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I am working with ordinal data (produced from Likert-types scales). I am of the understanding that results should be presented as a mode, which makes sense to me. However, when working in SPSS and utilising the Kruskal Wallis test, results are presented as a median (or mean rank).

I am therefore a little confused as to how best to present this data.

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  • $\begingroup$ "Present" in what sense? Do you just want to provide descriptive / summary statistics in a paper? Something else? $\endgroup$ – gung - Reinstate Monica May 9 '17 at 17:03
  • $\begingroup$ Perhaps present was the wrong word. I suppose I am looking more to understand why SPSS would present these as medians when ordinal data is more usually presented as a mode. $\endgroup$ – RStev May 9 '17 at 17:55
  • $\begingroup$ So is your question really just, 'why would the median be used to summarize ordinal data instead of the mode'? $\endgroup$ – gung - Reinstate Monica May 9 '17 at 19:23
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    $\begingroup$ The median can be defined without too much difficulty for ordinal data because ... they can be put in order. That's the easy bit. In practice ties can reduce its utility. The more contentious bit is to argue that often the mean works well in practice for ordinal data, whatever the measurement theorists say. More in stats.stackexchange.com/questions/67551/… and in @David Lane's answer. $\endgroup$ – Nick Cox May 10 '17 at 0:48
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    $\begingroup$ "How best to present the data" isn't only determined by its classification in Stevens' typology.-- your own needs, those of your audience, the particular things you're trying to convey and so on are all part of choosing. The median can be calculated on ordinal or higher on Stevens' scale, the mode on any of them. ... Why not present both? $\endgroup$ – Glen_b -Reinstate Monica May 10 '17 at 9:24
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One of the inherent problems of nonparametric statistics is that they, by definition, don't provide inferences about population parameters. Although it is theoretically possible to make up a situation in which comparing means on an ordinal scale would be misleading, such situations are very rare in the real world. I would recommend comparing means using ANOVA. See this article for more information: http://link.springer.com/article/10.1007/s10459-010-9222-y

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    $\begingroup$ Nonparametric statistics can certainly provide inference about population parameters (in the case of the Mann-Whitney, for example, the inference is about the Hodges-Lehmann difference -- $\text{median}(X_i-Y_j)$ for $i$, $j$ randomly selected from their populations) . If a difference in means was a suitable thing for the inference in this case, one could perform nonparametric inference about the difference in means quite easily, such as via a permutation test. What makes nonparametric tests nonparametric is that the distributional model is not finite-parametric. $\endgroup$ – Glen_b -Reinstate Monica May 10 '17 at 9:27
  • $\begingroup$ Thanks, I was not previously aware of pseudo medians. $\endgroup$ – David Lane May 10 '17 at 15:55
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Much of this is discussed in our classic thread on the topic: What are good basic statistics to use for ordinal data?

The classical thinking on the topic is that data can instantiate one of a set of levels of measurement (nominal, ordinal, interval, and ratio). While I think this theory is generally overblown, the standard recommendation is to use means to represent the central tendency of continuous (interval or ratio) data, medians to represent ordinal data, and the mode (potentially) to represent nominal data. The reason to choose the median is that it carries more information about the distribution than the mode and it is unambiguously acceptable for ordinal data (e.g., using the mean could be controversial, see: Calculate mean of ordinal variable). In truth, the mode is rarely ever used in my experience.

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