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If I were to give out a survey with questions based on a visual-analog scale, and I want to compare the results for each of these, which statistical test is generally the most appropriate?

If for example:

  • Q1 asked about the warmth or reception to the color Blue, given a visual-analog scale from 0 (extreme dislike) to 100 (extreme like)
  • Q2 asked about the warmth or reception to Babies, given the same scale.
  • Survey distributed to 1000 people
  • I want to know if people are generally more receptive to the color Blue vs. Babies (in reality the true question would be more comparable than color to baby).

My understanding here is:

  • The answers to the questions come from the same person => Does this automatically imply sample dependency and toss out t-test / Wilcoxon Ranked Sum? Or if I check the cor(Q1, Q2) to be roughly 0, can I claim independence?
  • The responses are inherently ordinal, which makes the mean values of the scores less meaningful than the rank. Can we automatically impose linearity here? My gut says no.
    • Sample size large enough for CTL to say sample distribution of means will be normal.

So ultimately... which test do we use?

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VAS scales from 0 to 100 are usually treated as continuous. I don't see a reason to treat them as ordinal here, but, if there is one, you can elaborate. Many variables are in a sort of gray area between ordinal and interval.

The simplest way to deal with the paired nature of the data in this case is a paired t-test. That will compare the means, which I think are meaningful. If you prefer (or if the assumptions of the paired t test are violated) you can use Wilcoxon signed rank test. In fact, that might even be a good starting point; it is almost as powerful as paired t test, even when the assumptions are met, and your N isn't small. The drawback is that it is less familiar than the paired t-test -- whether that is critical depends on your audience.

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  • $\begingroup$ Thanks Peter. I suppose my rationale was that if I have a value of 50 for 'Neutral', is it meaningful to treat that as 1/2 of the value of 100 for 'Very Receptive'? Or, does one 'Extreme Like' and one 'Extreme Dislike' average out to 'Neutral' in a meaningful way? With this in mind, can we really consider this to be ratio data? $\endgroup$ Nov 4 '19 at 18:19
  • $\begingroup$ Using "half" would imply ratio scale data. T-tests do not require that, only interval scale. So, is the difference between (say) 0 and 10 equal (in some sense) to the difference between 40 and 50? $\endgroup$
    – Peter Flom
    Nov 4 '19 at 18:37

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