Blocks and minimum numbers of rows

[djourdain]

Dear all,

I have a doubt about the minimum number of rows when doing a blocked design.

Suppose I want to make a design with 10 parameters to be estimated and two alternatives The number of parameter is high because of effects.coded variables.

Then the minimum number of rows is 10/(2-1) = 10.

Suppose I make a design with 18 rows (s > 10 is OK), but because I am afraid to propose 18 scenarios, I create two blocks of 9 rows. Is this still correct ? Or should I make a design with 20 rows so the each block have at least 10 rows ?


Damien

[Michiel Bliemer]

It is the total number of rows in the design that counts, and you can block that into as many smaller pieces as you like.
So in your case a design with 18 rows is fine, you can block this in 2 times 9, or 3 times 6, etc.

[djourdain]

Thank you again for your prompt answer.

Is there a citable source that I can read and cite if needed for this aspect? (I am actually trying to address a reviewer comment who says the opposite and claim that my design is not appropriate for this reason). I was convinced that I was right (and you convinced me completely now) but I cannot give a counter-argument.


Damien

[Michiel Bliemer]

You can for example refer to:

Rose, J.M. and M.C.J. Bliemer (2013) Sample size requirements for stated choice experiments. Transportation, Vol. 40, No. 5, pp. 1021-1041.

On page 1033, the formula (J-1)*S>=K is mentioned, where J is the number of alternatives, K is the number of parameters, and S is the number of choice tasks in the design (not in each block). It briefly mentions blocking on the same page, but it does not explicitly say that blocking has no impact on the minimum number of choice tasks required, but I think it is sufficiently clear that S is the total number of choice tasks in the entire design. Feel free to say that you have confirmed this with me that this is the case.

[djourdain]

Thank you again! Damien