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United States Department of Agriculture

Agricultural Research Service

Research Project: GENETIC IMPROVEMENT OF CITRUS

Location: Subtropical Insects and Horticulture Research

Title: Design of field experiments: Influence of treatment response relative to standard deviation and blocking factor characteristics on efficient blocking strategy

Authors
item Stover, Ed
item Portier, Kenneth -

Submitted to: Journal of American Pomological Society
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: July 1, 2010
Publication Date: January 1, 2011
Citation: Stover, E., Portier, K. 2011. Design of field experiments: Influence of treatment response relative to standard deviation and blocking factor characteristics on efficient blocking strategy. Journal of American Pomological Society. 65:2-16.

Interpretive Summary: The design of a field experiment can greatly affect the outcome of field research. This study used computer simulations to compare the ability of different field experimental designs to properly identify defined treatment differences, and the paper concludes with a section on practical use of the information obtained. In each comparison, a single experimental treatment, of defined effect and variability, was compared to a control treatment and each treatment was applied to twelve hypothetical trees. 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 all cases, the probability of correctly finding the treatment differencewas significantly greater when data were collected on single-trees, and decreased as the number of trees pooled per data point increased (and number of blocks decreased). When the blocking factor effect (ability to sort out differences between trees prior to the experiment and spread these differences carefully across treatments) was significant and there was a significant treatment by block interaction, use of a single tree per treatment per block had the least ability to show real differences, but more than two trees per block again were less effective than two. 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 demonstrating treatment effects, and that two trees per treatment per block is best when there is a significant treatment-by-blocking factor interaction. When the blocking factor displayed a distinct spatial trend (e.g. such as bigger trees as you move down a row), incorrectly using individual tree data from multi-tree experimental units resulted in finding treatment effects to be real even when they aren't. Researchers are cautioned on proper analysis of multi-tree experimental units to avoid misleading results.

Technical 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 single-tree 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-by-blocking 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 a=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.

Last Modified: 10/1/2014
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