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I am working on my MSc dissertation findings and I have data results from two 5-Point Likert scales. One Likert measured self-assessed behaviour, whilst the other measured attitude. (Both scales were labelled strongly disagree to strongly agree).

My hypothesis is that respondents who attributed a high score on one Likert will do the same on the other Likert.

Both population samples were the same (i.e. I distributed one survey, and the same respondents filled in both Likert scales at one point in time), so I understand that I must carry out a related samples tests.

Would I be correct in using Wilcoxon signed rank test?

I tried charting a scatterplot and carrying out correlation analysis but the output doesn't seem to make sense:enter image description here

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  • $\begingroup$ Thanks for your reply. I tried applying Spearman's but the first step is to determine if there is a monotonic relationship. With the dataset I have (17 responses), I'm having a hard time interpreting the scatterplot depicted above. $\endgroup$
    – YasG
    Commented Aug 10, 2023 at 6:32
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    $\begingroup$ Unfortunately, even if you have a larger sample that scatterplot might not be very helpful. You have limited number of categories in each variable. Maybe a different visualization helps, see this question. For small samples, some people recommend Kendall's Tau but I am not sure. $\endgroup$
    – T.E.G.
    Commented Aug 10, 2023 at 6:51
  • $\begingroup$ And sorry I deleted my previous comment by accident (on mobile). $\endgroup$
    – T.E.G.
    Commented Aug 10, 2023 at 6:53
  • $\begingroup$ Thank you!! I was thinking of carrying out a visualization instead of statistical testing, but I couldn't find different types of visualizations techniques. I'll try a heat map instead and see if my tutor is fine with it. $\endgroup$
    – YasG
    Commented Aug 10, 2023 at 8:59

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You seem to be interested in (at least) two things: 1. A test of whether the scores are the same on the two scales and 2. A plot of the scores.

For the plot, a simple variation to your scatter plot is to add jitter. This works well unless N is quite large. If jittering isn't enough, you can also make the points smaller, or transparent.

For the test, it depends on what exactly you are interested in. Although it is not strictly correct to take the mean of a Likert scale, it is often done, and probably doesn't distort things too much. You could also test medians (which are fine for Likert scales). But maybe you are interested in something else. For the medians, Wilcoxon signed rank is a fine choice.

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