuals D-18
20 10,10..0 Subject 160 Kriged Residuals D-19
,00 C,0 10 Subject 161 Kriged Residuals D-20
20 10 tf0 nps Subject 167 Kriged Residuals D-21
to 20-10 t0) Subject 171 Kriged Residuals D-22
fo 0 00 20 Subject 173 Kriged Residuals D-23
10 20 C,1 d.o Subject 176 Kriged Residuals D-24
10 ~0 re "10 Subject 183 Kriged Residuals D-25
20 co 10" Subject 185 Kriged Residuals D-26
~0 Subject 112 Kriged Residuals D-27
10 ioi 101 0, Subject 141 Kriged Residuals D-28
20 ~0 CIO 1 0 0) 100 Subject 152 Kriged Residuals D-29
20 t0 Jo,10... N0 Subject 156 Kriged Residuals D-30
20 10 I~bp Subject 199 Kriged Residuals D-31
Kriged Facial Surfaces This section provides the kriged facial surfaces for the 30 data sets. The kriged facial surfaces were obtained by combining the kriged residuals with the trend. D-32
200 150 5O, Subject 09 Kriged Surface D-33
200 150 5o. Subject 10 Kriged Surface D-34
200 150 IO0 Subject 60 Kriged Surface D-35
200 5o0 SfO0 5o 0 Subject 68 Kriged Surface D-36
200r 150. 00 50. Subject 114 Kriged Surface D-37
2001 160' l o.l _ 50 Subject 116 Kriged Surface D-38
20o 150 O00 go. Subject 118 Kriged Surface D-39
Ooo '900. fo 100 i Subject 122 Kriged Surface D-40
200 150 '60, Subject 130 Kriged Surface D-41
2000 ~5O too 50 0 Subject 133 Kriged Surface D-42
200. 500 60 Subject 136 Kriged Surface D-43
ZO0 F 150. Subject 140 Kriged Siirface D-44
,go- 100 50 Subject 142 Kriged Surface D-45
1600 50 Subject 153 Kriged Surface D-46
200 150 10 0 60. Subject 154 Kriged Surface D-47
200 15o- 6 0o 0 Subject 155 Kriged Surface D-48
2900 60a Subject 159 Kriged Surface D-49
200 06o Subject 160 Kriged Surface D-50
200 f go t oo- 50 Subject 161 Kriged Surface D-51
200,go 100 l oo go Subject 167 Kriged Surface D-52
200 150 D-- Subject 171 Kriged Surface D-53
200 150 60. Subject 173 Kriged Surface D-54
ZOo 160 50 Subject 176 Kriged Surface D-55
ZOO 15o. 55O Jill 4r D-56
650 50. Subject 185 Kriged Surface D-57
200-150 50O Subject 112 Kriged Surface D-58
,700 g0o. Subject 141 Kriged Surface D-59
0 0 150 10o, SJe 2i r).qp
200 150' 50 Su;. l5k. Kriged Surface
goo 150, 50. Siihiprt. I(YA Rriored Siirfai-p
Facial Surface Estimation Variances This section provides the kriging variances corresponding to the figures displayed in the previous sections. D-63
6m 1O 2! 0 Estimation Variances for Subject 09 D-64
fo 6.~4 c0 Estimation Variances for Subject 10 D-65
10 8-6.?4 Estimation Variances for Subject 60 D-66
fof 6 1 19 Estimation Variances for Subjezt 68 D-67
10,I 6 Estimation Variances for Subject 114 D-68
10 6 Estimation Variances for Subject 116 D-69
to- 6.~4 2 lip Estimation Variances for Subject 118 D-70
10 6 0) Estimation Variances for Subject 122 D-71
Ito, a 6. ~4. Estimation Variances for Subject 130 D-.72
Sm 6, lip. 4 0 Estimation Variances for Subject 133 D-73
t0 8. 6 4 Estimation Variances for Subject 136 D-74
to 8 V 6 4 Estimation Variances for Subject 140 D-75
to- 8 6 4-0 Estimation Variances for Subject 142 D-76
6 4 0 Estimation Variances for Subject 153 D-77
10L 8. 6 S4 Estimation Varia.nces for Subject 154 D-78
to- 0 1 Estimation Variances for Subject 155 D-79
6 4, 00 Estimation Variances for Subject 160 D-81
80 6.29 0 Estimation Variances for Subject 161 D-82
10 6 CC3 Estimation Variances for Subject 167 D-83
10 B Estimation Varihnces for Subject 171 D-84
i0 U fd 6 QP Estimation Variances for Subject 173 D-85
10 6 ~4-0,, Estimation Variances for Subject 176 D-86
to- 6 4-90 Estimation Variance; for Subject 183 D-87
10. 6 191 Estimation Variances for Subject 185 D-88
to S Estimation Variances for Subject 112 D-89
6 4-0, Estimation Variances for Subject 141 D-90
6, 0- Estimation Variances for Subject 152 D-91
10 6.~4 Estimation Variances for Subject 156 D-92
8 0, 6 4 0 Estimation Variances for Subject 199 D-93
Appendix E. Updated Surface Plots This appendix includes the updated surfaces and variances obtained by the updating procedure. The surfaces were produced sequentially beginning with the lowest numbered subject. Each surface represents the aggregate smr-i;ce or all the subjects up to and including the most recent update. Updated Facial Surfaces This section includes the surface estimates. E-1
200 150-100 50 Updated Surface After Subject 09 E-2
200, 150 Updated Surface After Subject 10 E-3
500 0 Updated Surface After Subject 60 E-4
200 150 1 00 Updated Surface After Subject 68 E-5
200 150 io0 50O Updated Surface After Subject 114 E-6
"200 r ~50 0o 50 Updated Surface After Subject 116 E-7
200 150 d 50 Updated Surface After Subject 118 E-8
200 150-50o 1o00 d 50 Updated Surface After Subject 122 E-9
200 150 60 Updated Surface After Subject 130 E-10
200 150 50 50 Updated Surface After Subject 133 E-11
200 150 Updated Surface After Subject 136 E-12
200 160 100 50 Updated Surface After Subject 140 E-13
15o.o io 200-5o- Updated Surface After Subject 142 E-14
100 150- Updated Surface After Subject 153 E- 15
150 50. Updated Surface After Subject 154 E-16
0oo 150 Stoo- 50 * 0O Updated Surface After Subject 155 E-17
200 150 Updated Surface After Subject 159 E-18
200.6O. t0o Updated Surface After Subject 160 E-19
200, 1500 0o 0 Updated Surface After Subject 161 E-20
200-200 - 150 Updated Surface After Subject 167 E-21
foo 50, Updated Surface After 3ubject 171 E-22
200-150 100 50 Updated Surface After Subject 173 E-23
200 150 Updated Surface After Subject 176 E-24
2o0 150 o0 Updated Surface After Subject 183 E-25
20O 150 Updated Surface After Subject 185 E-26
15o. 200' 50 Updated Surface After Subject 112 E-27
200 15o. i *4 00 60 Updated Surface After Subject 141 E-28
200 50o 10 Updated Surface After Subject 152 E-29
00. too 60o Updated Surface After Subject 156 E-30
200 50' SO0 p~np Updated Surface After Subject 199 E-31
Updated Estimation Variances This section includes the plots of the variances. E-32
3 Updated Variances After Subject 09 E-33
41 3-0f Updated Variances After Subject 10 E-34
4 IB Updated Variances After Subject 60 E-35
3.. Z, ot.. Updated Variances After Subject 68 E-36
o. 6 0.2 0.,g 04 0 Updated Variances After Siibject 114 E-37
f.0 0.8 0.6 " 0.4. 0. o*, Updated Variances After Subject 116 E-38
1.0 0',6 0.6 "0 0. Updated Variances After Subject 118 E-39
t.0 0.8-0.6 0. 6 0. Updated Variances After Subject 122 E-40
1.0. 0.8 0.6 ' 0.4. 0. 2 Updated Variances After Subject 130 E-41
1.0 0.8-0.6 '004.2 0" 0.9 0 Updated Variances After Subject 133 E-42
1.0O 0.8 0. 6 0.29 Updated Variances After Subject 136 E-43
f.0 0.8 0.6 0. 4 0.2 Updated Variances After Subject 140 E-44
I.e 0.8 0.6 4. 0.2 0.,. 1.p Updated Variances After Subject 142 E-45
1.0 0.8. 0.6 "0.. 0. 'o,. Updated Variances After Subject 153 E-46
0.8 0.6 0.2 Updated Variances After Subject 154 E-47
o.20 0. S0.1o 0.05 Updated Variances After Subject 155 E-48
0.20 0.10 0.05 0.0 Updated Variances After Subject 159 E-49
0.20 O.fg 0. 0.05 04b Updated Variances After Subject 160 E-50
O.2o 0.10 0.10 O.05 Updated Variances After Subject 161 E-51
0.20 0. 0.10 0.06 0.0 ole- Updated Variances After Subject 167 E-52
0.20 O. 0. 05 0. Updatk.d Variances After Subject 171 E-53
I V o - 0., 0. 0. 1 00 Updated Variances After Subject 173 E-54
0.20 0. o 00 0.0 Updated Variances After Subject 176 E-55
0.20 ~a 0.05- Updated Variances After Subject 183 E-56
0.Z0 0.1f5 0.05' S0.10 Updated Variances After Subject 18.5 E-57
f.0 0.8. 0.6 n I I I E-58
0.0 0.6. 0. 0.2 0 Updated Variances After Subject 141 E-.59
1.0 0.6 "0.9 0.: Updated Variances After Subject 152 E-60
0.20 S0.10 0.05. 0.0 Updated Variances After Subject 156 E-e 1
0.20.0.IO 10 0.05 Updated Variances After Subject 199 E-62