# Decision error - (Nov/24/2009 )

Hello all,

Sampling size has always been a headache for me. I've read that for most sampling sizes, one can opt to use the following formula

N> <(1.96)(1.96) (0.5)(0.5)> / <(0.05)(0.05)>

And it will give a size of about 384.

But recently I've seen in certain studies which apply the following formula instead.

N> <(1.96)(1.96) (0.5)(0.5)> / <(0.1)(0.1)> which gives a sample size of around 96.

Now I understand that the changes is for decision error as in the range of error which we allow. But why such a change is acceptable in certain studies?

Thanks in advance.

The error is the same in both instances (that’s where the 1.96 comes from).

In the first equation the analyst is expecting the difference between the means to be about 0.05 (10% of the size of the standard deviation =0.5), in the second equation the analyst is anticipating the difference between means to be greater (20% of the size of the standard deviation) and thus can use a smaller sample size for the same degree of error.