0 58. 16ns Error(b) 2 693. 16** Error (a) 4 14. 50 15. 67 65.
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It would be economical to randomly select any of the preparation methods, make the blend and divide it into four samples and cook each of them with one of the four cooking temperatures. If we ignore method, we would have an RCBD where the blocks are the individual preparations. 0 59. The experimental unit for diet is rat. 0 license.
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00 60. 67 54. 67 61. 0 45. 5 56.
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33 62. . Kowalski and Kevin J. 6753.
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67 13. 6756. of the B main effect • FAB=MSAB/MSEBtests the sig. You still need to identify which levels of nitrogen are different. 00 22.
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The experimenter wants to perform three replicates of this experiment on three different days each consisting of 12 runs (3 × 4). 67 13. 67 21. 67 18. The important issue here is the fact that making the pulp by any of the methods is cumbersome.
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16. Both of the approaches will be discussed but there will be more emphasis on the second approach, as it is more widely accepted for analysis of split-plot designs. The design consists of blocks (or whole plots) in which one factor (the whole plot factor) is applied to randomly. In this example, each replicate or block is divided into three parts called whole plots (Each preparation method is assigned to a whole plot). 67 54.
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65* Error (b) 18 120. Here, the whole plot section of the analysis of variance could be considered as a Randomized Complete Block Home or RCBD with Method as our single factor (If we didn’t have the blocks, it could be considered as a Complete Randomized Design or CRD). 00 53. The experimental unit for analytical technique is piece of liver. Of interest are differences in oat variety and nitrogen levels. 89 Potash x Phosphorus SSR=6*devsq(range) P K1 K2 K3 Mean 1 46.
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67 14. 33 55. 0 49. That makes this a split-plot design. 25 2 22.
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492Interpretation • Differences among varieties depended on planting date • Even so, variety differences and date differences were highly significant • Except for variety 3, each variety produced its maximum yield when planted on November 1. 22 17. Table 14. 5 57. 75 18. To each rat, one of three food diets was randomly assigned (T1, T2, and T3).
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To analyze the treatment effects we first follow the approach discussed in the book. 33 55. Next, we have pooled the sum of squares and their respective degrees of freedom to create the SP Error term as described. 28 24. 22 Block 2 1.
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5 57. The key is the experimental unit is different for each factor. 4. This method is a “hard to change” factor. Usually used with factorial sets when the assignment of treatments at random can cause difficulties large scale machinery required for one factor but not another irrigation tillage plots that receive the same treatment must be grouped togetherSplit-Plot Designs • Usually used with factorial sets when the assignment of treatments at random can cause difficulties • large scale machinery required for one factor but not another • irrigation • tillage • plots that receive the same treatment must be grouped together • for a treatment such as planting date, it may be necessary to group treatments to facilitate field operations • in a growth chamber experiment, some treatments must be applied to the whole chamber (light regime, humidity, temperature), so the chamber becomes the main plotDifferent size requirements • The split plot is a design which allows the levels of one factor to be applied to large plots while the levels of another factor are applied to small plots • Large plots are whole plots or main plots • Smaller plots are split plots or subplotsRandomization • Levels of the whole-plot factor are randomly assigned to the main plots, using a different randomization for each block (for an RBD) • Levels of the subplots are randomly assigned within each main plot using a separate randomization for each main plotRandomizaton Block I T3 T1 T2 V3 V4 V2 V1 V1 V4 V2 V3 V3 V4 V2 V1 Block II T1 T3 T2 V1 V2 V3 V3 V1 V4 V2 V3 V1 V4 V4 V2 Tillage treatments are main plots Varieties are the subplotsExperimental Errors • Because there are two sizes of plots, there are two experimental errors – one for each size plot • Usually the sub plot error is smaller and has more df • my website the main plot factor is estimated with less precision than the subplot and interaction effects • Precision is an important consideration in deciding which factor to assign to the main plotAdvantages • Permits the efficient use of some factors that require different sizes of plot for their application • Permits the introduction of new treatments into an experiment that is already in progressDisadvantages • Main plot factor is estimated with less precision so larger differences are required for significance – may be difficult to obtain adequate df for the main plot error • Statistical analysis is more complex because different standard errors are required for different comparisonsUses • In experiments where different factors require different size plots • To introduce new factors into an experiment that is already in progressData Analysis • This is a form of a factorial experiment so the analysis is handled in much the same manner • We will estimate and test the appropriate main effects and interactions • Analysis proceeds as follows: • Construct tables of means • Complete an analysis of variance • Perform significance tests • Compute means and standard errors • Interpret the analysisSplit-Plot Analysis of Variance Source df SS MS F Total rab-1 SSTot Block r-1 SSR MSR FR A a-1 SSA MSA FA Error(a) (r-1)(a-1) SSEA MSEAMain plot error B b-1 SSB MSB FB AB (a-1)(b-1) SSAB MSAB FAB Error(b) a(r-1)(b-1) SSEB MSEBSubplot errorComputations • Only the error terms are different from the usual two- factor analysis SSTot SSR SSA SSEA SSB SSAB SSEB SSTot – SSR – SSA – SSEA – SSB – SSABF Ratios • F ratios are computed somewhat differently because there are two errors • FR=MSR/MSEAtests the effectiveness of blocking • FA=MSA/MSEAtests the sig.
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