TREND ANALYSISDEVELOPED BY KIRK ET AL. 1980.

J.AM.SOC.HORT. SCI. STATISTICAL PROCEDURE TO ACCOUNT

FOR SPATIAL VARIBILITYEACH PLOT IS IDENTIFIED BY ROW AND

COLUMN TO FORM A GRID

TREND ANALYSISBACKGROUND VARIATION IS ACCOUNTED

FOR BY FITTING A POLYNOMIAL SURFACE MODEL ON THE GRID

RESIDUAL VALUES FOR EACH PLOT IS CALCULATED BY SUBTRACTING THE ENTRY MEAN FROM THE PLOT VALUE

THE PROGRAM EVALUATES POSSIBLE RESPONSE SURFACE MODELS

TREND ANALYSISTHE MODEL APPROXIMATES THE PATTERN

OF RESIDUAL VALUES IN THE EXPERIMENT

FROM THE POSSIBLE MODELS, ‘F’ TESTS ARE USED TO SELECT THE MODEL DESIRED

THE NUMBER OF TERMS IN THE MODEL IS RESTRICTED AS WELL AS THE SIGNIFICANCE LEVEL OF THE ‘F’ TEST

TREND ANALYSISADJUSTED ENTRY MEANS ARE

COMPUTED BASED ON THE SURFACE MODEL, I.E. PLOT VALUES IDENTIFIED WITH POSITIVE RESIDUAL VALUES ARE ADJUSTED DOWNWARD AND VICE VERSA

THE ADJUSTED ENTRY SUM OF SQUARES IS USED IN THE ANOVA

THE SS ASSOCIATED WITH THE SURFACE MODEL IS SUBTRACTED FROM THE TOTAL IN LIEU OF REPS OR BLOCKS

NECESSARY DATA INPUTS SAME AS WITH RCBD PLUS ROW NUMBER

AND COLUMN NUMBER BUT NO REP NUMBER

YOU CANNOT HAVE MISSING VALUES

RELATIVE EFFICIENCYFLUE-CURED TOBACCO = 97 TO 161%COTTON = 126 TO 130 % CORN =110 TO 147%

RCB TREND

SOURCE

df MS F SOURCE

df MS F

TOTAL 131 TOTAL 131

REP 2 2600 38.8* MODEL

5 1482 34.6**

ENTRY 43 90 1.4 ENTRY 43 90 2.1**

ENTRY ADJ.

43 105 2.4**

ERROR 86 67 ERROR 83 43

REQUIREMENTS FOR THE PC64 BIT COMPUTER

Trend Analysis -- 2011 Soybean Data------------------------------------------------ test=C Maturity=5 sub_mat=E Loc=1 ------------------------------------------------- ANALYSIS OF VARIANCE FOR THE DEPENDENT VARIABLE Yield SOURCE DF SUM OF SQUARES MEAN SQUARES CORR. TOTAL 99 10468.867931 Entry 19 7070.562003 372.13484229 RESIDUAL 80 3398.305928 42.47882409 F I T T I N G O F T H E R E S P O N S E S U R F A C E M O D E L NUMBER TERMS TERMS IN THE RESPONSE SURFACE MODEL RESULTING IN MINIMUM ERROR S S EMS R SQUARE 1 T1 33.90620951 .2118 2 R1 T1 30.83918790 .2922 3 R1 T1 R1T1 30.48219817 .3093 4 R1 T1 T2 R1T1 30.42357068 .3196 5 R1 R2 R3 R4 T1 28.33027323 .3748 6 R1 R2 R3 R4 T1 R3T1 27.83401422 .3939 7 R1 R2 R3 R4 R5 T1 R5T1 26.80253232 .4242 8 R1 R2 R3 R4 T1 T2 T3 R3T3 26.09494714 .4471

S E L E C T I O N O F T H E R E S P O N S E S U R F A C E M O D E L NUMBER ERROR ERROR MALLOWS REGRESSION REDUCTION TERMS DF SUM OF SQUARES MEAN SQUARES C(P) SUM OF SQUARES SUM OF SQUARES F VALUE PROB>F 1 79 2678.59055090 33.90620951 24.6479 719.71537668 719.71537668 27.581 .0001 2 78 2405.45665606 30.83918790 16.1809 992.84927153 273.13389484 10.467 .0018 3 77 2347.12925880 30.48219817 15.9457 1051.17666879 58.32739726 2.235 .1393 4 76 2312.19137147 30.42357068 16.6069 1086.11455611 34.93788732 1.339 .2511 5 75 2124.77049222 28.33027323 11.4246 1273.53543537 187.42087926 7.182 .0091 6 74 2059.71705251 27.83401422 10.9316 1338.58887508 65.05343971 2.493 .1187 7 73 1956.58485909 26.80253232 8.9795 1441.72106849 103.13219341 3.952 .0506 8 72 1878.83619410 26.09494714 8.0000 1519.46973348 77.74866499 2.979 .0886

SELECTED RESPONSE SURFACE MODEL SOURCE REGRESSION COEFF. SEQUENTIAL SS F VALUE PROB>F PARTIAL SS F VALUE PROB>F R1 .29137414 273.13389484 9.641 .0027 259.85848935 9.172 .0034 R2 -.00907770 6.11188122 .216 .6437 5.85148544 .207 .6508 R3 -.00030772 .06952623 .002 .9606 .16961231 .006 .9385 R4 -.00241547 274.50475639 9.689 .0026 274.50475639 9.689 .0026 T1 1.89699153 719.71537668 25.404 .0001 719.71537668 25.404 .0001

ANALYSIS OF VARIANCE FOR THE DEPENDENT VARIABLE Yield SOURCE DF SUM OF SQUARES MEAN SQUARES F VALUE PROB>F CORRECTED TOTAL 99 10468.8679310 Entry 19 7070.5620035 372.134842287 13.136 .0001 Entry (ADJUSTED) 19 7125.8865777 375.046661985 13.238 .0001 RESPONSE SURFACE 5 1273.5354354 254.707087073 8.991 .0001 ERROR 75 2124.7704922 28.330273230

Trend Analysis -- 2011 Soybean Data------------------------------------------------ test=C Maturity=5 sub_mat=E Loc=1 ------------------------------------------------- Entry MEANS FOR THE DEPENDENT VARIABLE Yield STANDARD ERROR Entry N MEANS ADJUSTED MEANS ADJUSTED MEANS 1 5 33.62148837 33.19709438 2.45950163 2 5 30.32825860 30.88234073 2.43008296 3 5 32.07842791 31.35763996 2.39875927 4 5 37.11608372 36.52581785 2.42301395 5 5 32.16516279 32.71897014 2.41574955 6 5 27.78083163 28.54246979 2.41569698 7 5 34.57791628 34.11451191 2.39606000 8 5 25.56334884 24.82098523 2.42005300 9 5 34.62925395 33.89677237 2.43625464 10 5 37.34253209 36.80177860 2.38884488 11 5 50.35323349 50.42916210 2.40164258 12 5 29.26856930 28.67307975 2.41150717 13 5 51.83604837 53.31078266 2.43422675 14 5 38.27329116 38.96011661 2.42292970 15 5 41.28029581 41.95464001 2.40185216 16 5 25.21746419 24.84757882 2.39570485 17 5 49.50827163 48.93608695 2.40456920 18 5 48.69941023 48.55953267 2.55227254 19 5 49.84782698 49.52107078 2.40360897 20 5 40.59133953 42.02862359 2.41295470

MULTIPLE COMPARISONS OF THE ADJUSTED MEANS USING THE BAYESIAN K-RATIO T TEST Entry N ADJUSTED MEANS 8 5 24.82098523 | 16 5 24.84757882 | | 6 5 28.54246979 | | | 12 5 28.67307975 | | | | 2 5 30.88234073 | | | 3 5 31.35763996 | | | | 5 5 32.71897014 | | | | | 1 5 33.19709438 | | | | | | 9 5 33.89677237 | | | | | | | 7 5 34.11451191 | | | | | | 4 5 36.52581785 | | | | | | 10 5 36.80177860 | | | | | | 14 5 38.96011661 | | | | | 15 5 41.95464001 | | | 20 5 42.02862359 | | | 18 5 48.55953267 | 17 5 48.93608695 | | 19 5 49.52107078 | | | 11 5 50.42916210 | | | | 13 5 53.31078266 | | | | BAYESIAN K - RATIO T VALUE USED: 1.576

CONCLUSIONSNEED 64 BIT COMPUTERPROVEN SPATIAL ANALYSIS WITH

REMARKABLE EFFICIENCIESNECESSARY TO HAVE NO MISSING PLOTSNEEDS AT LEAST 80 PLOTS TO BE

EFFICIENT