In article <S7gJ8.196523$[EMAIL PROTECTED]>, Jim Snow <[EMAIL PROTECTED]> wrote:
>"Glen Barnett" <[EMAIL PROTECTED]> wrote in message >[EMAIL PROTECTED]">news:[EMAIL PROTECTED]... >> Chia C Chong wrote: >> > Thanks for your advice Glen. >> No worries. If you still need to do some kind of goodness >> of fit test the first step is to discuss the alternatives >> of interest. >> Glen > It is certainly true that the procedure you choose must depend on the >alternative hypotheses of interest. If the alternatives are characterised by >over-dispersion or under dispersion, a specific goodness of fit test which >does not involve loss of information by grouping data uses R A Fisher's >"dispersion test" > X^2 = (sum of [(x(i) - xbar)^2]) >/xbar , > which is distributed, for a Poisson variate as a Chi squared >variable on n-1 degrees of freedom. > If the alternative of interest is over-dispersed , the rejection region >would be the upper tail of the Chisquare distribution and vice-versa. > Unfortunately, the reference I have to this is a very old one.-Cochran, >W.G., Biometrics,1954, quoted in my very old edition of Kendall and Stuart, >Advanced Theory of Statistics, volume 2 . One test which should be used more is the Kolmogorov-Smirnov or Kuiper test. These tests are not distribution-free for discrete distribution, but are conservative, and if the cell probabilities are small, is not that far off from the continuous ones. The power of these tests is not directly computable, but one can look at them from the standpoint of Bayes risk, where the test is given, and an approximation to the prior, but the level is chosen to minimize the prior Bayes risk. The asymptotics of this is usually easy, but the rate of convergence is slow. The nature of the alternative is still needed to determine the precise procedure, but the test is still in the ball park even if this is unclear. The chi-squared test has very low power. This is because it makes no use of the ordering of the possible values. If the probability that X=10 is off in a certain direction, then one would expect the same to hold for X=9 or X=11. The chi-squared test cannot use this to advantage. If the parameters are estimated, the first-order asymptotics for Bayes risk can still be handled. Again, I do not know how good this is; simulation will have to be used. -- This address is for information only. I do not claim that these views are those of the Statistics Department or of Purdue University. Herman Rubin, Dept. of Statistics, Purdue Univ., West Lafayette IN47907-1399 [EMAIL PROTECTED] Phone: (765)494-6054 FAX: (765)494-0558 . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
