# testing for significant diffs between proportions

#### TonyW

##### New Member
Thanks for stopping by,
I have a question about analysing responses from a multiple choice question.
I'm looking at a question on what topics people talk discuss most online- there was a list of about 30 topics, and participants were able to pick more than one option.
I'm not sure how to test if there is a significant difference between the two most popular options- of if that is even possible.

The top 3 are:

Movies -62%
Music -60%
COmedy – 55%

movies ranks first, but if the margin of error is +/- 5 %, the difference between movies and music is not actually statistically significant, right?

So my question is, what test do you use to show which proportions are significantly higher, aside from eyeballing it?
I've thought of using a z-test for proportions, but that is for 2 independent samples... http://www.dimensionresearch.com/resources/calculators/ztest.html
But these aren’t independent samples, right? They’re the same sample!
But it’s not like it’s a pair-wise design either....
Chi – square also works to show that there is a statistical difference between the different options, but doesn’t show which ones are different: music and movies don’t have to be significantly different to get an overall significant difference.
Right?
Is a z-test for proportions legitemate? I've read through a bunch of textbooks and websites and can't find anything that deals with this particular problem.
Thanks!
-Tony

Last edited by a moderator:

#### pmcc

##### New Member
I'm taking a wild guess here: the Wilcoxon signed-rank test? [EDIT: oops, that's not it. sorry, I noticed the assumption of independence too late]

- my 2 cents

Last edited:

#### spunky

##### Can't make spagetti
have a look at:

Wild, C.J. and Seber, G.A.F. (1993) "Comparing Two Proportions from the Same Survey" from the American Statistician, Vol. 47, No. 3.

i think you should be able to reproduce the logic of how to modify the test for independent proportions in order to test dependent ones.

ps-this question is NOT as easy as it sounds

#### spunky

##### Can't make spagetti
Is a z-test for proportions legitemate?
Nope, it is not because, as you correctly identified, these are not independent proportions. kudos to you for noticing what 99.9% of people who test proportions dont (and then they're left wondering why their manuscripts get rejected... )