On Sun, 27 Oct 2013 13:36:29 -0600, Virgil <email@example.com> wrote:
>In article <firstname.lastname@example.org>, > Jennifer Murphy <JenMurphy@jm.invalid> wrote: > >> There are many lists containing rankings of great books. Some are >> limited to a particular genre (historical novels, biographies, science >> fiction). Others are more general. Some are fairly short (50-100 books). >> Others are much longer (1,001 books). >> >> Is there a way to "average" the data from as many of these lists as >> possible to get some sort of composite ranking of all of the books that >> appear in any of the lists? >> >> I took a crack at it with a spreadsheet, but ran into problems. I will >> explain it briefly here. >> >> If the lists are all the same length and include exactly the the same >> books, the solution is relatively simple (I think). I can just average >> the ranks. I can even add a weighting factor to each list to adjust the >> influence on the composite ranking up or down. >> >> I ran into problems when the lists are of different lengths and contain >> different books. I could not think of a way to calculate a composite >> ranking (or rating) when the lists do not all contain the same books. >> >> Another complicationb is that at least one of the lists is unranked (The >> Time 100). Is there any way to make use of that list? >> >> I created a PDF document with some tables illustrating what I have >> tried. Here's the link to the DropBox folder: >> >> https://www.dropbox.com/sh/yrckul6tsrbp23p/zNHXxSdeOH > >One way to compare rankings when there are different numbers of objects >ranked in different rankings is to scale them all over the same range, >such as from 0% to 100%. > >Thus in all rankings a lowest rank would rank 0% and the highest 100%, >and the middle one, if there were one, would rank 50%. >Four items with no ties would rank 0%, 33 1/3%, 66 2/3% and 100%, >and so on. > >For something of rank r out of n ranks use (r-1)/(n-1) times 100%.
In the lists I have, the highest ranking entity is R=1, the lowest is R=N. For that, I think the formula is (N-R)/(N-1). No?
1. Do I then just average the ranks across the lists?
2. What scaled rank do I use for a book that is not ranked in a list?