using incomplete block designs to reduce uncontrolled variation in field experiments - such as...
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Using Incomplete Block Designs to Reduce Uncontrolled Variation in Field Experiments - Such as Variety Tests
Fred AllenDepartment of Plant Sciences
University of Tennessee
SCC33 Annual Meeting, Feb. 8-10, 2012New Orleans, LA
AGRONOMIC VARIETY TESTING
COUNTIES AND RESEARCH & EDUCATION CENTERS
Obion
Fayette
Madison
Gibson
Weakley
Carroll
Hardin
Dyer
Henry
Moore
Robertson
Tipton
Giles
Coffee
Fulton
Carlisle
BallardMcCracken
Kentucky Counties
Greene
Cumberland
Tobacco Research & Education Center
Maury
Knox
East Tennessee Research & Education Center
Plateau Research & Education Center
Middle TN Research & Education Center
Highland Rim Research & Education Center
West TN Research & Education CenterAmes Plantation
Milan Research & Education Center
Physiographic map of Tennessee
Cannon
Hickman
Franklin
BlountLoudon
MarionShelby
Agricenter International
HickmanGraves
SOURCES OF UNCONTROLLED VARIATION IN FIELD EXPERIMENTS:
* EXPERIMENTS WITH A LARGE NUMBER OF TRTS.(e.g. Large number of varieties)
* LARGE AMOUNT OF VARIATION IN THE FIELD SITE(e.g., soil type changes, moisture, fertility)
ONE WAY TO REDUCE THE UNCONTROLLED VARIATION IS TO USE AN INCOMPLETE BLOCK DESIGN
* DIVIDE EACH REP INTO SMALLER BLOCKS* CAN BE IMPOSED EX POST FACTO PLANTING* BLOCK SIZES FROM 8-14 HAVE BEEN OUR BEST
EXPERIENCE
TN WHEAT TEST 2011,EXAMPLE OF TWO LOCATION RANDOMIZATION
72 VARIETIES3 REPS PER LOCATION7 LOCATIONS
Year Entry Brand Variety 1 2 3 1 2 32011 W11001 Armor ARX 0179 1001 1105 1190 1001 1111 11452011 W11002 Armor ARX 0186 1002 1137 1168 1002 1103 11962011 W07005 Armor Renegade 1003 1112 1147 1003 1121 11572011 W10004 Armor Ricochet 1004 1080 1158 1004 1120 11812011 W08003 Cache River Valley Seed Dixie 454 1005 1110 1200 1005 1087 12152011 W11003 Cache River Valley Seed Dixie Kelsey 1006 1144 1160 1006 1141 11592011 W11004 Cache River Valley Seed Dixie McAlister 1007 1123 1204 1007 1126 12052011 W04020 Croplan Genetics 8302 1008 1141 1165 1008 1124 11682011 W11027 Croplan Genetics 8302 (FILL) 1009 1104 1191 1009 1105 11692011 W11005 Croplan Genetics 8614 1010 1102 1186 1010 1085 11992011 W10005 Croplan Genetics 8925 1011 1120 1180 1011 1100 11722011 W10006 Delta Grow 5000 1012 1129 1206 1012 1074 11912011 W11006 Delta Grow 7500 1013 1088 1213 1013 1086 11772011 W11007 Delta Grow 7900 1014 1140 1188 1014 1140 11902011 W10008 Delta Grow 8300 1015 1101 1157 1015 1106 11762011 W10009 Dyna-Gro 9012 1016 1135 1159 1016 1119 11532011 W11008 Dyna-Gro 9053 1017 1100 1199 1017 1073 11582011 W11009 Dyna-Gro 9171 1018 1083 1169 1018 1116 12082011 W09010 Dyna-Gro 9922 1019 1126 1154 1019 1097 11852011 W08016 Dyna-Gro Shirley 1020 1103 1197 1020 1134 12122011 W06021 MO Bess 1021 1138 1146 1021 1122 11552011 W08006 MO Milton 1022 1081 1150 1022 1079 11792011 W04026 MO Truman 1023 1124 1174 1023 1138 12022011 W10012 NC Exp. Yadkin 1024 1118 1195 1024 1088 11752011 W10014 OH Malabar 1025 1108 1215 1025 1091 11892011 W09018 Pioneer 25R32 1026 1134 1211 1026 1114 12002011 W04028 Pioneer 26R15 1027 1111 1161 1027 1101 11862011 W09017 Pioneer 26R20 1028 1095 1151 1028 1104 11472011 W05019 Pioneer 26R22 1029 1127 1209 1029 1092 12092011 W11010 Pioneer XW09H 1030 1130 1203 1030 1089 11782011 W08008 Progeny 117 1031 1114 1145 1031 1125 11652011 W05021 Progeny 125 1032 1125 1163 1032 1110 12072011 W03011 Progeny 166 1033 1075 1210 1033 1080 11842011 W05022 Progeny 185 1034 1084 1214 1034 1078 12132011 W11011 Progeny PGX10-2 1035 1090 1164 1035 1096 12062011 W11012 Progeny PGX10-5 1036 1106 1153 1036 1118 11822011 W11013 Progeny PGX10-7 1037 1086 1201 1037 1093 11612011 W06001 Syngenta Branson 1038 1143 1193 1038 1144 11622011 W09002 Syngenta Oakes 1039 1116 1184 1039 1083 11742011 W10003 Syngenta SY 9978 1040 1099 1185 1040 1131 12102011 W10001 Syngenta W1104 1041 1092 1149 1041 1128 11932011 W10017 Terral LA821 1042 1085 1216 1042 1094 11512011 W10015 Terral TV8558 1043 1133 1152 1043 1108 11602011 W10016 Terral TV8589 1044 1077 1207 1044 1107 11882011 W10018 Terral TV8861 1045 1128 1166 1045 1095 11522011 W11018 Terral TVX8460 1046 1121 1205 1046 1130 11492011 W11021 Terral TVX8525 1047 1098 1148 1047 1133 11732011 W11019 Terral TVX8535 1048 1096 1171 1048 1075 11672011 W11020 Terral TVX8626 1049 1113 1181 1049 1098 11662011 W11022 Terral TVX8848 1050 1117 1155 1050 1084 11702011 W11014 TN Exp. TN 1002 1051 1139 1189 1051 1142 11832011 W11015 TN Exp. TN 1101 1052 1132 1178 1052 1123 12112011 W11016 TN Exp. TN 1102 1053 1078 1194 1053 1127 11562011 W11017 TN Exp. TN 1103 1054 1136 1212 1054 1117 11542011 W10020 TN Exp. TN 902 1055 1119 1173 1055 1076 11502011 W09013 USG 3120 1056 1107 1170 1056 1143 11712011 W10022 USG 3201 1057 1082 1202 1057 1102 11982011 W00015 USG 3209 1058 1074 1176 1058 1132 12162011 W10023 USG 3251 1059 1109 1208 1059 1090 11952011 W06016 USG 3295 1060 1087 1182 1060 1135 11872011 W11023 USG 3345 1061 1094 1172 1061 1137 11802011 W03014 USG 3350 1062 1091 1198 1062 1113 11462011 W09023 USG 3409 1063 1079 1187 1063 1129 11642011 W10024 USG 3438 1064 1122 1183 1064 1081 11922011 W08013 USG 3555 1065 1142 1192 1065 1099 12142011 W09024 USG 3770 1066 1076 1162 1066 1139 12042011 W07024 VA Jamestown 1067 1089 1156 1067 1136 11942011 W09026 VA Merl 1068 1131 1196 1068 1077 11632011 W11024 VA Exp. VA05W-139 1069 1093 1179 1069 1082 12012011 W11025 VA Exp. VA05W-251 1070 1115 1177 1070 1112 12032011 W08019 Warren Seed McKay 100 1071 1073 1175 1071 1115 11482011 W11026 Warren Seed McKenna 200 1072 1097 1167 1072 1109 1197
ReplicationReplicationHighland Rim REC, SpringfieldEast TN REC, Knoxville
WHEAT VARIETY TEST, 2011 East TN Research & Education Center, Knoxville
1193 1194 1195 1196 1197 1198 1199 1200 1201 1202 1203 1204 1205 1206 1207 1208 1209 1210 1211 1212 1213 1214 1215 1216
1192 1191 1190 1189 1188 1187 1186 1185 1184 1183 1182 1181 1180 1179 1178 1177 1176 1175 1174 1173 1172 1171 1170 1169 Rep 3 9 incomplete blocks
1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 8 entries per block
1144 1143 1142 1141 1140 1139 1138 1137 1136 1135 1134 1133 1132 1131 1130 1129 1128 1127 1126 1125 1124 1123 1122 1121
1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 Rep 2 9 incomplete blocks
1096 1095 1094 1093 1092 1091 1090 1089 1088 1087 1086 1085 1084 1083 1082 1081 1080 1079 1078 1077 1076 1075 1074 1073 8 entries per block
1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072
1048 1047 1046 1045 1044 1043 1042 1041 1040 1039 1038 1037 1036 1035 1034 1033 1032 1031 1030 1029 1028 1027 1026 1025 Rep 1 9 incomplete blocks
1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 8 entries per block
8 varieties/block216 plots 27 blocks total (incomplete)72 Wheat Varieties 3 reps
9 Range Field Layout
WHEAT VARIETY TEST, 2011 Highland Rim Research & Education Center, Springfield
1216 1215 1214 1213 1212 1211 1210 1209 1208 1207 1206 1205 1204 1203 1202 1201 1200 1199 1198 1197 1196 1195 1194 1193 1192 1191 1190 1189 1188 1187 1186 1185 1184 1183 1182 1181 Rep 3
1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180
1144 1143 1142 1141 1140 1139 1138 1137 1136 1135 1134 1133 1132 1131 1130 1129 1128 1127 1126 1125 1124 1123 1122 1121 1120 1119 1118 1117 1116 1115 1114 1113 1112 1111 1110 1109 Rep 2
1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108
1072 1071 1070 1069 1068 1067 1066 1065 1064 1063 1062 1061 1060 1059 1058 1057 1056 1055 1054 1053 1052 1051 1050 1049 1048 1047 1046 1045 1044 1043 1042 1041 1040 1039 1038 1037 Rep 1
1001 1002 1003 1004 1005 1006 1007 1008 1009 1010 1011 1012 1013 1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036
8 varieties/block72 Wheat Varieties 3 reps 216 plots 27 blocks total (incomplete)
6 Range Field Layout
SAS CODE FOR ANALYSES KNOXVILLE DATA USING REPS AND NOT INCOMPLETE BLOCKS: . . PROC GLM DATA = KPSF; CLASS ENTRY REP; MODEL YLD=ENTRY REP; LSMEANS ENTRY/NOPRINT OUT=KYIELD; . . KNOXVILLE DATA USING INCOMPLETE BLOCKS INSTEAD OF REPS: . . PROC GLM DATA = KPSF; CLASS ENTRY BLOCK; MODEL YLD=ENTRY BLOCK; LSMEANS ENTRY/NOPRINT OUT=KYIELD; . . HIGHLAND RIM REC DATA: . . PROC GLM DATA=HRES; CLASS ENTRY BLOCK; *CLASS ENTRY REP; MODEL YLD=ENTRY BLOCK; *MODEL YLD=ENTRY REP; LSMEANS ENTRY/NOPRINT OUT=HYIELD; . . ANALYZING DATA ACROSS ALL LOCATIONS: . . PROC GLM DATA = AllLocs; CLASS ENTRY LOC BLOCK; *CLASS ENTRY LOC REP;
MODEL YLD=ENTRY LOC ENTRY*LOC BLOCK(LOC); *MODEL YLD=ENTRY LOC ENTRY*LOC REP(LOC); LSMEANS ENTRY/NOPRINT OUT=ALLYIELD;
. .
R-Square Coeff Var Root MSE KYLD Mean 0.765634 9.632272 7.662594 79.55127 Source DF Type III SS Mean Square F Value Pr > F ENTRY 71 23465.43460 330.49908 5.63 <.0001 REP 2 169.55500 84.77750 1.44 0.2400
R-Square Coeff Var Root MSE KYLD Mean 0.837789 8.887394 7.070034 79.55127 Source DF Type III SS Mean Square F Value Pr > F ENTRY 71 19240.73493 270.99627 5.42 <.0001 BLOCK 25 2393.00463 95.72019 1.91 0.0127
ANALYSIS OF HRREC USING REPS
ANALYSIS OF HRREC USING BLOCKS
R-Square Coeff Var Root MSE HRYLD Mean 0.512448 13.54781 8.804762 64.99028 Source DF Type III SS Mean Square F Value Pr > F ENTRY 71 9472.629583 133.417318 1.72 0.0032 REP 2 2097.895833 1048.947917 13.53 <.0001
R-Square Coeff Var Root MSE HRYLD Mean 0.826767 8.858842 5.757386 64.99028 Source DF Type III SS Mean Square F Value Pr > F ENTRY 71 6493.262354 91.454399 2.76 <.0001 BLOCK 26 9194.876104 353.649081 10.67 <.0001
ANALYSIS OF ETREC USING REPS
ANALYSIS OF ETREC USING BLOCKS
R-Square Coeff Var Root MSE YLD Mean 0.801021 11.53415 8.050194 69.79444 Source DF Type III SS Mean Square F Value Pr > F ENTRY 71 38593.0417 543.5640 8.39 <.0001 LOC 6 132165.9392 22027.6565 339.90 <.0001 ENTRY*LOC 426 57356.9635 134.6408 2.08 <.0001 REP(LOC) 14 14465.0627 1033.2188 15.94 <.0001
R-Square Coeff Var Root MSE YLD Mean 0.874957 10.08522 7.038922 69.79444 Source DF Type III SS Mean Square F Value Pr > F ENTRY 71 31872.1936 448.9041 9.06 <.0001 LOC 6 130305.2674 21717.5446 438.33 <.0001 ENTRY*LOC 426 45824.2173 107.5686 2.17 <.0001 BLOCK(LOC) 181 37052.4458 204.7096 4.13 <.0001
ANALYSIS ACROSS ALL 7 LOCS USING BLOCKS
ANALYSIS ACROSS ALL 7 LOCS USING REPS
Avg. Yield± Std Err. Knoxville Springfield
Brand Variety (n=7)‡ 10/19/10 § 10/28/10 --------------------------------------------------------------bu/a--------------------------------------------------------------
Pioneer 26R10 80 ± 2 107 73Terral TV8861 79 ± 2 91 79Progeny 357 78 ± 2 86 76Terral TV8848 78 ± 2 89 66Pioneer 26R15 78 ± 2 90 73Cache River Valley Seed Dixie McAlister 78 ± 2 95 74USG 3251 77 ± 2 91 65Dyna-Gro 9171 77 ± 2 91 72Progeny 870 76 ± 2 93 68Delta Grow 7500 76 ± 2 86 66Cache River Valley Seed Dixie Kelsey 76 ± 2 86 63Terral TV8626 76 ± 2 84 71Dyna-Gro Shirley 76 ± 2 95 70Croplan Genetics 8302 75 ± 2 90 65TN Exp. TN 1102 75 ± 2 83 73Dyna-Gro 9053 74 ± 2 84 71Dyna-Gro 9922 74 ± 2 81 63USG 3770 73 ± 2 79 67Syngenta SY 9978 73 ± 2 55 75Pioneer 26R22 73 ± 2 84 75Armor Ricochet 73 ± 2 84 70MO Milton 73 ± 2 87 62TN Exp. TN 902 72 ± 2 77 74Pioneer 26R20 72 ± 2 77 73VA Exp. VA05W-251 72 ± 2 85 62USG 3438 72 ± 2 83 67Dyna-Gro 9012 72 ± 2 86 59USG 3201 72 ± 2 77 67Terral TV8535 71 ± 2 89 59Warren Seed McKenna 200 71 ± 2 84 64Syngenta W1104 71 ± 2 78 66USG 3555 71 ± 2 90 65Terral TV8589 70 ± 2 68 72Armor Renegade 70 ± 2 80 63
Avg. Yield± Std Err. Knoxville Springfield
Brand Variety (n=7)‡ 10/19/10 § 10/28/10 --------------------------------------------------------------bu/a--------------------------------------------------------------
Pioneer 26R10 81 ± 2 105 75Pioneer 26R15 79 ± 2 91 78Cache River Valley Seed Dixie McAlister 79 ± 2 99 74Progeny PGX10-5 78 ± 2 95 78Delta Grow 7500 78 ± 2 91 74Progeny PGX10-7 78 ± 2 94 73Dyna-Gro 9171 78 ± 2 93 76Terral TV8861 77 ± 2 94 70Cache River Valley Seed Dixie Kelsey 77 ± 2 90 62Terral TVX8848 77 ± 2 86 64USG 3251 77 ± 2 87 58Armor Ricochet 77 ± 2 87 80Croplan Genetics 8302 75 ± 2 91 62Dyna-Gro Shirley 75 ± 2 88 69Terral TVX8626 74 ± 2 82 66USG 3438 73 ± 2 86 69Dyna-Gro 9922 73 ± 2 80 67Pioneer 26R22 73 ± 2 86 70MO Milton 73 ± 2 89 69USG 3201 73 ± 2 85 64Dyna-Gro 9012 73 ± 2 85 62TN Exp. TN 1102 73 ± 2 80 66Syngenta SY 9978 72 ± 2 54 76VA Exp. VA05W-251 72 ± 2 85 66Armor ARX 0186 72 ± 2 89 72Warren Seed McKenna 200 72 ± 2 82 66USG 3770 72 ± 2 79 65Pioneer 26R20 72 ± 2 77 70Terral TVX8535 72 ± 2 91 57Terral TV8589 72 ± 2 65 79Dyna-Gro 9053 71 ± 2 77 71Syngenta W1104 71 ± 2 79 62Armor Renegade 71 ± 2 82 61Pioneer 25R32 71 ± 2 78 69
PARTIAL SUMMARY OF VARIETY MEANS ACROSS LOCS AND FOR THE TWO LOC EXAMPLES
* CHANGE IN VALUE OF MEANS * CHANGE IN RANKS
ANALYZED BY REPS ANALYZED BY BLOCKS
MEDIUM CORN HYBRID YIELD TEST, 2011 East TN Research & Education Center, Knoxville
56 Corn Hybrids 3 reps 168 plots 21 blocks (incomplete) 8 entries per block
8168 8167 8166 8165 8164 8163 8162 8161 8160 8159 8158 8157 8156 8155
8141 8142 8143 8144 8145 8146 8147 8148 8149 8150 8151 8152 8153 8154 Rep 3 7 incomplete blocks
8140 8139 8138 8137 8136 8135 8134 8133 8132 8131 8130 8129 8128 8127 8 entries/block
8113 8114 8115 8116 8117 8118 8119 8120 8121 8122 8123 8124 8125 8126
8112 8111 8110 8109 8108 8107 8106 8105 8104 8103 8102 8101 8100 8099
8085 8086 8087 8088 8089 8090 8091 8092 8093 8094 8095 8096 8097 8098 Rep 2 7 incomplete blocks
8084 8083 8082 8081 8080 8079 8078 8077 8076 8075 8074 8073 8072 8071 8 entries/block
8057 8058 8059 8060 8061 8062 8063 8064 8065 8066 8067 8068 8069 8070
8056 8055 8054 8053 8052 8051 8050 8049 8048 8047 8046 8045 8044 8043
8029 8030 8031 8032 8033 8034 8035 8036 8037 8038 8039 8040 8041 8042 Rep 1 7 incomplete blocks
8028 8027 8026 8025 8024 8023 8022 8021 8020 8019 8018 8017 8016 8015 8 entries/block
8001 8002 8003 8004 8005 8006 8007 8008 8009 8010 8011 8012 8013 8014
CORN EXAMPLE SHOWING DIFFERENT # ENTRIES PER BLOCK
MEDIUM CORN HYBRID YIELD TEST, 2011 East TN Research & Education Center, Knoxville
56 Corn Hybrids 3 reps 168 plots 12 blocks (incomplete) 14 entries per block
8168 8167 8166 8165 8164 8163 8162 8161 8160 8159 8158 8157 8156 8155
8141 8142 8143 8144 8145 8146 8147 8148 8149 8150 8151 8152 8153 8154 Rep 3 4 incomplete blocks
8140 8139 8138 8137 8136 8135 8134 8133 8132 8131 8130 8129 8128 8127 14 entries/block
8113 8114 8115 8116 8117 8118 8119 8120 8121 8122 8123 8124 8125 8126
8112 8111 8110 8109 8108 8107 8106 8105 8104 8103 8102 8101 8100 8099
8085 8086 8087 8088 8089 8090 8091 8092 8093 8094 8095 8096 8097 8098 Rep 2 4 incomplete blocks
8084 8083 8082 8081 8080 8079 8078 8077 8076 8075 8074 8073 8072 8071 14 entries/block
8057 8058 8059 8060 8061 8062 8063 8064 8065 8066 8067 8068 8069 8070
8056 8055 8054 8053 8052 8051 8050 8049 8048 8047 8046 8045 8044 8043
8029 8030 8031 8032 8033 8034 8035 8036 8037 8038 8039 8040 8041 8042 Rep 1 4 incomplete blocks
8028 8027 8026 8025 8024 8023 8022 8021 8020 8019 8018 8017 8016 8015 14 entries/block
8001 8002 8003 8004 8005 8006 8007 8008 8009 8010 8011 8012 8013 8014
14 ENTRIES PER BLOCK
R-Square Coeff Var Root MSE KYLD 8B Mean 0.699923 9.897155 16.63969 168.1260 Source DF Type III SS Mean Square F Value Pr > F ENTRY 55 37386.04142 679.74621 2.46 0.0001 BLOCK 20 12796.14062 639.80703 2.31 0.0043
R-Square Coeff Var Root MSE YLD 14B Mean 0.691276 9.535078 16.03095 168.1260 Source DF Type III SS Mean Square F Value Pr > F ENTRY 55 38546.21035 700.84019 2.73 <.0001 BLOCK 11 12133.93493 1103.08499 4.29 <.0001
ANALYSIS USING 8 VARIETIES PER BLOCK
ANALYSIS USING 14 VARIETIES PER BLOCK
