Re: Simple stat question that shouldn't be posted here
- From: Aniko <aniko123_57@xxxxxxxxx>
- Date: 24 Apr 2007 08:48:23 -0700
On Apr 23, 5:51 pm, randovaro <randov...@xxxxxxxxx> wrote:
hun...@xxxxxxxxxxxxxxxxxxx wrote:
I could not find the sci.stat.idiot group, so sorry for the simplicity
of this post. My stat knowledge is missing after many years, and many
beers.
Looking to find an equation to compare rank vs. popularity; how to
weight ratings.
Example:
a ratings scale of 1 to 5.
x ratings on a single item.
Problem:
I don't want 1 rating of 5 to be as powerful as 15 ratings of 5.
(simple averaging)
I need to figure out how to weight each item-
I have searched for this simple problem, but have not found anything-
easy solutions, suggestions, or websites you can point me to?
thanks
hunter
Most ratings scales that I've seen (e.g. product reviews) display the
score along with the number of votes and leave it to the reader to make
up their own mind as to how much value to place on the opinion.
E.g. This movie scored an average 4.5 stars (based on 3 reviews)
Or sometimes they'll just leave it as "unrated" until a minimum number
of votes (e.g. 15) has been reached.
But to answer your specific question, I think you're on the right track.
Just keep it simple. For votes 1 to 15 multiply the average score by
an increasing "low vote factor" of 0.85 to 0.99. For more than 15 votes
the factor effectively stays at 1.
So one rating of 5=5*0.85=4.25
7 ratings of 5=5*0.91=4.55
15 ratings of 5=5*0.99=4.95
16 or more ratings of 5=5
My example of "low vote factor" is completely arbitrary.
An alternative approach would be to put it into what statisticians
would call a Bayesian framework. As randovaro's approach, it needs
input from you to taylor it to your expectations. I assume that you
want to rank a lot of items and, on average, the rating of 3 is
neutral. So without knowing anything about an item (0 ratings), you
would guess a 3. Now when you get your first rating, you update your
guess by averaging the 3 and the first rating, say 5, to get a 4. As
more ratings accumulate, the influence of the 3 added at the beginning
is washed out. An extension of this method is to add multiple 3's at
the beginning - that way you need more ratings to pull it up high (or
down low). So what you need to decide on is your prior expectations
about the rankings: should the blind guess be 3 or perhaps another
number? How strong is your prior guess (that is how many 3's do you
want to start with)?
One can get much fancier (and more technical) than this, but it should
be a good start.
Aniko
.
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