graeco - latin square designs-02
DESCRIPTION
Graeco-Latin Square Design ApproachesTRANSCRIPT
5. Process Improvement5.3. Choosing an experimental design5.3.3. How do you select an experimental design?5.3.3.2. Randomized block designs
Thesedesignshandle 3nuisancefactors
Graeco-Latin squares, as described on the previous page, areefficient designs to study the effect of one treatment factor inthe presence of 3 nuisance factors. They are restricted,however, to the case in which all the factors have the samenumber of levels.
Randomizeas much asdesignallows
Designs for 3-, 4-, and 5-level factors are given on this page.These designs show what the treatment combinations would befor each run. When using any of these designs, be sure torandomize the treatment units and trial order, as much as thedesign allows.
For example, one recommendation is that a Graeco-Latinsquare design be randomly selected from those available, thenrandomize the run order.
Graeco-Latin Square Designs for 3-, 4-, and 5-LevelFactors
Designs for3-levelfactors
3-Level FactorsX1 X2 X3 X4row
blockingfactor
columnblocking
factor
blockingfactor
treatmentfactor
1 1 1 11 2 2 21 3 3 32 1 2 32 2 3 12 3 1 23 1 3 23 2 1 33 3 2 1
with
5.3.3.2.2. Graeco-Latin square designs http://www.itl.nist.gov/div898/handbook/pri/section3/pri3322.htm
1 of 4 11/22/2013 8:38 PM
k = 4 factors (3 blocking factors and 1 primary factor)L1 = 3 levels of factor X1 (block)L2 = 3 levels of factor X2 (block)L3 = 3 levels of factor X3 (primary)L4 = 3 levels of factor X4 (primary)N = L1 * L2 = 9 runs
This can alternatively be represented as (A, B, and C representthe treatment factor and 1, 2, and 3 represent the blockingfactor):
A1 B2 C3C2 A3 B1B3 C1 A2
Designs for4-levelfactors
4-Level FactorsX1 X2 X3 X4row
blockingfactor
columnblocking
factor
blockingfactor
treatmentfactor
1 1 1 11 2 2 21 3 3 31 4 4 42 1 2 42 2 1 32 3 4 22 4 3 13 1 3 23 2 4 13 3 1 43 4 2 34 1 4 34 2 3 44 3 2 14 4 1 2
with
k = 4 factors (3 blocking factors and 1 primary factor)L1 = 3 levels of factor X1 (block)L2 = 3 levels of factor X2 (block)
5.3.3.2.2. Graeco-Latin square designs http://www.itl.nist.gov/div898/handbook/pri/section3/pri3322.htm
2 of 4 11/22/2013 8:38 PM
L3 = 3 levels of factor X3 (primary)L4 = 3 levels of factor X4 (primary)N = L1 * L2 = 16 runs
This can alternatively be represented as (A, B, C, and Drepresent the treatment factor and 1, 2, 3, and 4 represent theblocking factor):
A1 B2 C3 D4D2 C1 B4 A3B3 A4 D1 C2C4 D3 A2 B1
Designs for5-levelfactors
5-Level FactorsX1 X2 X3 X4row
blockingfactor
columnblocking
factor
blockingfactor
treatmentfactor
1 1 1 11 2 2 21 3 3 31 4 4 41 5 5 52 1 2 32 2 3 42 3 4 52 4 5 12 5 1 23 1 3 53 2 4 13 3 5 23 4 1 33 5 2 44 1 4 24 2 5 34 3 1 44 4 2 54 5 3 15 1 5 45 2 1 5
5.3.3.2.2. Graeco-Latin square designs http://www.itl.nist.gov/div898/handbook/pri/section3/pri3322.htm
3 of 4 11/22/2013 8:38 PM
5 3 2 15 4 3 25 5 4 3
with
k = 4 factors (3 blocking factors and 1 primary factor)L1 = 3 levels of factor X1 (block)L2 = 3 levels of factor X2 (block)L3 = 3 levels of factor X3 (primary)L4 = 3 levels of factor X4 (primary)N = L1 * L2 = 25 runs
This can alternatively be represented as (A, B, C, D, and Erepresent the treatment factor and 1, 2, 3, 4, and 5 representthe blocking factor):
A1 B2 C3 D4 E5C2 D3 E4 A5 B1E3 A4 B5 C1 D2B4 C5 D1 E2 A3D5 E1 A2 B3 C4
Furtherinformation
More designs are given in Box, Hunter, and Hunter (1978).
5.3.3.2.2. Graeco-Latin square designs http://www.itl.nist.gov/div898/handbook/pri/section3/pri3322.htm
4 of 4 11/22/2013 8:38 PM