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Split Block Designs

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What is a mixed or split plot design?

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A split-Plot design is a "blocked experiment" in which the blocks serve as experimental units for a subset of factors" (Jones & Nachtshem 2009). In other words, according to Jones and Nachtshem, the blocks are considered as whole plots, and contained within the plots are split plots, split units or space plots. They provide an explanation in the following example. Consider Factor A and two fertilizers methods (Factor B) on the yield of a crop, using four available fields as experimental units. In the irrigation, it is not possible to apply different irrigation methods (factor A) in areas smaller than a field. However, different fertilizer types (Factor B) could be applied in smaller areas. Hence, one whole plot (filed) will be divided into split plots, and each of the fertilizer types can be applied once within each whole plot (p. 340). Based on the split plot design, the two irrigation types are randomly assigned to the four field (whole plots). Jones and Nachtshem explain why one would use a split-plot design, and provide three potential reasons: (a) cost, (b) efficiency, and (c) validity. Cost suggests that a ...

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This solution describes the nature of split-plot or mixed designs.

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This problem shows how to analyze a split plot experiment in SAS. The analysis of the data was done in SAS using PROC GLM. The SAS program and the output of that program are included in a separate document.

The effects of variety upon the learning of the mathematical concepts of Boolean set union and intersection were studied. Ss from 5th and 7th grades were selected from four randomly selected schools. They were randomly assigned to four fixed experimental conditions which varied in two ways. Ss in the large variety conditions were given 48 different problems to solve. Subjects in the small variety conditions were given eight problems to solve with each problem repeated six times. The stimuli employed with one-half on the Ss were familiar geometric forms for which a verbal label was readily available. Stimuli for the remaining Ss were unfamiliar random forms they had never seen before.

(See the attached file for data table)

1- State the model and the hypotheses to be tested using α = 0.05
2- Verify all model assumptions
3- Perform the ANOVA and discuss your findings.

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