sample size for blocked full factorial designs

[Anat Tchetchik]

Dear Ngene users,

I designed a labelled design with 6 labelled alternatives (i.e. the alts. one faces regarding the use of old cell phones: (1) sell on eBay, (2) sell to a Mobile Phone Recycling organisation, (3) sell to the cellphone provider, (4) give to friend/relative, (5) donate, (5) throw away).

The only attribute here is the Receipt received on the phone. This attribute applies only to the 3 first alts. The 3 other alternatives has only alternative specific constants.

I think that the full factorial design will be best here; it results with only 27 scenarios which can be blocked into 3 blocks.
My question is (assuming I'm not terribly wrong in choosing full fact.) how many respondents do I need for each block?

This is the design I created is:
Design
;alts = Resyclcomp, Ebay, returnCellComp, giveaway, donate, throw
;rows = all
;fact
;block=3
;model:
U(Resyclcomp) = a1 + b2 *priceL[0,1,2] /
U(Ebay) = b1+ b2 *priceH[4,5,6] /
U(returnCellComp)=c1 +b2*priceM[2,3,4]/
U (giveaway)= d1 /
U(donate)= e1 $
Best wishes!
Anat Tchetchik

[Michiel Bliemer]

The full factorial would work, but you can likely do much better.
I am not sure what your levels stand for, but if the first has a price of 0, the second of 6, and the third of 2, then it seems that the second alternative may be dominant and you will not collect much info. Using a fractional factorial design (with only a subset of 27 questions containing only the 'best' questions) you could create a more efficient design, likely avoiding to block at all.

There is no way of telling how many respondents you need without having any prior information on your coefficients. If you put in the priors, Ngene will compute the S-estimates and S-error, which tells you the sample size you need (given that those priors are correct). In case you do not have any priors, you could use your full factorial design, give it to friends, family, colleagues to fill out (they may be willing to answer all 27), and use that data to estimate a model and get your priors. Then use those priors to create an efficient design with, say, 8 or 12 choice tasks. It depends on how many you think a person can handle (it also depends whether it is an internet survey or a survey with a person sitting next to you).

[Anat Tchetchik]

Dear Michiel,

Thanks much for your response..
I'm not quite sure I understand the problem you indicate
" If the first has a price of 0, the second of 6, and the third of 2, then it seems that the second alternative may be dominant and you will not collect much info.."
The levels stand for the payments a respondent receives for his old cell-phone when he sells it to each of the three different buyers - alternatives (e.g. e-bay, his cell-phone operator, recycling corp.).

The labels themselves carry meaning (e-bay requires more effort and time, recycling corp is more environmental but usually you receive lower payment etc.) so having explain that do you still see the dominance problem you mentioned?

Also, since the avg. price is the highest for the E-bay alt., and lowest for the recycling corp, we used three attributes PriceH, PriceM, and PriceL each with different price range, is this possible?

again this is the design..
Design
;alts = Resyclcomp, Ebay, returnCellComp, giveaway, donate, throw
;rows = all
;fact
;block=3
;model:
U(Resyclcomp) = a1 + b2 *priceL[0,1,2] /
U(Ebay) = b1+ b2 *priceH[4,5,6] /
U(returnCellComp)=c1 +b2*priceM[2,3,4]/
U (giveaway)= d1 /
U(donate)= e1 $
Very best wishes,
Anat

[Michiel Bliemer]

I did not mean to say that the alternative would be dominant, but MAY be (e.g., in case all your constants are close to zero; you actually set them to zero by not specifying the priors). Since you state not to have any idea about the parameter priors, there is no way to tell. If you put in priors that come from a pilot study or literature, then you provide more information and the design would be much better. Without providing any priors your design will not be efficient, as there is no information to optimise it on besides varying the levels as much as possible. Full factorial designs usually contain many questions from which not much information is gathered.

Yes you can have varying price levels even if you are estimating a generic price parameter, not a problem.

[Anat Tchetchik]

Thank you very much!