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I wish to study the correlation of responses of 150 participants to two concurrently-administered previously-validated questionnaires (each giving numerical summary scores as output). Both questionnaires give off numerical scores that are directly proportional to perceived quality of life (higher scores = perception of better quality of life).

Since each participant will answer both questionnaires, I assume that this will be a case of paired analysis (one pair of scores from two questionnaires per participant) and the appropriate tool is the intraclass correlation coefficient. However, the feedback I received from one of our institutional statisticians details that I should use Pearson (if data is normally-distributed) or Spearman (if unlikely to be normally-distributed) correlation coefficient instead, which I think is more suitable for unpaired/independent data.

I would like to respectfully ask for another opinion on the aforementioned scenario. Thank you!

EDIT: As corrected by Stephen Kolassa, ..."Note that a normal distribution is not relevant for the choice between Pearson's and Spearman's correlation. Rather, decide whether you are more interested in a linear correlation (use Pearson) or in a more general monotonic one (use Spearman)..."

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    $\begingroup$ Why are you mentioning "intraclass"? What are the classes? $\endgroup$ Commented Dec 12, 2023 at 11:05
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    $\begingroup$ All these measures measure slightly different things of potential interest, and you may compute and report them all. Regarding the "normal distribution assumption", as always model assumptions do not need to be perfectly fulfilled (they never are), rather it would be of interest whether they are violated in a critical way, which we can't tell without seeing the data. Same regarding linearity by the way. $\endgroup$ Commented Dec 12, 2023 at 11:09
  • $\begingroup$ "you may compute and report them all" except the ICC, which has nothing to recommend it if you're considering there to be 150 groups with one participant in each. $\endgroup$
    – rolando2
    Commented Dec 12, 2023 at 15:08

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Since you are comparing two questionnaires which aim to measure the same "thing", you might be more interested in agreement than correlation. For example, two parallel lines with huge distance between them have a high correlation (1), but does not agree at all. There is a tag here that you could peruse.

One often used measure of agreement is which you could also have a look at.

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