then would equal 28, which is above the cutoff of 20, indicating that sample size may be a E bit too large, and six animals per group might be more appropriate. Cumulative distribution function Let = 1, 2, ..., be independent observations taken from a with unknown mean and Xi, i n μ known variance Let us consider two hypotheses, a : σ2. and an alternative hypothesis: for some 'smallest significant This is the smallest value for which we care difference' μ* >0. about observing a difference. Now, if we wish to (1) reject with a probability of at least H0 when is true (i.e. a of 1-β), and (2) reject with probability when is true, then Ha H0 H0 β α we need the following: If is the upper percentage point of the standard normal distribution, then zα α and so 'Reject if our sample average () is more than ' H0 is a which satisfies (2). (Note, this is a 1-tailed test) Now we wish for this to happen with a probability at least 1-β when is true. In this case, Ha our sample average will come from a Normal distribution with mean we require μ*. Therefore Through careful manipulation, this can be shown to happen when where is the normal . Stratified sample size With more complicated sampling techniques, such as , the sample can often be split up into sub-samples. Typically, if there are such sub-samples (from different strata) then each of H H them will have a sample size = 1, 2, ..., These must conform to the rule that + nh, h H. nh n1
then E would equal 28, which is above the cutoff of 20, indicating that sample size may be a bit too large, and six animals per group might be more appropriate. Cumulative distribution function Let Xi, i = 1, 2, ..., n be independent observations taken from a with unknown mean μ and known variance σ2. Let us consider two hypotheses, a : and an alternative hypothesis: for some 'smallest significant difference' μ* >0. This is the smallest value for which we care about observing a difference. Now, if we wish to (1) reject H0 with a probability of at least when Ha is true (i.e. a of 1-β), and (2) reject H0 with probability α when H0 is true, then we need the following: If zα is the upper α percentage point of the standard normal distribution, then and so 'Reject H0 if our sample average () is more than ' is a which satisfies (2). (Note, this is a 1-tailed test) Now we wish for this to happen with a probability at least 1-β when Ha is true. In this case, our sample average will come from a Normal distribution with mean μ*. Therefore we require Through careful manipulation, this can be shown to happen when where is the normal . Stratified sample size With more complicated sampling techniques, such as , the sample can often be split up into sub-samples. Typically, if there are H such sub-samples (from H different strata) then each of them will have a sample size nh, h = 1, 2, ..., H. These nh must conform to the rule that n1 + β
I%20Observational%20study.docx