Statistics for Paired Comparisons - Head melting!

GTE

Hi there,

I am very much in the deep end coming from a practical background into the area of statistics, but I normally can work things out in my head so I need a bit of a push in the right direction. . . or a couple of pushes.

Here is the background to a paired comparison I am running soon.

There are three things being presented to participants.
A, B and C.

Participants will be presented these in paired comparisons.
A v B
A v C
B v C

Participants will do this 12 times. This means there are four instances of A, B and C.

First instance
A v B
A v C
B v C

Second instance
A v B
A v C
B v C

Third instance
A v B
A v C
B v C

Fourth instance
A v B
A v C
B v C

For each thing versus thing there is, there will be 5 questions. A preference and 4 questions about which of the things has more of an attribute.

So that is the test in full.

I just can't for the life of me make sense of the binomial tests, t-tests, chi-squared etc. I can't figure out what is suitable and oddly enough, the learning material never touched on paired comparisons.

My Thoughts
Lets take one instance with 20 participants dealing with just preference. With that figured out, it should be repeatable across the other questions and instances.

thing versus thing = number of answers for each thing
A v B = 18 v 2
A v C = 16 v 4
B v C = 12 v 8

This link tells me that all but the third paired comparison are statistically significant (95%). That is fine, it is saying that the first two show signs of significant preference while the third is judge to be roughly the same or

But I don't know how that was worked out and there is little point in me using a calc if I can't explain what the heck was going on! I read this, and my brain fried so I don't know if this is relevant or not.

With that issue put to the side, I think what I would want to do next is add up all the A v B etc. results across the 4 instances of the test and do those calculations again to see what it is like on the whole.

A is very different to B and C in term so of make up. Say A is an apple and B are two types of orange. That type of thing. Could I then get all the B preferences and C preferences, add them up and compare with the A preferences? I suppose that would be lopsided and not valid.


I have all the data collection sorted out in Excel, but it is just a matter of getting to processing what they mean. Lets say I figured out how the calculator does its job, should I be applying other tests as well? Or do any others work with the set of information I am gathering?

Thanks for any advice you can offer. Once I can get the logic of what is going on I can have a whack at creating that in Excel.

GTE

With A v B having 5 questions (preferences and 4 attributes), would I be right in saying that a chi-square test of contingency could be useful.

Lets say the bigger preference is B and in the contingency column there is some kind of attribute from another question, then the amount of times the attribute is listed can be see as a factor in B being chosen the most?

http://www.psychstat.missouristate.edu/introbook/sbk28m.htm

GTE

Final post before I rest my weary head.

I created a spreadsheet with some made up results to see what was what. It is pictured in the attachment.

In it, you can see the 12 paired comparison test with their 5 questions.
From top down, you can see the three things being compared to each other (A v B,A v C, B v C)

Except now I have given them their proper designations. On the right hand side, you can see the total of each question. Each paired comparison, A v B, is done 4 times so the totals from that are what are in the green section.

I just can not find anywhere which explains a binomial for preference or what could be suitable given a study of these types of results.

I would be particularly interested in if there was a way to see if the answers of space, envelop, clear and natural could in some way have a relation to the outright preference questions.

GTE

I came across a correlation equation (see attachment)

I used the the sum of the Trad preference score with the sum of the Trad Space score.
x= 70
x^2= 4900
y =60
y^2 = 3600
N = 160
xy=4200

For the top of the I got 667800 and for the bottom I got 779100*572400

The answer had an E in it, so confused I put a load of decimal places in and I got
0.00000149745432764301000000

The correlation equation info said I should be looking for answers around about 0 or around about 1. So that looks okay?