Hence we have treatment means and standard error


 Treatment A B C D
 Mean 306 421 537 559


Standard error of difference = 12.8

Example 4: Reblocking an on-farm experiment

Sometimes it may become clear on observing an experiment that the blocking should have been arranged
differently. It is then possible to redefine the blocking to match the pattern which is believed to correspond
to the real field variation. This should not be done lightly and particularly it is a dangerous procedure if
many alternative post-experiment blocking systems are tried, and the most successful one used, or if the re-
blocking is based on the numerical yield data rather than on practical assessment of the plot patterns.

The danger derives from the prospect that by trying too hard to define the correct re-blocking system the
estimate of the random plot variance, deduced from the error mean square, will be biased downwards. The
error mean square is, under normal randomization procedures, an unbiased estimate of the plot variability,
after allowing for block differences and treatment effects. It will underestimate the normally expected plot
variability if the form of analysis is pressured too much to make it small rather than appropriate. It is
possible to try too hard!

When we use a different blocking system from that intended in the original design specification it is very
likely that the treatments will not be complete in each block. In the example considered here the original
design was for five herbicide treatments in three randomized complete blocks. On inspecting the plot
Jonathan Woolley and I felt that there were clear patches running diagonally across the blocks. The
experimental plan was


Block 3 Plot 11 Plot 12 Plot 13 Plot 14 Plot 15
 TI T4 T3 T2 T5

Block 2 Plot 10 Plot 9 Plot 8 Plot 7 Plot 6
 T2 T5 T4 T3 TI

Block 1 Plot 1 Plot 2 Plot 3 Plot 4 Plot 5
 T5 TI T2 T4 T3


The patches perceived by us were approximately

 (1) plots 4,5,6,7,15;
 (2) plots 2,3,8,13,14;
 (3) plots 1,9,10,11,12.