# Share of preference sig testing

I have a simulator built in excel that includes individual part worth utilities, and individual share of preference.

I'd like to test for sig difference in SOP between 2 mutually exclusive groups (cell1 and cell2).

From previous posts that I saw on the topic, I saw that this can be done utilizing a t-test.
t = (cell1 share - cell2 share)/sqrt( (SE cell1)^2 + (SE cell2)^2 )

My uncertainty is how to calculate SE for the 2 cells.

Should SE for a particular cell =

(1) sqrt(share*(1-share)/n)
where 'share' = the aggregate level share, reported in the simulator for that cell

OR

(2) SE = standard deviation of respondent level shares within that cell/sqrt(n)
where n = the size of that cell.

Thank you.
asked Apr 23, 2012
retagged Sep 13, 2012

## 1 Answer

0 votes
Your equation #1 will work if you are using a First-Choice rule simulator.  (Each respondent fully gives his vote to just one product).

But, if you are using a method that "splits votes" such as Share of Preference (Logit Rule) or RFC, then you'll need to estimate the standard deviation of the shares across respondents, and divide by sqrt(n).
answered Apr 23, 2012 by Platinum (154,105 points)
Thank you so much for the response Bryan.  We're not simulating first choice, but rather share of preference: 'split votes'.

One follow up question:  We asked category frequency in the questionnaire as well, and would like to account for this when reporting SOP in the sim by weighting the shares by the respondents volume.  To stat test these weighted shares, I would need to calculate the effective base to use as 'n' in the t-test formula, correct?
effective base = {(sum of volumes)^2}/ (sum of the squared volumes)

Thanks again Bryan.  Greatly appreciated.