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I work in the corporate research space producing white papers from survey data. When writing up results of these investigations, our writers are inclined to use the term 'likely' when referring to differing proportions among binomials variables. Example:

Group A: 28.6%, Group B: 22.4%

"Group A is more likely to engage in XYZ than group B."

Now, without having conducting logistic regression on the actually likelihood of the event arising under either condition I tend to be quick to stifle this terminology in favor of more context-appropriate wording. Am I being over-sensitive to their creative license given that this isn't an academic paper, or is this appropriate?

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  • $\begingroup$ I think your example language is problematic and should be edited to read "Individuals [or whatever the unit of analysis is] in group A are more likely to engage in XYZ than individuals in group B." $\endgroup$ – Alexis Nov 8 '19 at 16:02
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    $\begingroup$ Also: your colleagues are not using "creative license", but the plain language meaning of "likely". I just checked four English dictionaries, and the first definition for "likely" was as a synonym for "probable" which is on point. :) $\endgroup$ – Alexis Nov 8 '19 at 16:04
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If the scale of the survey is adequate and sampling is random from the population of interest, then the plain-English usage here should be OK.

If all you care about is a difference in frequency of XYZ between 2 groups, you don't need to do logistic regression; a simple Fisher exact test or chi-squared test can determine if the 2 groups differ. In your particular example, a quick check indicates that your particular example would be statistically significant at the usual p = 0.05 level provided that there were more than 400 or so individuals sampled from each group.

You generally don't just want to know, however, if behaviors are "more likely." To make informed decisions about resource allocations you typically want to know how much more likely and how certain you are about the magnitude of the difference. So providing confidence intervals for the estimated frequencies would be much more informative.

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