I'm working on a research and stumbled upon a study that evaluated participant scores to a 5-point Likert scale. I'm having trouble trying to interpret those results. I want to evaluate the correlation between the scores from the study with my own data (which is scored between 0 and 1).

My first instict was to simply divide the Likert scores by 5 but some thing seems inherently flawed about this method as I feel I'm missing out on a lot of information through this generalisation. Is there a standard way to doing this?

The study I mention only provides with the scores, participant count and basic criteria that the participants could choose from in the method. https://program.ismir2020.net/poster_1-02.html < here's the link to the study in case you want to take a look at it.

  • 2
    $\begingroup$ Dividing scores by 5 won't make any difference to (a) the result of any correlation or (b) whether a correlation with such scores is valid or defensible. Just because one variable ranges from 0 to 1 doesn't mean that the other variable must fall in the same range. More positively, you're losing precisely no information if you divide by 5, which can be seen by realising that multiplying by 5 is sufficient to restore the original values. $\endgroup$
    – Nick Cox
    Jan 12 at 15:20
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    $\begingroup$ The main point is that putting Likert scores into a (Pearson) correlation treats them as if they were measured values (meaning, on an interval or ratio scale). Many threads here touch on whether that is a good idea, and the spectrum of opinion ranges from purist (that's just wrong on principle) to pragmatic (try it and think to what extent it gives you helpful or interesting results). Using a Spearman or Kendall correlation is one alternative; ordered logit or probit modelling is another. $\endgroup$
    – Nick Cox
    Jan 12 at 15:22
  • $\begingroup$ So what you’re saying, if I understood you correctly, is that I could very well use a spearman r on the two varying scales and obtain a relevant correlation? $\endgroup$ Jan 12 at 15:38
  • $\begingroup$ Indeed; only ordinal scales are needed for that. But watch out, with lots of ties, which are inevitable, the correlation is, as it were, defensible but not necessarily helpful. $\endgroup$
    – Nick Cox
    Jan 12 at 16:44

I think the standard way is using ridit scores.

Suppose $x_i$ is the number of observations in category $i$ for $i=1, 2, 3, 4, 5$ and $N$ is the total number.

The scores are
$\frac{\frac{x_1}2}{N}, \frac{x_1+\frac{x_2}2}{N}, \frac{x_1+x_2+\frac{x_3}2}{N}, \frac{x_1+x_2+x_3+\frac{x_4}2}{N}, \frac{x_1+x_2+x_3+x_4+\frac{x_5}2}{N}$
Use these 5 values in place of the Likert scores 1, 2, 3, 4, 5.

  • $\begingroup$ This is essentially equivalent to Spearman correlation, as the latter will used midranks for a tied variable. $\endgroup$
    – Nick Cox
    Jan 13 at 14:15

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