# Testing the importance of an item among a finite set of items

Consider the following survey question:

Q: How would you classify the importance for you of the following 5 items:

A
B
C
D
E


Assign to each item a number in the set {1,2,3,4,5}, with 1 meaning the highest importance and 5 meaning the lowest importance; the number used to an item cannot be used in any other item.

• How can one test whether item A is the most important item for a sample with 100 individuals?
-

The naive approach would be to compute the marginal distribution of rankings (e.g., mean score for each item), but it would throw away a lot of information as it does not account for the within-person relationship between ranks.

As an extension to paired preference model (e.g., the Bradley-Terry model, described in Agresti's CDA pp. 436-439), there exist model for ordinal or likert-type comparison data with or without subject covariates, as well as model for ranking data (baiscally, it relies on the use of log-linear model). Here is a short intro to the package, and a mathematical explanation in this technical report: Fitting Paired Comparison Models in R. You will find everything you need in the prefmod R package, see the pattR.fit() function which expects data in the form you described:

 The responses have to be coded as consecutive integers starting
with 1.  The value of 1 means highest rank according to the
underlying scale.  Each column in the data file corresponds to one
of the ranked objects. For example, if we have 3 objects denoted
by ‘A’,‘B’,and ‘C’, with corresponding columns in the data matrix,
the response pattern ‘(3,1,2)’ represents: object ‘B’ ranked
highest, ‘C’ ranked second, and ‘A’ ranked lowest. Missing values
are coded as ‘NA’, ties are not allowed (in that case use
‘pattL.fit’.  Rows with less than 2 ranked objects are removed
from the fit and a message is printed.