Hello all,
I have a tricky situation here. I need a % and SDs of drug-negative urine tests across a methamphetamine study for a meta-analysis.
However, the study brings the % and SDs of drug-positive urine tests. Let's say mean 89%, with SD=19%.
I have two questions:
1) Can we infer from this information that the main percentage of drug-negative tests is 11%?
2) Is the SD for drug-negative tests possible to calculate from this info?
Thanks in advance!
A little algebra shows that the mean of the negative proportions s is indeed 1- mean of positive proportions and the SD of negative proportions is the same as the SD of positive proportions.
suppose k studies, sizes N1- Nk
no. positives study k is nk
then mean of negative proportions (Mn) is
sigma (over k) (Nk-nk) Nk / sigma Nk = 1- sigma nk/sigma Nk = 1- mean positives (Mp) .
variance negative proportions is
sigma ( 1- nk/Nk - (Mn)) 2 / sigma N = sigma (1- nk/Nk -(1-Mp ) 2 /sigma N
=sigma (Mp -nk/Nk)2 / sigma n = variance of positive proportions.
SD = sqrt (variance)
Agree with @James Leigh answer.
Anyway, is an SD good interval estimate for your percentage of negative or positive tests? Distribution appears highly skewed.
Dear James Leigh , thanks for your thoughtful explanation. This make a lot of sense and makes me feel safer about my procedures.
Michal S. Karbownik those were arbitrary examples, but which do you suggest instead of SDs?
Thanks guys! Great discussion
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