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Latin Square Designs

 
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PostPosted: Thu Jun 03, 2010 5:06 pm    Post subject: Latin Square Designs Reply with quote


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 treatments
into your SIMS 2000 Experimental Plans under the Blocks tab.

Reference excel spreadsheet with preset Latin Square Williams Designs for 2 to 26 treatments. Latin-Square-Williams-Designs.xls

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 product in each position an equal number of times.
Latin Squares are not fully balanced randomized designs, and generally intended when n is not large.
Latin Squares are for complete blocks only.

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
- Williams Designs require fewer subjects than those based on complete sets of Latin squares

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

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