t – number of levels of the treatment factor b – number of blocks k – number of experimental units per block r – number of replicates of each treatment.

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t – number of levels of the treatment factor b – number of blocks k – number of experimental units per block r – number of replicates of each treatment level in the design in RCB design k = t, k < t → incomplete block design where only a subset of the treatment factor levels are tested in each block. λ – number of times each treatment level occurs with every other treatment level in a block

Simplest way to form a BIB is to take all possible combinations of k from t Example t = 6, k = 3 λ =4, r =10

There may be other BIB designs with necessary conditions for existence of a BIB

1.When BIB designs require too many blocks 2.When physical constraints prevent some treatment levels from being tested with certain other treatments in the same block Relax BIB requirements that 1) Every treatment level be replicated the same number of times 2) Every treatment be tested with every other treatment in a block the same number of times

I wanted to test the accuracy of a home blood pressure monitoring device, by comparing it to other monitors Example

I decided to do an experiment to compare it to automatic blood pressure monitors available in stores.

Sources of Variation in Blood Pressure Blood pressure monitor Person to person Time to time for a particular person Morning Noon Evening Sleep Blood Pressure Subject 1 Subject 2 pressure is most consistent for one person within a short period of time 5-7 minutes

Treatment Levels were : 1=Portable 2= Store A 3 = Store B 4= Store C

BTIB (Balanced with respect to treatment PBIB) – Each treatment level occurs in a block the same number (λ 0 ) with a control or standard treatment level and the same number of times (λ 1 ) with every other treatment level This gives more precision to comparisons with the standard or control treatment level and less precision to other comparisons λ 0 = 2, λ 1 = 0

Dishwashing Experiment 2 4 Factors: A=Water Temperature B=Soap Amount C=Soap Brand D=Soaking Time

Experimental Unit: Blocking factor: Block 1 = W.F., 1:30 Block 2 = W.F., 1:00 Block 3 = Prego, 1:30 Block 4 = Prego, 1:00 4 E.U’s per block Confound AC, ABD

Response: Number of Clean grid squares Model:

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