Determine if a test procedure is unbiased

[LBJking123]

I am asked to determine if a test procedure is unbiased.

I have the power function and all of that, but I can't figure out what I need to do to determine if the test is unbiased or not. I am guessing I need to find the expected value of the power function or something, but what is that supposed to equal if the test is unbiased??

Also when determining the size of a test, is it better to have a lower or higher size. I am comparing two procedures.

I am kinda lost, any help would be greatly appreciated.

Thanks!

 

[chiro]

Hey LBJking123.

What test statistic are you trying to prove un-biased-ness for?

Basically given a test statistic T that estimates theta, then you will need to show that E[T] = theta for all possible test statistics T that estimate theta.

 

[Stephen Tashi]

I notice the Wikiipedia article http://en.wikipedia.org/wiki/Bias_(statistics) gives a definition for an "ubiased" hypothesis test, which is distinct from the definition of an unbiased statistic. ( Gah! The terminology of statistics sounds like advertising hype. It over-promises what can be delivered.)