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Experimenal Designs

 
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PostPosted: Wed Dec 15, 2010 9:18 am    Post subject: Experimenal Designs Reply with quote


SIMS 2000 Experimental Designs & Experimental Plans


Experimental Designs

The Experimental Design is one of three components of the SIMS 2000 Test Definition. Set up your number of samples, randomization of your sample presentations, sample blinding codes. etc. SIMS 2000 does include and make available many of the industry's popular predefined experimental plans, such as Cochran & Cox, Latin Squares, Permutations and Combinations.


Experimental Plans

Experimental Plans specify exactly how a group of experimental samples are arranged in a series
of subsets (blocks) for testing. Statisticians have created popular plans that depend on the
Number of Samples (t in the conventional statistical formulas), the Number of Samples Presented (k)
and the Number of Blocks (b, different sets of samples). SIMS 2000 provides the test designer with
over 100 such plans from which you can choose when creating Experimental Designs.
In addition, you have the capability to create your own customized plans.


PERMUTATIONS and COMBINATIONS

Permutations: All possible ordered combinations of items from a set of items.
For example, with the set of numbers 1, 2 and 3, there are six possible permutations:
123, 132, 213, 231, 312 and 321 in a Complete Block.

For Complete Blocks, Number of Permutations = t! (where t is number of Samples, Factorial mathematics)
Examples: 3 samples 3!=6 blocks (3x2x1), 4 samples 4!=24, 5 samples 5!=120, etc.

Combinations: All possible Unordered combinations of items from a set of items.
For example, with the set of numbers 1, 2 and 3, there is one possible combination:
1, 2, and 3 in a Complete Block.

For Complete Blocks, Number of Combinations = 1
For Incomplete Blocks, Number of Combinations = t! / ( k!(t-k)! )
where t is the number of samples from which you can choose and k is the number to be presented.


Beyond the Permuations and Combinations discussed above, there are two additional ways to further Randomize Sample Presentations from the EXperimental Designs screens. From Experimental Design screens select option for Randomized Block Presentations and/or select option for Randomized Sample Presentations. Experimental Design will automatically Randomize Samples as efficiently as possible. Experimental Design level randomization options for Blocks and Samples will generally produce good balanced presentations, including BIBD Balanced Incomplete Block Designs. In some cases this may be easier then trying to achieve Balance via Experimental Plans. Alternately if you select 'As In Plan', Sample Presentations will exactly follow Experimental Plan.

Please check your Test Definition Rotation Plan in the Test Definition area, this is will show exacly what samples and order that will be presented in your test.


Latin Square Designs Randomization

SIMS 2000 utilizes Latin Square randomization techniques for many randomization needs in SIMS 2000.
Optional experimental design sample randomizations and/or your custom experimental plans.
See your SIMS 2000 Test Definition rotation plan report for final verification of your test's sample presentations.

In SIMS 2000 you can pre-select any of the preset Latin Square Williams Designs for 2 to 26 samples
into your SIMS 2000 Experimental Plans under the Blocks tab.

Latin Square definition: a Latin square is an n n table filled with n different treatments in such a way
that each treatment occurs exactly once in each row and exactly once in each column. Here is an example:
1 2 3 / 2 3 1 / 3 1 2

Latin Squares places each sample in each position an equal number of times.
Latin Squares are for complete blocks only.
Latin Squares are not fully balanced randomized designs, and generally intended when n is not large.
- since all possible ordered combinations of items are not in the n blocks, see permutations.

Tom Carr, June 2010, Latin Square Williams Designs.
Good cross-over design, balanced with respect to first-order carry-over effects.
Every treatment follows every other treatment the same number of times, i.e. crossover counts.
- when the number of blocks is the same, or multiple of, the block row counts as shown below.
Williams Designs require fewer subjects than those based on complete sets of Latin squares.

Permutations are generally preferred over Latin squares if n is large enough.
Permutations are: All possible ordered combinations of items from a set of items.
For Complete Blocks, Number of Permutations = t! (where t is number of Samples, Factorial mathematics)
Examples: 3 samples 3!=6 blocks (3x2x1), 4 samples 4!=24 blocks, 5 samples 5!=120 blocks, etc.


References: Sensory Evaluation Techniques, Civille, pg 264 (2nd Ed), pg 295 (3rd Ed), pg 346 (4th Ed).
References: Wikipedia websites: http://en.wikipedia.org/wiki/Latin_square
References: Latin Square Williams Designs: http://statpages.org/latinsq.html

See our Sensory Computer Systems website Forum pages for additional infomation on Latin Squares:
Website Forum Link on Latin Squares:
http://www.sensorycomputersystems.com/phpbb2/viewtopic.php?t=106



Latin Square Williams Designs - Details for 2 to 26 Samples
Size = 2

1 2
2 1


Size = 3

1 2 3
2 3 1
3 1 2
3 2 1
1 3 2
2 1 3


Size = 4

1 2 4 3
2 3 1 4
3 4 2 1
4 1 3 2



Size = 5

1 2 5 3 4
2 3 1 4 5
3 4 2 5 1
4 5 3 1 2
5 1 4 2 3
4 3 5 2 1
5 4 1 3 2
1 5 2 4 3
2 1 3 5 4
3 2 4 1 5


Size = 6

1 2 6 3 5 4
2 3 1 4 6 5
3 4 2 5 1 6
4 5 3 6 2 1
5 6 4 1 3 2
6 1 5 2 4 3


Size = 7

1 2 7 3 6 4 5
2 3 1 4 7 5 6
3 4 2 5 1 6 7
4 5 3 6 2 7 1
5 6 4 7 3 1 2
6 7 5 1 4 2 3
7 1 6 2 5 3 4
5 4 6 3 7 2 1
6 5 7 4 1 3 2
7 6 1 5 2 4 3
1 7 2 6 3 5 4
2 1 3 7 4 6 5
3 2 4 1 5 7 6
4 3 5 2 6 1 7


Size = 8

1 2 8 3 7 4 6 5
2 3 1 4 8 5 7 6
3 4 2 5 1 6 8 7
4 5 3 6 2 7 1 8
5 6 4 7 3 8 2 1
6 7 5 8 4 1 3 2
7 8 6 1 5 2 4 3
8 1 7 2 6 3 5 4


Size = 9

1 2 9 3 8 4 7 5 6
2 3 1 4 9 5 8 6 7
3 4 2 5 1 6 9 7 8
4 5 3 6 2 7 1 8 9
5 6 4 7 3 8 2 9 1
6 7 5 8 4 9 3 1 2
7 8 6 9 5 1 4 2 3
8 9 7 1 6 2 5 3 4
9 1 8 2 7 3 6 4 5
6 5 7 4 8 3 9 2 1
7 6 8 5 9 4 1 3 2
8 7 9 6 1 5 2 4 3
9 8 1 7 2 6 3 5 4
1 9 2 8 3 7 4 6 5
2 1 3 9 4 8 5 7 6
3 2 4 1 5 9 6 8 7
4 3 5 2 6 1 7 9 8
5 4 6 3 7 2 8 1 9


Size = 10

1 2 10 3 9 4 8 5 7 6
2 3 1 4 10 5 9 6 8 7
3 4 2 5 1 6 10 7 9 8
4 5 3 6 2 7 1 8 10 9
5 6 4 7 3 8 2 9 1 10
6 7 5 8 4 9 3 10 2 1
7 8 6 9 5 10 4 1 3 2
8 9 7 10 6 1 5 2 4 3
9 10 8 1 7 2 6 3 5 4
10 1 9 2 8 3 7 4 6 5


Size = 11

1 2 11 3 10 4 9 5 8 6 7
2 3 1 4 11 5 10 6 9 7 8
3 4 2 5 1 6 11 7 10 8 9
4 5 3 6 2 7 1 8 11 9 10
5 6 4 7 3 8 2 9 1 10 11
6 7 5 8 4 9 3 10 2 11 1
7 8 6 9 5 10 4 11 3 1 2
8 9 7 10 6 11 5 1 4 2 3
9 10 8 11 7 1 6 2 5 3 4
10 11 9 1 8 2 7 3 6 4 5
11 1 10 2 9 3 8 4 7 5 6
7 6 8 5 9 4 10 3 11 2 1
8 7 9 6 10 5 11 4 1 3 2
9 8 10 7 11 6 1 5 2 4 3
10 9 11 8 1 7 2 6 3 5 4
11 10 1 9 2 8 3 7 4 6 5
1 11 2 10 3 9 4 8 5 7 6
2 1 3 11 4 10 5 9 6 8 7
3 2 4 1 5 11 6 10 7 9 8
4 3 5 2 6 1 7 11 8 10 9
5 4 6 3 7 2 8 1 9 11 10
6 5 7 4 8 3 9 2 10 1 11


Size = 12

1 2 12 3 11 4 10 5 9 6 8 7
2 3 1 4 12 5 11 6 10 7 9 8
3 4 2 5 1 6 12 7 11 8 10 9
4 5 3 6 2 7 1 8 12 9 11 10
5 6 4 7 3 8 2 9 1 10 12 11
6 7 5 8 4 9 3 10 2 11 1 12
7 8 6 9 5 10 4 11 3 12 2 1
8 9 7 10 6 11 5 12 4 1 3 2
9 10 8 11 7 12 6 1 5 2 4 3
10 11 9 12 8 1 7 2 6 3 5 4
11 12 10 1 9 2 8 3 7 4 6 5
12 1 11 2 10 3 9 4 8 5 7 6


Size = 13

1 2 13 3 12 4 11 5 10 6 9 7 8
2 3 1 4 13 5 12 6 11 7 10 8 9
3 4 2 5 1 6 13 7 12 8 11 9 10
4 5 3 6 2 7 1 8 13 9 12 10 11
5 6 4 7 3 8 2 9 1 10 13 11 12
6 7 5 8 4 9 3 10 2 11 1 12 13
7 8 6 9 5 10 4 11 3 12 2 13 1
8 9 7 10 6 11 5 12 4 13 3 1 2
9 10 8 11 7 12 6 13 5 1 4 2 3
10 11 9 12 8 13 7 1 6 2 5 3 4
11 12 10 13 9 1 8 2 7 3 6 4 5
12 13 11 1 10 2 9 3 8 4 7 5 6
13 1 12 2 11 3 10 4 9 5 8 6 7
8 7 9 6 10 5 11 4 12 3 13 2 1
9 8 10 7 11 6 12 5 13 4 1 3 2
10 9 11 8 12 7 13 6 1 5 2 4 3
11 10 12 9 13 8 1 7 2 6 3 5 4
12 11 13 10 1 9 2 8 3 7 4 6 5
13 12 1 11 2 10 3 9 4 8 5 7 6
1 13 2 12 3 11 4 10 5 9 6 8 7
2 1 3 13 4 12 5 11 6 10 7 9 8
3 2 4 1 5 13 6 12 7 11 8 10 9
4 3 5 2 6 1 7 13 8 12 9 11 10
5 4 6 3 7 2 8 1 9 13 10 12 11
6 5 7 4 8 3 9 2 10 1 11 13 12
7 6 8 5 9 4 10 3 11 2 12 1 13


Size = 14

1 2 14 3 13 4 12 5 11 6 10 7 9 8
2 3 1 4 14 5 13 6 12 7 11 8 10 9
3 4 2 5 1 6 14 7 13 8 12 9 11 10
4 5 3 6 2 7 1 8 14 9 13 10 12 11
5 6 4 7 3 8 2 9 1 10 14 11 13 12
6 7 5 8 4 9 3 10 2 11 1 12 14 13
7 8 6 9 5 10 4 11 3 12 2 13 1 14
8 9 7 10 6 11 5 12 4 13 3 14 2 1
9 10 8 11 7 12 6 13 5 14 4 1 3 2
10 11 9 12 8 13 7 14 6 1 5 2 4 3
11 12 10 13 9 14 8 1 7 2 6 3 5 4
12 13 11 14 10 1 9 2 8 3 7 4 6 5
13 14 12 1 11 2 10 3 9 4 8 5 7 6
14 1 13 2 12 3 11 4 10 5 9 6 8 7


Size = 15

1 2 15 3 14 4 13 5 12 6 11 7 10 8 9
2 3 1 4 15 5 14 6 13 7 12 8 11 9 10
3 4 2 5 1 6 15 7 14 8 13 9 12 10 11
4 5 3 6 2 7 1 8 15 9 14 10 13 11 12
5 6 4 7 3 8 2 9 1 10 15 11 14 12 13
6 7 5 8 4 9 3 10 2 11 1 12 15 13 14
7 8 6 9 5 10 4 11 3 12 2 13 1 14 15
8 9 7 10 6 11 5 12 4 13 3 14 2 15 1
9 10 8 11 7 12 6 13 5 14 4 15 3 1 2
10 11 9 12 8 13 7 14 6 15 5 1 4 2 3
11 12 10 13 9 14 8 15 7 1 6 2 5 3 4
12 13 11 14 10 15 9 1 8 2 7 3 6 4 5
13 14 12 15 11 1 10 2 9 3 8 4 7 5 6
14 15 13 1 12 2 11 3 10 4 9 5 8 6 7
15 1 14 2 13 3 12 4 11 5 10 6 9 7 8
9 8 10 7 11 6 12 5 13 4 14 3 15 2 1
10 9 11 8 12 7 13 6 14 5 15 4 1 3 2
11 10 12 9 13 8 14 7 15 6 1 5 2 4 3
12 11 13 10 14 9 15 8 1 7 2 6 3 5 4
13 12 14 11 15 10 1 9 2 8 3 7 4 6 5
14 13 15 12 1 11 2 10 3 9 4 8 5 7 6
15 14 1 13 2 12 3 11 4 10 5 9 6 8 7
1 15 2 14 3 13 4 12 5 11 6 10 7 9 8
2 1 3 15 4 14 5 13 6 12 7 11 8 10 9
3 2 4 1 5 15 6 14 7 13 8 12 9 11 10
4 3 5 2 6 1 7 15 8 14 9 13 10 12 11
5 4 6 3 7 2 8 1 9 15 10 14 11 13 12
6 5 7 4 8 3 9 2 10 1 11 15 12 14 13
7 6 8 5 9 4 10 3 11 2 12 1 13 15 14
8 7 9 6 10 5 11 4 12 3 13 2 14 1 15


Size = 16

1 2 16 3 15 4 14 5 13 6 12 7 11 8 10 9
2 3 1 4 16 5 15 6 14 7 13 8 12 9 11 10
3 4 2 5 1 6 16 7 15 8 14 9 13 10 12 11
4 5 3 6 2 7 1 8 16 9 15 10 14 11 13 12
5 6 4 7 3 8 2 9 1 10 16 11 15 12 14 13
6 7 5 8 4 9 3 10 2 11 1 12 16 13 15 14
7 8 6 9 5 10 4 11 3 12 2 13 1 14 16 15
8 9 7 10 6 11 5 12 4 13 3 14 2 15 1 16
9 10 8 11 7 12 6 13 5 14 4 15 3 16 2 1
10 11 9 12 8 13 7 14 6 15 5 16 4 1 3 2
11 12 10 13 9 14 8 15 7 16 6 1 5 2 4 3
12 13 11 14 10 15 9 16 8 1 7 2 6 3 5 4
13 14 12 15 11 16 10 1 9 2 8 3 7 4 6 5
14 15 13 16 12 1 11 2 10 3 9 4 8 5 7 6
15 16 14 1 13 2 12 3 11 4 10 5 9 6 8 7
16 1 15 2 14 3 13 4 12 5 11 6 10 7 9 8


Size = 17

1 2 17 3 16 4 15 5 14 6 13 7 12 8 11 9 10
2 3 1 4 17 5 16 6 15 7 14 8 13 9 12 10 11
3 4 2 5 1 6 17 7 16 8 15 9 14 10 13 11 12
4 5 3 6 2 7 1 8 17 9 16 10 15 11 14 12 13
5 6 4 7 3 8 2 9 1 10 17 11 16 12 15 13 14
6 7 5 8 4 9 3 10 2 11 1 12 17 13 16 14 15
7 8 6 9 5 10 4 11 3 12 2 13 1 14 17 15 16
8 9 7 10 6 11 5 12 4 13 3 14 2 15 1 16 17
9 10 8 11 7 12 6 13 5 14 4 15 3 16 2 17 1
10 11 9 12 8 13 7 14 6 15 5 16 4 17 3 1 2
11 12 10 13 9 14 8 15 7 16 6 17 5 1 4 2 3
12 13 11 14 10 15 9 16 8 17 7 1 6 2 5 3 4
13 14 12 15 11 16 10 17 9 1 8 2 7 3 6 4 5
14 15 13 16 12 17 11 1 10 2 9 3 8 4 7 5 6
15 16 14 17 13 1 12 2 11 3 10 4 9 5 8 6 7
16 17 15 1 14 2 13 3 12 4 11 5 10 6 9 7 8
17 1 16 2 15 3 14 4 13 5 12 6 11 7 10 8 9
10 9 11 8 12 7 13 6 14 5 15 4 16 3 17 2 1
11 10 12 9 13 8 14 7 15 6 16 5 17 4 1 3 2
12 11 13 10 14 9 15 8 16 7 17 6 1 5 2 4 3
13 12 14 11 15 10 16 9 17 8 1 7 2 6 3 5 4
14 13 15 12 16 11 17 10 1 9 2 8 3 7 4 6 5
15 14 16 13 17 12 1 11 2 10 3 9 4 8 5 7 6
16 15 17 14 1 13 2 12 3 11 4 10 5 9 6 8 7
17 16 1 15 2 14 3 13 4 12 5 11 6 10 7 9 8
1 17 2 16 3 15 4 14 5 13 6 12 7 11 8 10 9
2 1 3 17 4 16 5 15 6 14 7 13 8 12 9 11 10
3 2 4 1 5 17 6 16 7 15 8 14 9 13 10 12 11
4 3 5 2 6 1 7 17 8 16 9 15 10 14 11 13 12
5 4 6 3 7 2 8 1 9 17 10 16 11 15 12 14 13
6 5 7 4 8 3 9 2 10 1 11 17 12 16 13 15 14
7 6 8 5 9 4 10 3 11 2 12 1 13 17 14 16 15
8 7 9 6 10 5 11 4 12 3 13 2 14 1 15 17 16
9 8 10 7 11 6 12 5 13 4 14 3 15 2 16 1 17


Size = 18

1 2 18 3 17 4 16 5 15 6 14 7 13 8 12 9 11 10
2 3 1 4 18 5 17 6 16 7 15 8 14 9 13 10 12 11
3 4 2 5 1 6 18 7 17 8 16 9 15 10 14 11 13 12
4 5 3 6 2 7 1 8 18 9 17 10 16 11 15 12 14 13
5 6 4 7 3 8 2 9 1 10 18 11 17 12 16 13 15 14
6 7 5 8 4 9 3 10 2 11 1 12 18 13 17 14 16 15
7 8 6 9 5 10 4 11 3 12 2 13 1 14 18 15 17 16
8 9 7 10 6 11 5 12 4 13 3 14 2 15 1 16 18 17
9 10 8 11 7 12 6 13 5 14 4 15 3 16 2 17 1 18
10 11 9 12 8 13 7 14 6 15 5 16 4 17 3 18 2 1
11 12 10 13 9 14 8 15 7 16 6 17 5 18 4 1 3 2
12 13 11 14 10 15 9 16 8 17 7 18 6 1 5 2 4 3
13 14 12 15 11 16 10 17 9 18 8 1 7 2 6 3 5 4
14 15 13 16 12 17 11 18 10 1 9 2 8 3 7 4 6 5
15 16 14 17 13 18 12 1 11 2 10 3 9 4 8 5 7 6
16 17 15 18 14 1 13 2 12 3 11 4 10 5 9 6 8 7
17 18 16 1 15 2 14 3 13 4 12 5 11 6 10 7 9 8
18 1 17 2 16 3 15 4 14 5 13 6 12 7 11 8 10 9


Size = 19

1 2 19 3 18 4 17 5 16 6 15 7 14 8 13 9 12 10 11
2 3 1 4 19 5 18 6 17 7 16 8 15 9 14 10 13 11 12
3 4 2 5 1 6 19 7 18 8 17 9 16 10 15 11 14 12 13
4 5 3 6 2 7 1 8 19 9 18 10 17 11 16 12 15 13 14
5 6 4 7 3 8 2 9 1 10 19 11 18 12 17 13 16 14 15
6 7 5 8 4 9 3 10 2 11 1 12 19 13 18 14 17 15 16
7 8 6 9 5 10 4 11 3 12 2 13 1 14 19 15 18 16 17
8 9 7 10 6 11 5 12 4 13 3 14 2 15 1 16 19 17 18
9 10 8 11 7 12 6 13 5 14 4 15 3 16 2 17 1 18 19
10 11 9 12 8 13 7 14 6 15 5 16 4 17 3 18 2 19 1
11 12 10 13 9 14 8 15 7 16 6 17 5 18 4

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