Wikipedia:Reference desk/Archives/Mathematics/2013 April 12

= April 12 =

Kendall's tau and confidence intervals
What's the best way to calculate confidence intervals for Kendall's tau (specifically tau-b)? I've seen a lot of pages on the web saying it's possible, but none of them necessarily say how. (I guess that might mean that it much more complex than calculating tau itself.) I'm interested in the general formula, but if there's an R package which can calculate it automatically, that would be great. (I did find the "Kendall" package in R, which apparently gives the variance of the numerator for Kendall's tau, but provides little assistance in transforming that into a confidence interval on tau itself.) -- 205.175.124.30 (talk) 03:51, 12 April 2013 (UTC)

True Manhattan distance ?
This is a question on terminology. Consider the following:

7 ^ +---+  6 |  |   |  5 |  | | |G 4 | | | |  3 |  |S| 2 | +-+ 1 |          o--> 1 2 3 4 5 6 7

The Manhattan distance from the start node S (2,3) to goal node G (4,5), ignoring obstructions, is abs(4-2) + abs(5-3), or 4.

However, when we consider obstructions, the number of steps to get from S to G is 10, as shown below:

7 ^ +---+ 6 |  |. .|  5 |  |.|.|G 4 | |.|.|. 3 |  |S|. . 2 | +-+ 1 |          o--> 1 2 3 4 5 6 7

I've been calling this "true Manhattan distance". Is this the correct term ? If not, what is ? StuRat (talk) 23:33, 12 April 2013 (UTC)


 * I'd just call it path length i.e. the length of the path from S to G.--Salix (talk): 03:40, 13 April 2013 (UTC)


 * Thanks, but that link leads to a chemistry article. StuRat (talk) 15:41, 13 April 2013 (UTC)


 * This is usually construed as a path on a graph (a subgraph of a lattice graph). Then no term like "Manhattan" is needed to qualify the metric.  --Tardis (talk) 16:44, 13 April 2013 (UTC)