I am analysing a simple study where users were asked questions on 5-point likert scales. I use interquartile range (IQR) to assess the variability in the answers of the respondents. In particular, I want to

  1. somehow compare the difference between treatment and control groups (especially the difference in count of positive/negative ratings) to the within-group variability, and
  2. assess whether the two groups have similar variability.

Note that I am not doing hypothesis testing, I just want to let the reader have some intuitive understanding of the amount variability.

The problem I see is that the IQR is often the same even though intuitively the variability is different. For example:

Group A: 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4
Group B: 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3

In both cases, the lower quartile is 2 and the higher quartile is 3, so IQR is 1, although group A is intuitively more polarised on the subject.

My idea is to report something along those lines: "Group A and B have the same IQR, but in group A 62% of responses fall within IQR, while in group B it is 100%"

Is there any standard way of measuring/reporting ordinal data variability with better precision than IQR? The reader can always check bar charts of the data, but quantifying the variability seems useful.

  • 1
    $\begingroup$ What is wrong with a boxplot? Include the FNS and then you have both. $\endgroup$ – mandata May 5 '15 at 14:19

Personally, I don't shy away from using standard deviation on likert scales, but there are other measures that might make you more comfortable. Like mean absolute deviation or median absolute deviation. Few people are familiar with these statistics, however. Likert scale statistics are often presented in terms of what the questioner cares about, such as "50% in the two top boxes." So you might consider something like that, such as 100% in the three middle boxes for B and 13/16% in the three middle boxes for A, which suggests the split responses in A.

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