Experimental Design STAT 507
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Mr. Alex Berge
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This 2 page Class Notes was uploaded by Mr. Alex Berge on Friday October 23, 2015. The Class Notes belongs to STAT 507 at University of Idaho taught by Staff in Fall. Since its upload, it has received 24 views. For similar materials see /class/227942/stat-507-university-of-idaho in Statistics at University of Idaho.
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Date Created: 10/23/15
1 Incomplete Block Designs Incomplete block designs are needed when we cannot t all levels of a treatment into our blocks The book has a good example where the treatment levels are 3 types of eyedrops The concepts of resolvability and connectedness are useful for distinguishing different kinds of incomplete block designs 11 Balanced Incomplete Block Designs BIBD In this design each block has It units which is not equal to the total 9 number of treatment levels The 7balanced7 condition refers to the fact that in this design all pairs of treatment levels occur together in the same number of blocks so that the variance of estimated treatment differences 3i 7 3139 is the same for all pairs of treatments If each treatment is applied to 7 units and 12 blocks are used the total number of units N satis es N kl Tgi As discussed in the text the number of times that two treatments occur together is A Tk 7 lg 7 I so if A is not a whole number then a BIBD does not exist for that combination of k b r and g A BIBD always exists however as long as k lt gr Table 141 gives a nice example of a resolvable BIBD for g 9 treatments in b 12 blocks of size It 3 The book also gives a nice description of a threestep process of randomization in a BIBDI The usual analysis of data from a BIBD called the intrablock analysis consists of obtaining the sums of squares for treatments after rst adjusting for blocks this is just the Type III SS approach that we have seen before for analyzing unbalanced factorial experiments The text also introduces the concept of recovery of interblock information which is particularly useful when blocking has not been effective 1 2 Youden squares When we want to block on two factors but do not have blocks large enough for a Latin square we can use Youden squares which can be obtained by omitting rows from a Latin square design The resulting rectangles are BIBD7s in the columns but have treatments and columns appearing once in each row as in a complete block design The usual analysis of a Youden square is the same kind of intrablock analysis as mentioned for BIBD7s 13 Partially Balanced Incomplete Block Designs PBIBD If it is not possible to construct a BIBD in a particular situation it may be possible to construct a slightly more complicated design called a partially bal anced incomplete block design In this design not all pairs of treatments occur together in the same number of blocks We use the concept of associate classes to describe this more complicated arrangement of treatments into the blocks An associate class is a set of treatment pairs where each pair from the set occur together the same number of times M i These classes are ordered so that the class with the largest Ai value is the rst associate class and so on In the example in section 143 of our text there are two associate classes With A1 4 and A2 3 The same kind of intrablock analysis used for BIBDls and Youden squares is usually used for these designs also 14 Related topics The text discusses the ef ciency of these designs to RCB designs and gives a formula for BIBD designsi There is also discussion of three types of incomplete block designs that can be easily constructed Cyclic designs Lattice designs and Alpha designsi
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