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February 7th, 2014, 07:05 AM   #1
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Analysing Paired Comparison Tests


Google may have saved the day by bring up this place. 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

For each "x versus y" there is, there will be 5 questions. The first asking what the participants preference between the two is and then 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. because I can't figure out what is suitable or where the starting point should be 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.

x versus y = number of answers for each thing
A v B = 18 v 2
A v C = 16 v 4
B v C = 12 v 8
The above 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 parity. I can get that 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 to one side
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. From then, I should be able to replicate that in Excel, should I be applying other tests as well? Or do any others work with the set of information I am gathering?

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? ... sbk28m.htm

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.

Attached I have a picture of some fake results as I have not run the test proper yet.
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.
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February 7th, 2014, 07:31 AM   #2
Joined: Feb 2014

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Re: Analysing Paired Comparison Tests

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

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

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