# Psychometric scale with items in sets where responses imply a rank order of items

My question is related to psychometry. One survey is measured in this way:

Question 1
Claim 1     0 1 2 3 4 5 M
Claim 2     0 1 2 3 4 5 M
Claim 3     0 1 2 3 4 5 M
Claim 4     0 1 2 3 4 5 M


There are 25 questions of this kind. Participants should choose one '0' and one 'M' and one number for every of the claims, but numbers shouldn't be the same. Results are 2 independent factors, which combined produce 4 types in profile. The theory is that those factors are independent.

My questions are:

1. Is there any literature which will explain this type of measurement?
2. How to measure alphas for this questionnaire or conduct factor analysis
3. Is there a way to see/count Pearson coefficients (or any other type of correlation) for this survey and some other which are measured in traditional way with Likert scale?

Edit: ie.

Question1:
I am calm and organized      0 1 2 3 4 5 M (My options are all of them, i choose 0)
I like to go to Gardaland    X 1 2 3 4 5 M (My options are all except 0, i choose 5)
Everyone is paranoic         X 1 2 3 4 X M (My options are 1, 2 3 4 and M, i choose 3)
My mother was a good person  X 1 2 X 4 X M (My option is M because 0 and M are mandatory)


after that there is question 2 to question 25 which follow the same format.

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Could you describe the following a bit better please? (update your question) "Participants should choose one '0' and one 'M' and one number for every of the claims, but numbers shouldn't be the same." I'm not quite certain what you mean. –  Steven Jeuris Jun 4 '13 at 12:31
Could you further elaborate? What does it mean to give a response of 0, 1,2,3,4 or 5? What does M represent? What do the "x's" represent in your updated example? –  Jeromy Anglim Jun 5 '13 at 8:20
Yes I can. It is personality test, based on C.G. Jung attitude and preferences. It uses attitude: introversion-extraversion factor and thinking feeling factor to combine four types: I-T I-F E-T and E-F. In this survey it is not measured attitude and preference directly. Instead of that Mentioned types (I-T ... E-T) are measured directly with four sentences (claims) in 25 questions. –  ICanFeelIt Jun 5 '13 at 9:46
Every sentence (claim) is measured by lickert scale 0 - 6. 6 is maximum 0 is minimum. and they are combined so only one answer of same kind could be choosen. So in one question it should be one 0 and one M, because it is mandatory to choose maximum and minimum. and beside that in 2 claims person can choose two numbers, but those numbers shouldnt be the same. ie s/he can choose 3 or 4, 3 or 5 etc... –  ICanFeelIt Jun 5 '13 at 9:50
I made survey on 750+ people with this and have interview after that (in 2 years) so i can witness that there is face validity, but i suspected that those are not induced by Jungian types. Instead i suspect on cognitive styles ie The Field dependence-independence mode or another... so my question could be reformulated: how to make comparison between this type of measurement and some other cognitive style instruments. –  ICanFeelIt Jun 5 '13 at 9:54

Okay. I think I finally get what you are saying. You have constructed a form of partially ipsative or forced choice scale.

In my words, I would say that you have 100 items in total. The 100 items are grouped into sets of 4 items, and you have 25 sets. Each item is rated on a 0 to 6 scale, and within each set participants need to give different responses for each item in the set. They must give a 0 and a 6.

This is a variant on the idea of rank ordering the items in a set. However, you would also get a little bit of additional individual difference information because participants are not just ranking items.

For further discussion, definitions, and a critique of ipsative tests see Johnson, Wood, and Blinkhorn (1988).

### References

• Johnson, C. E., Wood, R., & Blinkhorn, S. F. (1988). Spuriouser and spuriouser: The use of ipsative personality tests. Journal of Occupational Psychology, 61(2), 153-162.
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also when I have those 100 items. do i apply factor analysis or inner consistency test like data was collected with usual likert scale (like they are not grouped into sets of 4?) –  ICanFeelIt Jun 5 '13 at 15:48