Class Notes
(810,824)

Canada
(494,273)

University of Alberta
(12,947)

Statistics
(237)

STAT368
(25)

Douglas Wiens
(25)

Lecture

# Balanced Incomplete Block Designs.pdf

Unlock Document

University of Alberta

Statistics

STAT368

Douglas Wiens

Winter

Description

95
13. Balanced Incomplete Block Designs
In the RCBD, C=Complete means that each block
contains each treatment.E.g. each coupon is sub-
jected to each of the 4 tips. Suppose that a coupon
is only large enough that 3 tips can be usThen
the blocks would be incompleteOne way to run
the experiment is to randomly assign 3 tips to each
block, perhaps requiring that each tip appears 3 times
in total.There is a more e cient way.An incom-
plete block design is balanced if any two treatments
appear in the same block an equal number of times.
This is then a Balanced Incomplete Block Design.
Hardness testing
BIBD design and data.
Coupon
Tip 1 2 3 4
1 9 3 9 4 10 0 28 7 1000
2 9 3 9 8 9 9 29 0 1667
3 9 2 9 4 9 5 28 1 4333
4 9 7 10 0 10 2 29 9 7000
28 2 28 1 29 3 30 1 96
Notation:
= # of treatments, = # of blocks. = 4 = 4.
= # of treatments per block. = 3.
= # of times each treatment appears in the entire
experiment. = 3.
= = = # of observations. = 12.
= # of times each pair of treatments appears to-
gether. = 2. It can be shown that
= ( 1)
1
Since these parameters have to be integers, BIBD de-
signs dont exist for all choices of . There
are tables available of the ones that do exist. 97
Model is as for a RCBD:
= + + + ,
with both sums of e ects va³ishinA´ usual, the
P 2
total sum of squares = ¯ on 1
P ³ ´2
d.f. and the SS for Blocks is = =1 ¯ ¯
on 1 d.f. The treatment SS depends on the ad-
justed total for thtreatment
1X
=
=1
where = 1 if treatmentappears in blockand
= 0 otherwise. So P is the total of the
=1
block totals, counting only those blocks that contain
treatment :
1
1 = 28 7 (28 2 + 28 1 + 30 1) 1000
3
1
2 = 29 0 3 (28 1 + 29 3 + 30 1) 1667
1
3 = 28 1 (28 2 + 28 1 + 29 3) 4333
3
1
4 = 29 9 3 (28 2 + 29 3 + 30 1) = 7000

More
Less
Related notes for STAT368