23a_SplitPlot

23a_SplitPlot - Statistical Techniques II EXST7015...

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Statistical Techniques II EXST7015 Split-plot and Repeated Measures Designs 1 12 2 3 4 5 6 7 8 9 10 11 23a_SplitPlot 1
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Split-plot and Repeated Measure Designs The Split-plot and Repeated Measures "Designs" combine elements of design (error structure) and treatment arrangement concepts. These are designs with two levels, a "Main Plot", with its own treatment and error, and a "Sub-plot", with its own treatment and error. It is possible to have more than just an " a priori " treatment in both levels. 23a_SplitPlot 2
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Split-plot Designs (continued) The (minimum of) two treatments (from the main and sub plots) are usually cross classified . Either Main or Subplot may have nested error structure. The simplest split plot would have the following model (CRD). Y ijk = µ + τ 1i + γ ij + τ 2k + τ 1 τ 2ik + ε ijk 23a_SplitPlot 3
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Split-plot Designs (continued) C A AB B A A BC C A BB C C Example with CRD main plot. 23a_SplitPlot 4
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Split-plot Designs (continued) Each plot SPLIT for a new treatment. C A AB B A A BC C A BB C C FG GF 23a_SplitPlot 5
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Split-plot Designs (continued) Source d.f. Treatment1 t 1 -1 = 2 Error(a) t 1 (n-1) = 12 Treatment 2 t 2 -1 = 1 Tmt1*Tmt2 (t 1 -1)(t 2 -1) = 2 Error(b) t 1 *(t 2 -1)(n-1) = 12 Total t 1 *t 2* n-1 = 29 Split-plot design source table. The d.f. for error(b) is the usual t 1 *t 2 *(n-1) less the d.f. for error(a), t 1 *(n-1), giving t 1 *(t 2 -1)(n-1). 23a_SplitPlot 6
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Split-plot Designs (continued) Split-plot design - examples of splits We may split a plot to do a new treatment, e.g. an agricultural experiment with fertilizer treatments in plots may have a herbicide applied to half of each plot an not to the other half. A soil study of contaminants may measure levels of the chemical of interest at various levels in a soil core (0-5 cm, 6-10 cm, 11-15 cm, etc), so the core is split. 23a_SplitPlot 7
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Split-plot Designs (continued) Split-plot split examples (continued ) A study of the growth of plants, e.g. Spartina in a marsh, may split the plant into above ground, root and rhizome biomass. Anytime a treatment occurs within an experimental unit, we have a split-plot. If we are studying diets of fish, and put a male and female fish in each aquaria, weight gain of hogs with large and small hogs in each pen, etc.
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This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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23a_SplitPlot - Statistical Techniques II EXST7015...

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