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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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Jennifer Murphy

Posts: 24
Registered: 2/23/12
Re: Is there a way to calculate an average ranking from uneven lists?
Posted: Oct 27, 2013 5:06 PM
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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?

Two questions:

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?



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