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I want to compare the number of lesions worsening and non worsening on superior to inferior side of the eye of a group of patients. I want to compare if the proportional results (the total sum of worsening and total sum of non worsening in the superior vs inferior side ) have a significant difference. In my data I have:

  • worsening 2618 (66.8%) INFERIOR

  • non worsening 1298 (33.1) INFERIOR

  • worsening 2981 71.4% SUPERIOR

  • non worsening 1190 28.5% SUPERIOR

Which method should I use since these proportions are dependent (it comes from the same patient), but not paired(there is no before after rather different locations)?

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1 Answer 1

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Those are definitely paired. Pairing is not restricted to 'before-after' comparisons.

Anything where within-pair values (like values from two locations on a single patient) would tend to be more alike than out-pair values (values from the corresponding two locations on two different patients) are paired.

(This is a disturbingly common error -- presumably there's some widely-used elementary books promulgating this mistaken notion.)

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  • $\begingroup$ Thanks for clarifying, however when I look up in the literature which method use to compare proportions I found chi square for independent variables, which method should i used for proportions if these are dependent variables? $\endgroup$
    – D.Vega
    Nov 12, 2018 at 22:50
  • $\begingroup$ It's not clear what your null and alternative hypothesis is when comparing four proportions. Can you clarify? (It will likely be some form of chi-squared test, but more information is needed). Is the fact that the first pair of percentages and the second pair don't quite add to 100% just rounding error or is there a (tiny) third category? $\endgroup$
    – Glen_b
    Nov 12, 2018 at 23:22
  • $\begingroup$ You are right, there was a rounding error, well I like to compare first the proportions of worsening category (INF 66.9 vs SUP 71.5) and compare the proportions of non worsening as well (INF 33.1 vs SUP 28.5) and I would have two result for statistical significance $\endgroup$
    – D.Vega
    Nov 12, 2018 at 23:53
  • $\begingroup$ Thanks for the clarification The two comparisons are dependent, since 66.9 = 100-33.1 and 28.5 = 100-71.5. If one is different it would imply that the other is. $\endgroup$
    – Glen_b
    Nov 12, 2018 at 23:55
  • $\begingroup$ I wasn't clear sorry about that, My null hypothesis: no difference in proportions between sup e inf, I want to compare just two proportions but the chi square didn't seem appropriate because it assumes these 2 proportions are independent when in fact are dependent hence my confussion. I really appreciate your help Glen_b!! $\endgroup$
    – D.Vega
    Nov 12, 2018 at 23:57

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