Volume 65 Number 1 Article 1 Pages: 2-16
Year 2011 Month 1
Title: Design of Field Experiments: Influence of Treatment Response Relative to Standard Deviation and Blocking Factor Characteristics on Efficient Blocking Strategy
Authors: E. Stover and K. Portier
Citation
Abstract:
Selection of experimental design can markedly influence efficiency of field research.
This study used Monte
Carlo simulations to compare the ability of different field experimental designs to distinguish defined treatment
differences, and the paper concludes with a section on practical use of the information obtained.
In each simulation,
a single experimental treatment was compared to a control treatment and each treatment was applied to
twelve trees representing similar research effort.
Experimental designs compared were twelve blocks with a single
tree per treatment, six blocks of two trees per treatment, four blocks of three trees per treatment, and two blocks
with six trees per treatment.
In each case, analyses were compared in which data were collected with single tree
experimental units (multiple trees independently assigned the same treatment within each block) or as is often
done with spatial blocking, data were pooled on a group of trees (one data point per multiple tree experimental
unit). Trees were blocked according to a specified factor, which was quantified for these comparisons but could
represent a qualitative factor such as spatial position.
The probability of rejecting the null hypothesis was computed
for a range of situations including small and large values for the following parameters: treatment response,
standard deviations of the response, blocking factor effects, and blocking factor standard deviations.
In all cases,
the probability of rejecting a false null hypothesis was significantly greater when data were collected on singletree
experimental units, and decreased as the number of trees pooled per data point increased (and number of
blocks decreased). When data were collected on single-tree experimental units and the factor used for blocking
actually had no relationship to the response variable, all four designs had similar probabilities of rejecting the null
hypothesis; however, power decreased with increasing block size (more trees per block but fewer blocks) when
the blocking factor was significantly correlated with the response variable but treatment did not change the slope
of the blocking factor vs. response variable.
When the blocking factor effect was significant and there was a significant
treatment-by-block interaction, use of a single tree per treatment per block had the least power, but power
decreased substantially with block size greater than two trees per treatment.
In the last case, failing to account
for block by treatment interaction effects resulted in test statistics having little power to reject the null hypothesis
even when treatment effects were strong.
These analyses indicate that use of one or two trees per treatment per
block with data collected on individual-tree experimental units provides the greatest efficiency in distinguishing
treatment effects, and that two trees per treatment per block is superior when there is a significant treatment-byblocking
factor interaction.
When the blocking factor displayed a distinct spatial trend, incorrectly using individual
tree data from multi-tree experimental units as pseudo-replicates resulted in false rejections of the null hypothesis
well beyond the specified α=0.05, sometimes approaching P=0.50. Researchers are cautioned that proper analysis
of multi-tree experimental units yields the same F-test using individual subsample data or single mean values
representing each collective experimental unit.
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