adjusting pattern for larger needle/wool

[cavegrrl]

Hi every one...my first post here, but have been reading for a while...

I have a pattern for a winter hat for my kids. The pattern calls for size 2-3 needles and corresponding yarn. I made the hat and it is great but a little too thin for our winters. This year I want to make the hat in thicker wool, worsted and size 6/7/8 needles. How do i go about adjusting the pattern? Is there some sort of universal formula for this?

Thanks a bunch

Tanya