About Vivian Expertise I can answer questions on probability, distributions, statistical inference, statistical estimation, hypothesis testing, analysis of categorical data, linear regression, generalized linear regression, ANOVA, and linear mixed models. I cannot answer questions on stochastic processes.
Experience I have worked as a research assistant at the University of Michigan, Ann Arbor for two years.
Organizations American Statistical Association
Education/Credentials University of Michigan, Ann Arbor
Master of Science
Question Simplified terms: If n=75 and population "A" is 10,000 and population "B" is 10,000,000. Would n=75 for both populations provide an unbiased representative test.
Answer Whether a test is unbiased or biased is not dependent on the sample size. Also, whether an estimator is unbiased or biased is not dependent on the sample size. But, to control error probabilities (Type I Error probability and Type II Error probability), you have to control your sample size. But it is still not related to the population size.
You may not want to know the reason. But if you want, please see the below:
A test with power function f (theta) is unbiased if f (theta1)>=f (theta2) for every theta1 belongs to the alternative hypothesis and theta2 belongs to the null hypothesis
A simple example:
H0 (the null hypothesis): theta=0 vs. H1 (the alternative hypothesis): theta=1
A test with power function f (theta) is unbiased if f (1)>=f (0)
The definition of power function here at http://www.merriam-webster.com/dictionary/power+functionis is : a function of a parameter under statistical test whose value for a particular value of the parameter is the probability of rejecting the null hypothesis if that value of the parameter happens to be true. I do not like this definition because it looks involved. You may find a better one by googling or reading a book.
