On 18 Aug 2009, at 20:46, joel wrote:
No, it's more subtle than that. Almost all of the time there will be a difference between A and B, however this difference is just 'noise' around zero. In order for there to be a meaningful difference the natural random variations of the differences should be significantly different from zero. What's the difference between this and "most of the time A and B go at
Edward Grace wrote: the same speed" ? apologize my stats ignorance :)
No problem. You are (I think) confusing probability and probability density. If - for the sake of argument and to keep the maths easy - you assume that A and B are both continuous and normally distributed then so will their difference. [In practice neither of these assumptions are true but it doesn't change the basic point.] This normal distribution of the differences will be normal too. This distribution is a probability density - to obtain a probability you must integrate it over a region (dT). http://en.wikipedia.org/wiki/Probability_density_function If that region has zero width then the probability will also be zero. Therefore, the probability that you observe A and B going at the same speed (A-B == 0) is zero. In other words, paraphrasing your comment, "All of the time you will observe A and B do not go at the same speed." [*] That difference however can be an illusion (purely the result of chance). -ed [*] Due to the assumptions above being incorrect this may not be true - the discrete nature of the distribution can lead to differences that are exactly zero. ------------------------------------------------ "No more boom and bust." -- Dr. J. G. Brown, 1997