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Randomized complete block designs.pdf

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Douglas Wiens

68 9. Randomized complete block designs • Example: A hardness testing machine presses a pointed rod (the ‘tip’) into a metal specimen (a ‘coupon’), with a known force. The depth of the depression is a measure of the hardness of the specimen. It is feared that, depending on the kind of tip used, the machine might give di erent readings. The experimenter wants 4 observa- tions on each of the 4 types of tips. Note that the di erences in readings might also depend on which type of metal specimen is used, i.e. on the coupons. • A Completely Randomized design would use 16 coupons, making 1 depression in each. The coupons would be randomly assigned to the tips, hoping that this would average out any di erences between the coupons. Here ‘coupon type’ is a ‘nuisance factor’ - it may a ect the readings, but we aren’t very interested in measuring its e ect. 69 It is also controllable, by blocking: we can use 4 coupons (the ‘blocks’) and apply each of the 4 treatments (the tips) to each coupon. This is preferable to hoping that randomization alone will do the job; it also uses fewer coupons. • There may be unknown and uncontrollable fac- tors a ecting the readings (the eyesight of the operator, ... think of others). Here is where ran- domization might help - within each block, the treatments are applied in random order. So each block can be viewed as one CR designed experi- ment. This is a Randomized Complete Block De- sign (RCBD). ‘Complete’ means that each block contains all of the treatments. • Common blocking variables: Day of week, per- son, batch of raw material, ... . A basic idea is that the responses should be less highly varied within a block than between blocks. 70 Hardness testing design and data. = machine reading for tip , coupon ; order in parentheses. Coupon Tip 1 2 3 4 ¯ 1 9 3 (3) 9 4 (3) 9 6 (2) 10 0 (1) 9 575 2 9 4 (1) 9 3 (4) 9 8 (1) 9 9 (4) 9 600 3 9 2 (4) 9 4 (2) 9 5 (3) 9 7 (3) 9 450 4 9 7 (2) 9 6 (1) 10 0 (4) 10 2 (2)
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