On 25 May 2004 15:48:08 -0700, [EMAIL PROTECTED] (Xinmiao) wrote: >I have the following question: suppose one is limited by the total >number of data points (# sampling points * # replicates), in order to >get better curve fitting, which way is more preferable: to have fewer >sampling points and more replicates at each point, or to have more >sampling points and fewer replicates? I suspect that it is the latter, >but I don't know any statistical reference or background for that. Can >someone please kindly help me out here?
No good answer here, but some insight, I hope: 1. if you are certain of the form of the curve (eg. that it is a straight line), then you take the smallest number of sampling points that will allow you to estimate the parameters of the curve, in order to have as much replication as possible. (For a straight line y=a+bx, you put 50% of your observations at the smallest possible value of x and 50% at the largest possible value.) 2. If you are completely uncertain of the form of the curve, then you sample at as many different points as possible, in order to get the best idea of the shape of the curve. These are two extremes; 1. gives you no chance to assess alternative models from the same data set (eg. a quadratic relationship instead of a straight line), while 2. gives you no chance (or, at least, less chance) to assess the fit of the data to the curve you are fitting. So it depends on how certain you are about the shape of your curve. If there is solid theory that predicts a particular shape, then you can use optimal design theory to pick your sampling points (there are typically not very many) and concentrate on replication. Otherwise, you'll need to sample at more different points, and lose the benefits of replication. Cheers, Ken. -- Ken Butler, Lecturer (Statistics) University of Toronto at Scarborough butler (at) utsc.utoronto.ca http://www.utsc.utoronto.ca/~butler . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
