It is in the APA style guide: "In addition to using words to express numbers below 10, use words to also express:

Numbers beginning a sentence, title, or text heading"

https://owl.purdue.edu/owl/research_and_citation/apa6_style/...

That is in tension with using numerals for "Numbers that represent statistical or mathematical functions, fractional or decimal quantities, percentages, ratios..." And the tie-breaker is below:

If you’re unsure which modifier to write and which to express numerically, try it both ways. Be sure the way you express the numbers is in the clearest way possible.

Yes but at least they are consistent with the pattern word of numeral, which is often a good rule to use if not employing a specific styleguide.

For example, using the APA guide[1] for numbers (thanks @OJFord for pointing out my error): “Six to 15”, “12 of 18”, Six of 24”.

Edit: As @temp8964 correctly pointed out, there are situations where words are recommended[2].

–

[1]: https://apastyle.apa.org/

[2]: https://apastyle.apa.org/style-grammar-guidelines/numbers/wo...

Switching within a phrase, like “six to 15”, strikes me as pointless hobgobblin-ey consistency, especially when the numbers are close to the cutoff.

I find it so much more jarring than either “six to fifteen” or “6–15.”

Don't you have that backwards? I'm not familiar with APA style guide but I was taught at school (UK) to use words below ten (at least, and to be consistent, i.e. saying 'ten' just then is fine as long as I don't now start saying '10' or '11') - I'd be surprised if APA advocated exactly the opposite, based on your example.

Hah! You're right, of course. My mind must have been elsewhere when writing the example, considering that I was literally reading the APA guide and thinking of the rule you laid out while at it.