Control of Experimental Error. Blocking - A block is a group of homogeneous experimental units Maximize the variation among blocks in order to minimize the variation within blocks Reasons for blocking To remove block to block variation from the experimental error (increase precision)
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Just replication
Blocking
Other ways to minimize variation within blocks:
Source df SS MS F
Total rt-1 SSTot =
Block r-1 SSB = MSB = MSB/MSE
SSB/(r-1)
Treatment t-1 SST = MST = MST/MSE
SST/(t-1)
Error (r-1)(t-1) SSE = MSE =
SSTot-SSB-SSTSSE/(r-1)(t-1)
MSE is the divisor for all F ratios
Standard Error of a treatment mean
Confidence interval estimate
Standard Error of a difference
Confidence interval estimate on a difference
t to test difference between two means
Source(NH4)2SO4NH4NO3CO(NH2)2Ca(NO3)2NaNO3Control
Mean36.2532.3829.4231.0230.7025.35
Sourcedf SSMSF
Total23 492.36
Soils (Block)3192.5664.1921.61**
Fertilizer (Trt)5255.2851.0617.19**
Error1544.52 2.97
Standard error of a treatment mean = 0.86CV = 5.6%
Standard error of a difference between two treatment means = 1.22
Confidence Interval Estimates
34.4130.5429.1928.86 27.5923.51
36.2532.3831.0230.7029.4225.35
38.0934.2132.8632.5431.2627.19
Full Irrigation
Irrigated Pre-Plant
No Irrigation
Yij = ( rBi + tTj - G)/[(r-1)(t-1)]
^
Yij = ( rBi + tTj - G)/[(r-1)(t-1)]
RE = [(r-1)MSB + r(t-1)MSE]/(rt-1)MSE
Estimated Error for a CRD
Observed Error for RBD