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ANOVA Diagnostics Start     

D2. Do this Verify that you have no block*treatment interaction

Block InteractionIn experimental designs with a blocking factor, the test for treatment differences is based on an error term involving block by treatment interactions. This error variation can occur due to random noise, or due to real interactions between the blocks and treatments, such that in some blocks the ranking of treatments, or differences among them, changes. The latter variation will increase the size of the error term, making treatment tests unable to pick up differences (loss of power).

The %MMAOV macro calculates a test for these interactions, the Tukey's Single DF Test for Additivity, and produces two plots to allow visual assessment of interactions. Both plots give the same information, use the one that is easier to interpret (usually the one with fewer lines in the graph). One displays how blocks change across treatment combinations, the other displays how treatments change across blocks.

A typical example is shown here (click plots to see full sized versions).

The Tukey test is printed as a title for the graph. Here the P-value is >0.05, leading to acceptance of Ho:, and concluding that true block by treatment interactions do not exist. As usual with diagnostic tests, this test is too sensitive, will reject Ho: too often, so visual examination of the plots is essential when p<0.05. See if the lines in the graph are "close" to parallel. Parallel responses indicate no interactions, as the rankings do not change.

In the bottom Tukey Test plot, responses look reasonably parallel, with one exception. Treatment combination 1 shows a dramatic increase between years 2000 and 2001, quite different from the other treatments.

Based on these diagnostic results, there appears to be no great concern that block by treatment interactions are increasing the error term. However, you might consider a scientific examination of treatment combination 1 data in 2000, why were measured values much lower than expected?

In general, if block by treatment interactions are found, the following approaches can be used to correct the problem.

  • Re-examine data for outliers. Even if outliers were not found in the standard diagnostics, look at all data for unusual block-treatment conditions to verify they are scientifically valid.
  • Consider if data for the entire treatment should be deleted from this block, and the analysis rerun.
  • Consider if the entire block, including all treatment data, should be discarded from the analysis. If this block is behaving differently, do you want your conclusions altered by an unusual block?
  • Transformations may correct block*treatment interaction, so that is another option (see Step F).
If you have a larger experiment, and several blocks showed the low response in treatment combination 1, you could analyze those blocks separately. Basically divide the data into groups of blocks that behave consistently, and analyze each group separately.

next >> ( Return to Step D )

  H I N T S :
  Values in the plot are coded. The codes are translated in a table printed on the SAS output page following the graphs.
  Decisions about deleting data are also discussed in Step A. This also tells you how to rerun the analysis.

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