Compare effect size to interval scaled mean... how?

Because of poor design choices at the begin of my work, I end up with what feels like a mess.
Do you guys know of any possibility of comparing an effect size, which I took from a Meta-analysis, with a variable conducted from my questionnaire? The variable would be the mean of an 11 point likert-scale (0-10).
Ive thought about transforming the effect size to r, transform the variable to 0-1 and put them up for a t-test...?!
I'm up for any suggestions, because at this point I can't change the design anymore.
Thanks for reading