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Topic: Is there a way to calculate an average ranking from uneven lists?
Replies: 12   Last Post: Nov 2, 2013 12:55 PM

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Virgil

Posts: 9,012
Registered: 1/6/11
Re: Is there a way to calculate an average ranking from uneven lists?
Posted: Oct 27, 2013 7:01 PM
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In article <2ivq699o8a81ppiu5qognbecbgm9et2sov@4ax.com>,
Jennifer Murphy <JenMurphy@jm.invalid> wrote:

> On Sun, 27 Oct 2013 13:36:29 -0600, Virgil <virgil@ligriv.com> wrote:
>

> >In article <chpq69prq63kh364qqmphkmqedhgm5ti6h@4ax.com>,
> > 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?


Works for me!
>
> Two questions:
>
> 1. Do I then just average the ranks across the lists?


That ought to work. but th effect of your averaging will be to compress
the pattern of rankings towards o.5 with fewer near either 1 or 0.
>
> 2. What scaled rank do I use for a book that is not ranked in a list?


If no preferences are evident, I would either leave it out entirely or
give each book mentioned the same score of 0.5 ( or 50%).
--





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