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I have several 5-item likert scales and would like to compare the results between different surveys.

Is there any logical way to score the likert results and compare? Averages don't seem to capture any differences, especially with the restrictive 1-5 scale.

Ideally, I would like a metric that represents the relative standing of the particular survey's likert results within the population of surveys either by question or overall.

Ex.: following table shows avgs by question; I also have individual data so some sort of ANOVA could be used as well.

╔══════════╤═════╤═════╤═════╤═════╤═════╗
║ Question │ S1  │ S2  │ S3  │ S4  │ S5  ║
╠══════════╪═════╪═════╪═════╪═════╪═════╣
║ Q1.avg   │ 3.1 │ 2.2 │ 4.4 │ 5.0 │ 4.6 ║
╟──────────┼─────┼─────┼─────┼─────┼─────╢
║ Q2.avg   │ 2.6 │ 4.8 │ 4.5 │ 3.1 │ 2.2 ║
╟──────────┼─────┼─────┼─────┼─────┼─────╢
║ Q3.avg   │ 2.7 │ 1.1 │ 2.9 │ 2.6 │ 4.4 ║
╟──────────┼─────┼─────┼─────┼─────┼─────╢
║ Q4.avg   │ 3.9 │ 3.3 │ 3.9 │ 3.7 │ 4.1 ║
╟──────────┼─────┼─────┼─────┼─────┼─────╢
║ Q5.avg   │ 4.3 │ 2.8 │ 4.2 │ 1.7 │ 3.6 ║
╚══════════╧═════╧═════╧═════╧═════╧═════╝
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"Likert scale" has two different meanings. The more technical meaning is that it refers to a set of say 10 different questions, each measured on a five-point scale, where you sum together the answers from all of these questions. As far as I know, these are almost always analyzed by computing an average.

If you mean that you have a five-point rating measuring agreement, which is commonly called a likert scale as well, then you need to split apart how you present the difference versus how you test for differences.

When dealing with presentation, the norm is to either compare the averages, as you have done, or, to compute the percentgage of people who chose the two highest options on the scale (e.g., Somewhat agree + Strongly agree), and then compare these percentages. Depending on the data there can be other ways as well (e.g., just compared Strongly Disagree, or compare Strongly Agree - Strongly Disagree).

In terms of testing, an ANOVA may well be fine, but it would be more orthodox to use either an ordered logit model or a nonparametric test (e.g., Mann-Whitney).

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  • $\begingroup$ The scales are strongly disagree-strongly agree (but basically 1-5). I am using Kruskal-Wallis to evaluate differences between demographics within each survey and that seems to work well, but how could the same method be applied to finding differences between the surveys. Averages seem to remove a lot of the variance (ie some score high, some score low=avg of 3). This effect is compounded when the individual questions are scaled up into an overall/categorical score. Any advice? $\endgroup$ – UBHDNNX Feb 28 '19 at 16:02

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