Can you add a feature to the DOE platform to generate simple Latin Squares for Complete Block and incomplete block designs. It would take the base size calculation, and suggest the best number of products for each to see, and then create an array data table. You can just about get there with the randomisation option when you make the table, but you still have a lot of formatting to do, and it is not obvious what to input where to get the design
https://damienmasson.com/tools/latin_square/
https://justinmacdonald.net/block_designs/
To build on this request, here are some additional design specs / features that would be great to incorporate into this kind of a tool.
1. The user would input the number of products/treatments (k) and the number of periods (p) and the desired base size (n). (So, if k=p, it's a complete block design; and if k>p, it's an incomplete block design).
2. The objective of the design is to create as balanced a design as possible:
a. the number of times each product appears
b. the number of times each product appears at each period
c. the number of times each product appears with other products
d. the number of times each product appears immediately after another product (1st order carryover)
3. Summary tables would provide frequency counts to describe the balance for the chosen base size.
4. The program would calculate the minimum sample size (block size) needed to obtain a balanced design according criteria #2. (e.g. for k=p=5, it's n=10. for k=p=6, it's n=6. for k=7, p=3, it's n=42).
5. For balanced incomplete block designs, the program would calculated the efficiency of the design relative to a complete block design and the sample size multiplier necessary to have the same power as a complete block design. Multiplier = k / (p * efficiency)
6. Once the block size is determined and the final base size is chosen, the program would create the design, randomizing the rows (panelists/patients) within blocks but not between blocks.
Thank you for submitting this request and adding more information!
