# How to find sample size give the power of each test at 80%

• Jan 20th 2014, 08:29 PM
nivek0078
How to find sample size give the power of each test at 80%
Hello,

I am very confused on how to solve the problem below. How do I find sample size n based off an 80% power? Also how do I find the standard deviation. Are these the right equations to use? http://sphweb.bumc.bu.edu/otlt/MPH-M...wer/Power4.png and http://sphweb.bumc.bu.edu/otlt/MPH-M...wer/Power5.png if so what is Z1-B , u1 and u2 equal to?

Consider a scenario where a drug company has 100 compounds for treating a type of cancer. Unbe-
knownst to the company, only 10 of the compounds are aff ective and the other 90 are of no value (i.e.
they do not work). For each compound, the company does an experiment and tests the aff ectiveness of
the compound using a hypothesis test with signi cance level = 0:05. They choose a sample size for
each experiment so that the power of each test is 80% which is a standard value. What percentage of
the compounds found to be a ffective from the testing actually work? To answer this, do the following
parts:

a) For each test of a compound, state in words the null hypothesis for the statistical test.
b) How many of the a ffective compounds would you expect to be found to work? Why? (Round
c) How many of the non-aff ective compounds are expected to be found to work? Why?
d) From parts (b) and (c), what percent of compounds found to be a ffective actually work?
e) The term \false discovery rate" (FDR) is the proportion statistically signifi cant results which are
actually false positives. What is the FDR in this example?

Nivek
• Jan 21st 2014, 12:46 AM
chiro
Re: How to find sample size give the power of each test at 80%
Hey nivek0078.

The first thing you should do is figure out what the test statistic and its distribution is. Once you do this you can then figure out the power by solving the various unknown (sample size given a specific power). If it is a normal distribution, then you should check if the above equations are adequate.

I say this because it will help you understand what is really going on and how these problems are solved from first principles.
• Jan 21st 2014, 06:20 PM
nivek0078
Re: How to find sample size give the power of each test at 80%
Thank you Chiro for your response.

This is what I have so far:

Power = P(rejecting Null / when Null is false)

Null hypothesis = compound doesn't work

P(Ho Fc / Ho F) = .8 or written a another way it is P(concluded False / False)

P(conclude effective, effective)
=> P(Ho Fc / Ho F) = P(Ho Fc / Ho F) x P(Ho F)

So am I going in the right direction? If so where do I go from here to solve the problem? How do I correctly break this down?

Nivek
• Jan 21st 2014, 07:54 PM
nivek0078
Re: How to find sample size give the power of each test at 80%
I'm still greatly confused on how to find the sample size when no means or standard deviation is given. I tried to go a different route with the equation below trying to solve for n but without knowing sigma or the error E i can't do it. So my question is how do i solve this problem.

E equals z of alpha over 2, times sigma over square root of n
• Jan 22nd 2014, 12:48 AM
chiro
Re: How to find sample size give the power of each test at 80%
Can you tell me what your statistic and distribution for said statistic is?
• Jan 22nd 2014, 04:14 AM
nivek0078
Re: How to find sample size give the power of each test at 80%
Chiro thank you for responding. Since the information is not given for the distribution I am assuming it is normally distributed. As far as the test statistic that's where the problem lies! The only information given is what is stated in the problem which is the significant level = .05 so the confidence level is 95%, the power that they want to use is 80%, total number of sample = 100 and the fact that 10 of them work and 90 of them don't. The problem does not provide a mean or standard deviation to compute a proper answer. I am assuming that since the total number of sample is 100 that the mean is 50 but I could be wrong. I honestly do not have a clue how to solve this!