26anova_RBD

# 26anova_RBD - Statistical Techniques I EXST7005 Randomized...

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Unformatted text preview: Statistical Techniques I EXST7005 Randomized Block Designs Similar in many ways to a &quot;two-way&quot; ANOVA The CRD is defined by the linear model Yij = + i + ij The version above has one treatment and one err term The Randomized Block Design The factorial treatment arrangement we saw occurred within a CRD, and it had a subdivided treatment. Yijk = + i + j + i j + ijk This model has two treatments and one error. It could have many more treatments, and it would sti be a factorial design. This is a treatment The Randomized Block Design (continued) But there are other modifications of a CRD that could be done. Instead of subdividing the treatments, we may find it expedient to subdivide the error term! Why would we do this? Perhaps there is some variation that is not of interest. If we ignore it, th variation will go to the error term. The Randomized Block Design (continued) The Randomized Block Design (continued) For example, suppose we had a large agricultur experiment, and had to do our experiment in 8 different fields. Or due to space limitations, we had to separate our experiment into several part in 3 different greenhouses or 5 different incubators. Now there is a source of variation that is due to different fields, or different greenhouses or incubators! The Randomized Block Design (continued) If we do it as a CRD, we put our treatments in th model, but if there is some variation due to field, greenhouse or incubator it will go to the error term. This would inflate our error term an make it more difficult to detect a difference (we would loose power). How do we prevent this? The Randomized Block Design (continued) First, make sure each treatment occurs in each field, greenhouse or incubator (preferably balanced). Then we would factor the new variation out of th error term by putting it in the model. Yijk = + i + j + i j + ijk This is not a new treatment. We will call it a BLOCK . The Randomized Block Design (continued) This looks like a factorial, but it is not because th blocks are not a source of variation that we are interested in discussing. Also, in a factorial the interaction term is likely to be something of interest. In a block design the interaction is an error term, representing random variation of experimental units across treatments The Randomized Block Design (continued) Another difference, treatments can be either fixe or random. If both treatments are fixed, the interaction is fixed. However, blocks are usually random, and the block interaction is always random. So why are we blocking?...
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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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26anova_RBD - Statistical Techniques I EXST7005 Randomized...

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