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→See also: Hierarchical linear modeling |
→Split-plot experimental examples: legible minus signs replacing stubby little hyphens |
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|Error (Subplot) = Rep*Temp*Current*Conc
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====Example: batch process====
Consider running the experiment under the second condition listed above (i.e., a batch process) for which four copper strips are placed in the solution at one time. A specified level of current can be applied to an individual strip within the solution. The same 16 treatment combinations (a replicated 2<sup>3</sup> factorial) are run as were run under the first scenario. However, the way in which the experiment is performed would be different. There are four treatment combinations of solution temperature and solution concentration: (
Running the experiment in this way also results in a split-plot design in which the whole-plot factors are now solution concentration and solution temperature, and the subplot factor is current.
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As can be seen from these three scenarios, one of the major differences in split-plot designs versus simple [[factorial design]]s is the number of different sizes of experimental units in the experiment. Split-plot designs have more than one size experimental unit, i.e., more than one error term. Since these designs involve different sizes of experimental units and different variances, the [[standard error]]s of the various mean comparisons involve one or more of the variances. Specifying the appropriate model for a split-plot design involves being able to identify each size of experimental unit. The way an experimental unit is defined relative to the design structure (for example, a [[completely randomized design]] versus a [[randomized complete block design]]) and the treatment structure (for example, a full 2<sup>3</sup> factorial, a resolution V half fraction, a two-way treatment structure with a [[control group]], etc.). As a result of having greater than one size experimental unit, the appropriate model used to analyze split-plot designs is a [[mixed model]].
If the data from an experiment are analyzed with only one error term used in the model, misleading and invalid conclusions can be drawn from the results.
==Strip-Plot Designs==
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