I have conducted an online survey and used ordinal rating scales to measure 5 different variables. Each of these variables were measured by 3 different questions. All used the same 1-5 likert scale rating.
I have found the median of each of the 3 questions. This is a number between 1 and 5 that is now the final score for each participant for each variable I measured - is this final number still ordinal data?
Annie Paul-Baig Yes, the median of 3 ordinal scale items is still ordinal. Though, I question how well three items accurately reflect the central tendency.
For instance, if a participant answered as follows on the three items:
Strongly agree = 5
Somewhat disagree = 2
Strongly disagree = 1
their median is 2 = somewhat disagree. However, their scores range from the highest to lowest rank. This may actually be a case where using the mean would be the better option (*despite the aversion by some of using the mean from ordinal items)
Hi,
with having a 5 point rating scale, you have two options
1) you are strict and perceive it as ordinal. The implies that you cannot do anything such as computing means, sums etc.
2) you believe that the scale is at least approximately interval-scaled (which I would do). Then you can do all the stuff but you really shouldn't use the term ordinal anymore. You cannot have it both ways.
Having "ordinal" in a sentence together with "I computed xyz" is a red flag :)
All the best,
Holger
I agree with Holger Steinmetz about your options. If you want to determine whether you can treat create 5 scales, the first step is to assess coefficient alpha for each of them. (When you do so, be sure that each set of 3 variables is coded in the same direction, i.e., all positive correlations).
Hi all,
two more ideas.
1) In my view, you could conduct a scatter plot with each ordinal indicator and some validation criterion and add a spline to it (i.e., a curve). if this spline is approximately linear (and has no jumps), I would assume interval scaling.
2) With regard to computing alpha: a) makes only sense when the data generating process underlying the variables is a common factor model and b) the loadings are identical. If "a" is correct (check this first with a CFA) and "b" not, better compute Omega. If neither is correct (and you have rather an index then a reflective scale), then don't calculate internal consistency estimates. Then the only way is re-test reliability.
HTH
Holger
Seems to me that applying 'mode', 'mean' etc.--which implies also using a concept of specific distance between points---to ordinal data represented by Likert scale numbers can only ever give you a 'kind of' accuracy in determining survey responses because ordinal 'distance' as represented by the wording behind the numbers (e.g. 'strongly agree', 'agree' etc.) is subjective.
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