B_Miner

03-03-2010, 07:50 PM

This is probably staring me in the face, but my face has been staring at it for many hours ... ;)

In basic power analysis of a mean, using the CLT, testing a lower tail hypothesis I have:

X_lower_critical = qnorm(alpha | mu_null, sigma/sqrt(n))

and also

X_lower_critical = qnorm(1-beta | mu_alternative, sigma/sqrt(n))

where qnorm is the quantile with alpha (or 1-beta) area to the left.

The author then says "standardizing X_lower_critical both way":

mu_null - qnorm(alpha | 0,1) * (sigma/sqrt(n)) =

mu_alternative + qnorm(1-beta | 0,1) * (sigma/sqrt(n))

Can anyone help me, how are they getting this last step?

Thanks!

Brian

In basic power analysis of a mean, using the CLT, testing a lower tail hypothesis I have:

X_lower_critical = qnorm(alpha | mu_null, sigma/sqrt(n))

and also

X_lower_critical = qnorm(1-beta | mu_alternative, sigma/sqrt(n))

where qnorm is the quantile with alpha (or 1-beta) area to the left.

The author then says "standardizing X_lower_critical both way":

mu_null - qnorm(alpha | 0,1) * (sigma/sqrt(n)) =

mu_alternative + qnorm(1-beta | 0,1) * (sigma/sqrt(n))

Can anyone help me, how are they getting this last step?

Thanks!

Brian