let's see ... say you have two overlapping distributions ... on the left,
the null distribution ... and on the right, the assumed to be true sampling
distribution ...
now, in setting up the power problem ... you have to set alpha ... say that
is a two tailed .05 test ... and really the upper critical value is of most
interest ... so, that value might be like a t of 2.02 ... to the right of
the middle of the null distribution ...
now, depending on what you are allowing power to be ... then, beta is 1 -
power ... so, say that power is desired to be .7 ... the beta will be .3 ...
that means on the true sampling distribution ... TO THE LEFT OF THE CENTER
OF THAT TRUE DISTRIBUTION ... beta will be the area FURTHER TO THE LEFT ...
or, in this case, the lower 30% of the true (distribution on the right)
sampling distribution ...
that is ... what is about the 97.5 percentile rank for the critical t value
at the upper end of the null distribution ... will be at the 30 percentile
rank value in the (hoped for) assumed to be true sampling distribution ...
would that not simply be the t value ... that produces the 30th percentile
rank?
let's assume for arguments sake .... n = 40 so, we have df = 39 ... in a
single sample kind of case ...
the critical value for the null (right side of the null distribution) would
be in minitab
MTB > invcdf .975;
SUBC> t 39.
Inverse Cumulative Distribution Function
Student's t distribution with 39 DF
P( X <= x ) x
0.9750 2.0227 <<< critical value for null test
MTB > invcdf .3;
SUBC> t 39.
Inverse Cumulative Distribution Function
Student's t distribution with 39 DF
P( X <= x ) x
0.3000 -0.5287 <<< critical value (where to the left will be
beta of about .3)
it helps to try to draw out two overlapping distributions ... fill in what
you know or want ... and then see about solving the problem you have to solve
MT
'm posting this message on behalf of my friend.
>Any help would be greatly appreciated.
=================================================================
Instructions for joining and leaving this list and remarks about
the problem of INAPPROPRIATE MESSAGES are available at
http://jse.stat.ncsu.edu/
=================================================================
