Now we know that precision expresses our level of certainty about an average.
But how do we use precision to weight our studies?
In simple terms, you do that by multiplying each study’s results by its precision before you combine your results.
In reality, statisticians have to take one more step. To make the formula work properly, they have to standardize the precisions, so when they’re all combined they add up to 1. If you’re curious, they do this by dividing each weight by the sum of all the weights. This is just another way of making sure the weights are all on the same scale.