On 11/10/2005 7:31 AM, Adaikalavan Ramasamy wrote: > If my usage is wrong please correct me. Thank you. > > Here are my reason : > > 1. p-value is a (cumulative) probability and always ranges from 0 to 1. > A test statistic depending on its definition can wider range of possible > values. > > 2. A test statistics is one that is calculated from the data without the > need of assuming a null distribution. Whereas to calculate p-values, you > need to assume a null distribution or estimate it empirically using > permutation techniques. > > 3. The directionality of a test statistics may be ignored. For example a > t-statistics of -5 and 5 are equally interesting in a two-sided testing. > But the smaller the p-value, more evidence against the null hypothesis. > > Regards, Adai
Thanks for your explanation. I think your interpretation is one that is sometimes taught, but I think it's more useful to think of a p-value as just another statistic, whose null distribution (in the ideal case, but not always in practice) is a uniform distribution on (0,1), and whose distribution when the alternative is true (again, ideally) tends to be more concentrated near 0. This takes a lot of the mysticism out of them. Duncan Murdoch > > > On Thu, 2005-11-10 at 06:05 -0500, Duncan Murdoch wrote: > >>On 11/9/2005 10:01 PM, Adaikalavan Ramasamy wrote: >> >>>I think an alternative is to use a p-value from F distribution. Even >>>tough it is not a statistics, it is much easier to explain and popular >>>than 1/F. Better yet to report the confidence intervals. >> >>Just curious about your usage: why do you say a p-value is not a statistic? >> >>Duncan Murdoch >> >> >>>Regards, Adai >>> >>> >>> >>>On Wed, 2005-11-09 at 17:09 -0600, Mike Miller wrote: >>> >>> >>>>On Wed, 9 Nov 2005, Gao Fay wrote: >>>> >>>> >>>> >>>>>Hi there, >>>>> >>>>>Suppose mu is constant, and error is normally distributed with mean 0 and >>>>>fixed variance s. I need to find a statistics that: >>>>>Y_i = mu + beta1* I1_i beta2*I2_i + beta3*I1_i*I2_i + +error, where I_i is >>>>>1 >>>>>Y_i is from group A, and 0 if Y_i is from group B. >>>>> >>>>>It is large when beta1=beta2=0 >>>>>It is small when beta1 and/or beta2 is not equal to 0 >>>>> >>>>>How can I find it by R? Thank you very much for your time. >>>> >>>> >>>>That's a funny question. Usually we want a statistic that is small when >>>>beta1=beta2=0 and large otherwise. >>>> >>>>Why not compute the usual F statistic for the null beta1=beta2=0 and then >>>>use 1/F as your statistic? >>>> >>>>Mike >>>> >>>>______________________________________________ >>>>R-help@stat.math.ethz.ch mailing list >>>>https://stat.ethz.ch/mailman/listinfo/r-help >>>>PLEASE do read the posting guide! >>>>http://www.R-project.org/posting-guide.html >>>> >>> >>> >>>______________________________________________ >>>R-help@stat.math.ethz.ch mailing list >>>https://stat.ethz.ch/mailman/listinfo/r-help >>>PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html >> >> ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html