Wednesday, July 24, 2002

For Lori

"... For testing one-sided hypotheses about M, we will use the binomial distribution to determine the rejection region. The testing procedure is called the sign test and is constructed as follows. Let y1... Yn be a random sample from a population having median M. Let the null value of M be M0 and define W1 = y1 - M0. The sign test statistic B is the number of positives Wis. Note that B is simply the number of y1s that are greater than M0. Because M is the population median, 50 percent of the data values are greater than the M and 50 percent are less than M. Now, if M = M0, then there is a 50% chance that y1s is greater than Mo and hence a 50% chance that Wi is positive. Because the Wis are independent, each Wi has a 50 percent chance of being positive whenever M = M0 and B counts the number of positive Wis under H0, B is a binomial random variable with pi = .5 and the percentiles from the binomial distribution pi =.5, given in .... "

No comments: