On Wed, 14 Apr 2004 15:47:58 GMT, "Luigi" <[EMAIL PROTECTED]> wrote:
> Hello to everyone, > > I have a question for you. > I have a two samples and I need to run a test on percentgate. > > Suppose to have the following two samples: > > N_1: 100 > N_1: 100 [ oops, N_2=100 I presume] > > P_1: 70% > P_2: 56% > > If I run a two-sided test I get p=0.0416 (4.16%) > > Therefore the difference is significant if I consider alfa=5% (type I > error). > > But what about the beta error (type II error)? How can I compute beta? > Notice, you did not "compute" alpha: You set it, to 5%, then proclaimed an 'apparent difference' -- making you subject to being guilty of Type 1 error, falsely proclaiming a difference, if that was by chance.. Since you proclaim a difference, you are not guilty of *missing* a real difference, which would be the Type 2 error. If you assume that the underlying rates are actually 70% and 56%, then you could ask, "What is the power for a 5% two-tailed test, comparing two samples of 100?" - Power is (1-beta), and power is what is usually tabled and discussed. - Since the sample did show the difference, the power is above 50%; since it did not show the difference very strongly, (4%) the power is not *much* above 50%. For that question, the beta-error is thus about 45% or so (power 55-60%). i would find the exact power by computing the 2x2 chisquared as the test, and using the chisquared or the phi as entry into the appropriate table in Cohen's text. For something *this* straightforward, I would consider using a computer program to show various powers for various comparisons. -- RIch Ulrich, [EMAIL PROTECTED] http://www.pitt.edu/~wpilib/index.html . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
