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For my data (based on 5-item numeric likert scales), I have tried to calculate correlations. As the data is not normally distributed (according to a Shapiro-Wilk test), I have used Spearman correlations.

For most of my variables, Spearman correlation results and scatter plots agree - results are not significant and I can't see any relationship in the scatter plots - unfortunate for my hypotheses, but at least not confusing. However, for one case, the scatter plot looks like there is no relationship, but the Spearman correlation is significant (and negative which is also very much against my hypothesis and previous literature).

So now I'm just really confused on:

  1. whether I've done it right, and
  2. which result is right?

EDIT: I have now added jitter to the plot, please see the attached picture below. However, I am still not quite sure on what the right answer is - is the correlation right or the scatter plot (or can I just not see any relationship in the plot, but it exists)?

EDIT 2: I have now ranked the data first and then added jitter to the new plot. Looks very similar to the non-ranked one though, so not sure if I did this right! As I can only have two pictures in here, please let me know if you need the correlations back and I will gladly add them instead

Scatter Plot with Jitter and Ranks

Scatter Plot with Jitter

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  • $\begingroup$ In some sense, a p-value of 0.045 means that if you look at ~20 random datasets, you'd expect to see this result. It is not overwhelmingly significant. It just means that there is some chance the null hypothesis is false. $\endgroup$ – Ami Tavory Jul 26 '17 at 16:26
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    $\begingroup$ Also, since you mention plural variables (as in "most of my variables"), you might want to do a Bonferroni correction here. That is, multiply the p-values by the number of variables, and only then see whether they are below some threshold. $\endgroup$ – Ami Tavory Jul 26 '17 at 16:29
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    $\begingroup$ 1. You're judging something other than statistical significance by eye; you shouldn't expect it to correspond. 2. The discreteness is an issue with the plot; you can't hope to even judge whether there's a positive, negative or other relationship unless you can see how many points are plotted on top of other points. $\endgroup$ – Glen_b Jul 26 '17 at 23:52
  • $\begingroup$ @AmiTavory Thank you for your input. I have tried to establish relationships between different independent variables (e.g. internal motivation, external motivation) and the same dependent variable (job suitability ratings). Not sure if a Bonferroni works then? $\endgroup$ – Leonie Evian Jul 27 '17 at 11:15
  • $\begingroup$ Several useful points have been made about your comparison. First, scatterplots do not test significance. Next, many data points can be masked by a single point on the plot. Moreover, visualizing the full set can create an unhelpful blur. Given that, the schematic structure of the relationships between x and y might be better captured if you were to average the information by the 15 (or so) buckets on the x-axis and plot the reduced results (15 or so data points) from that against y. $\endgroup$ – Mike Hunter Jul 27 '17 at 12:40
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There are two points to bear in mind here:

  1. The Spearman correlation is based on ranks, not the original data.
  2. You have a lot of data plotted on top of each other such that you have lots of mass at certain points, but you can't see that in your plot.

The rank issue is probably not as big a deal here, although you might as well convert your data to ranks and plot those. Then, you need to jitter your ranks slightly and make them semi-transparent to better see what's going on. I don't have access to your data, but you can get the idea from my answer here: How to extract information from a scatterplot matrix when you have large N, discrete data, & many variables?

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  • $\begingroup$ Agree. @Leonie, request jittering or bloating of the identical values on the plot. $\endgroup$ – ttnphns Jul 26 '17 at 16:58
  • $\begingroup$ @ttnphns, what is "bloating"? $\endgroup$ – gung - Reinstate Monica Jul 26 '17 at 17:07
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    $\begingroup$ gung, bubble where the size is defined by count. $\endgroup$ – ttnphns Jul 26 '17 at 17:21
  • $\begingroup$ @LeonieEvian, turn values into ranks, then plot and add jitter. Your eye then could discern little negative correlation (add regession line, too) $\endgroup$ – ttnphns Jul 27 '17 at 11:17
  • $\begingroup$ @ttnphns I just did, thank you for all your efforts. Looks highly similar to the old (non-ranked one) though...? $\endgroup$ – Leonie Evian Jul 27 '17 at 11:38

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