Comprehensive information on Nitrogen Use Efficiency for cereal crop production, N use Efficiency

 

Research Methods in Agriculture

RCBD vs CRD

Split Plot (Tillage)

Contrasts (orthogonal contrast coefficients)
Contrasts for Unequal Treatment Spacing

Treatment N rate Tillage
  lb/ac  
1 0 zero
2 50 zero
3 100 zero
4 150 zero
5 0 conv
6 50 conv
7 100 conv
8 150 conv

 

CRD   CRD   RCBD   RCBD-(split)  
Source of variation df Source of variation df Source of variation df Source of variation df
Total (4*8)-1 31 Total (4*8)-1 31 Total (4*8)-1 31 Total (4*8)-1 31
        block 3 block 3
treatment 7 treatment 7 treatment 7 tillage 1
Tillage 1         block*tillage 3 (a)
Nrate 3         nrate 3
nrate*height 3         nrate*tillage 3
error 24 error 24 error 21 error 18 (b)

RCBD versus CRD

data one;
input rep nrate tillage yield preP;
cards;
1 0 0 20 16
1 50 0 25 13
1 100 0 29 9
1 150 0 35 8
1 0 1 35 18
1 50 1 35 6
1 100 1 38 9
1 150 1 39 19
2 0 0 20 22
2 50 0 26 23
2 100 0 30 28
2 150 0 32 25
2 0 1 36 4
2 50 1 36 8
2 100 1 37 6
2 150 1 40 7
3 0 0 17 8
3 50 0 22 19
3 100 0 25 48
3 150 0 29 22
3 0 1 29 23
3 50 1 34 25
3 100 1 38 24
3 150 1 40 18
proc print;
proc glm;
classes tillage nrate;
model yield = nrate tillage tillage*nrate/e3;
contrast 'Nrate_lin' nrate -3 -1 1 3;
contrast 'Nrate_quad' nrate 1 -1 -1 1;
contrast 'Nrate_cub' nrate -1 3 -3 1;
contrast 'tillage*nrate_lin' tillage*nrate -3 -1 1 3 3 1 -1 -3;
contrast 'tillage*nrate_quad' tillage*nrate 1 -1 -1 1 -1 1 1 -1;
means nrate tillage nrate*tillage;
run;
 
zero (1)       conv (-1)      
0 50 100 150 0 50 100 150
 
linear
-3 -1 1 3 3 1 -1 -3
quadratic
1 -1 -1 1 -1 1 1 -1

 

What if Tillage was a "SPLIT"?

Trt Tillage N Rate Till No-till
1 1 0 2 7 8 3
2 1 50 5 3 1 5 Rep 1
3 1 100 6 4 2 4
4 1 150 8 1 6 7
5 2 0
6 2 50 4 8 7 6
7 2 100 3 7 5 1 Rep 2
8 2 150 1 6 3 2
2 5 8 4
2 8 8 6
7 6 4 7 Rep 3
5 4 1 5
3 1 2 3

model yield = rep tillage rep*tillage nrate nrate*tillage;
test h = rep tillage e = rep*tillage;
means tillage nrate nrate*tillage;

Weaknesses of the split plot is the power in testing the difference in tillage because the rep*tillage must be used as the error term.
----------------------------------------------------------------------------------------------

Factorial Arrangement of Treatments    (xx factorial design xx  )
   Tillage 2   N Rates 4  Factorial Treatment Structure = 2 * 4 = 8 total treatments
   All levels of N Rates evaluated over all levels of Tillage
   Factorial treatment structure allows for testing the interaction between the two ( or nrate*tillage )
     ?  Did N rates respond the same for the two different tillage systems  ?
     ?  This is the value of the factorial treatment structure  ?  BUT....  does it use up too many treatments


  13 Treatments 13 Treatments
  4 Reps 3 Reps
Source of Variation df df
Total 52-1 = 51 39-1 = 38
Rep 4-1 = 3 3-1=2
Treatment 13-1 = 12 13-1=12
Error  51-3-12 = 37 38-2-12=24


If the World were 100 People?

6.7 % hold college degree's


Linear interaction

Contrast Program for Unequal Spacing

proc iml;
dens={0 100 600 1200}; **
p=orpol(dens);
t=nrow(p);
do i=1 to t;
  pr=abs(p[,i]);
  pr[rank(abs(p[,i]))]=abs(p[,i]);
  do j=t to 1 by -1;
    if pr[j] > 1.e-10 then scale=pr[j];
    if abs(p[j,i]) < 1.e-10 then p[j,i]=0;
  end;
  p[,i]=p[,i]/scale;
end;
print p;
run;

The only thing that needs to be changed is the trt values.

Output

Trt              P            lin              quad              cubic

0                1             -3.8           19.416667    -11

100           1             -3               1                    14.4

600           1             1                -40.66667     -4.4

1200         1             5.8             20.25             1

 

Experiment #222


data one;
input rep trt buac;
cards;

1 1 20.78765244
1 2 35.3777439
1 3 41.24329268
1 4 .
1 5 42.1839939
1 6 62.49207317
1 7 59.35640244
1 8 40.00746951
1 9 52.97439024
1 10 18.24222561
1 11 59.55929878
1 12 46.51859756
1 13 34.97195122
2 1 19.44115854
2 2 24.73490854
2 3 37.11158537
2 4 63.98612805
2 5 41.9257622
2 6 46.38948171
2 7 38.9929878
2 8 31.06158537
2 9 53.93353659
2 10 18.62957317
2 11 48.76890244
2 12 49.43292683
2 13 41.53841463
3 1 21.04588415
3 2 30.17621951
3 3 47.58841463
3 4 41.35
3 5 47.82820122
3 6 41.0035061
3 7 .
3 8 37.09314024
3 9 41.48307927
3 10 13.53871951
3 11 57.3089939
3 12 49.67271341
3 13 30.12088415
4 1 18.96158537
4 2 23.70198171
4 3 39.25121951
4 4 54.35777439
4 5 34.3632622
4 6 50.22606707
4 7 28.09192073
4 8 30.82179878
4 9 25.82317073
4 10 14.64542683
4 11 43.2722561
4 12 20.49253049
4 13 28.18414634
proc print;

proc
glm;
classes rep trt;
model buac = rep trt;
means trt;

run;
proc mixed; class rep trt;
model buac = trt/ddfm=satterth;
random rep;
lsmeans trt/diff;
run;

quit;

Experiment #502
data one;
input rep trt buac gn;
cards;

1 1 29.88109756 1.970387936
1 2 32.0945122 1.914626837
1 3 53.95198171 1.851969123
1 4 50.35518293 1.821092963
1 5 71.93597561 1.963828087
1 6 80.78963415 2.209946632
1 7 88.8132622 2.672821283
1 8 70.27591463 2.546777248
1 9 73.31935976 2.218581676
1 10 83.27972561 2.157410383
1 11 73.04268293 2.675846577
1 12 97.94359756 2.663606405
1 13 71.38262195 .
1 14 76.63948171 2.125741243
2 1 22.6875 1.89458847
2 2 39.56478659 1.776858568
2 3 44.26829268 1.875116944
2 4 73.59603659 2.396464348
2 5 69.9992378 1.872512221
2 6 98.77362805 2.288419008
2 7 84.93978659 2.727875233
2 8 74.14939024 2.210676908
2 9 90.47332317 2.218745947
2 10 97.11356707 2.209470749
2 11 87.15320122 2.309687138
2 12 97.66692073 2.404773235
2 13 77.74618902 2.741914749
2 14 95.73018293 2.243032694
3 1 32.0945122 1.838460803
3 2 38.7347561 1.839552999
3 3 63.08231707 1.93320477
3 4 74.42606707 1.997364521
3 5 73.31935976 2.284578085
3 6 91.85670732 2.508112431
3 7 85.76981707 2.434265614
3 8 91.58003049 2.200210571
3 9 72.48932927 2.121579409
3 10 96.00685976 2.188293457
3 11 86.87652439 0.002466053
3 12 78.57621951 2.470286846
3 13 71.93597561 3.035435438
3 14 88.25990854 2.087241888
4 1 36.79801829 1.906446576
4 2 48.14176829 2.077796221
4 3 57.54878049 1.905510187
4 4 72.7660061 2.263180017
4 5 87.70655488 2.21556139
4 6 85.49314024 2.750952721
4 7 93.79344512 2.628683805
4 8 81.89634146 2.195582151
4 9 93.79344512 2.303760767
4 10 89.08993902 2.525472641
4 11 89.64329268 2.401524544
4 12 100.1570122 2.290474653
4 13 68.33917683 2.729845285
4 14 96.00685976 2.053695917
proc print;
data two; set one;
gnuptake = (buac*60)*(gn/100);
proc glm data = two;
class rep trt;
model buac gn gnuptake = rep trt;
contrast '1-5 versus 6,7' trt 1 1 1 1 1 -2.5 -2.5 0 0 0 0 0 0 0;
contrast '1-5 versus 6,7' trt 1 1 1 1 1 -2.5 -2.5;
contrast '2-5 versus 6,7' trt 0 1 1 1 1 -2 -2;
means trt;
lsmeans trt;
run;