Emil O W Kirkegaard

so you want to plug in d, n1, n2, reliabilities and get corrected d?

I mean you could do that but it would only look more messy and not add any information, would it?

2*((d/sqrt(d^2 + ((n1 + n2)^2/(n1*n2))))/sqrt(rl1 * rl2)))/sqrt(1-((d/sqrt(d^2 + ((n1 + n2)^2/(n1*n2))))/sqrt(rl1 * rl2))^2

with rl1 and rl2 being the reliabilities. but if I was doing that in my code, I'd prefer multiple lines, way more readable

aaaah, okay! Now I see. I actually think that the multiple line solution is neater, don't think you can simplify much

with n = n1, m = n2, a = rel1, b = rel2: https://www.wolframalpha.com/input/?i=simplify+2*((d%2Fsqrt(d%5E2+%2B+((n+%2B+m)%5E2%2F(n*m))))%2Fsqrt(a+*+b)))%2Fsqrt(1-((d%2Fsqrt(d%5E2+%2B+((n+%2B+m)%5E2%2F(n*m))))%2Fsqrt(a+*+b))%5E2 …

the alternate form assuming all numbers are positive is actually quite okay, isn't it?