Converting rating scales

[Courk]

Let's say a 5-point rating system has been used in the past for rating anything subjectively -- books, movies, whatever. What's the best way to convert that to a 10-point rating system? On the surface it seems just multiplying everything by 2 would work, but I'm not sure that's necessarily the best, considering people are doing the scoring. I would think there'd be something slightly off, with someone who thinks something was not quite perfect giving it the second highest score, meaning a lot of 4/5s would be more equivalent to 9/10s, rather than 8/10s.

[MTGAP]

Maybe it could be optimized with something involving logarithms. That could make a nice curve.

I would think it should be something like this:

1/5 = 1/10
2/5 = 3/10
3/5 = 5/10
4/5 = 8/10
5/5 = 10/10
_________________
This statement is false.

[Lepton*]

For me, the range 1-4 (out of 5) maps onto the range 1-9 (out of 10), with the extremities being maintained as extremes,so:
0 - 0
1 - 1
2 - 3.6...
3 - 6.3...
4 - 9
5 - 10

[Courk]

It starts at 1, how does that affect it?

And how are you figuring this out? That's what I'm most curious about.

[Chuck]

1 stays as 1
2 stays as 2
3 discarded for not caring
4 becomes 9
5 becomes 10

[Zag]

Do you have full data of who gave what rating? If so, you should bell-curve the ratings of each individual. For instance, if Easy Ed made 100 ratings, and they are all 4's and 5's (of 5) then you should convert them to, say 4's and 8's. On the other hand, Harsh Harry similarly gave 100 ratings but they are one 1, four 2's. ninety 3's, four 4's, and one 5, then I would convert his so that 1=1, 2=2, 3=5, 4=9, 5=10. Etc.

[Dread Pirate Westley]

This is why you should never tell anyone the scale on which you are rating things. I typically use a scale from 3 to 8.5, but it can vary. I do rate movies from 1 to 10, but it's logarithmic.

[Samadhi]

I read the OP as:
Q. How can you subjectively convert one subjective scale to another?

My answer: It depends...
_________________
And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.

[Scurra]

I tend to subscribe to the Duke Ellington school of ratings. He said there were two sorts of music: good music and bad music. (The fun part is that we all violently disagree about which is which... and none of us are necessarily right )
That's not too far off Chuck's scale actually, except that that version has a little bit more "give" in it.
_________________
_{still Quiz Olympiad champion. Must get a life.
New definitions: COFFEE - someone who is coughed upon}

[Frankie*]

You will need to have some folks rate according to both systems.
You might be able to use Rasch Scaling / Rasc Modelling, which would also help you identify harsh (or easy) raters and strange items.

[Dragon Phoenix]

For a music discussion site, I rate songs according to:

10/10 - brilliant, one of the best 200 songs of all time
9/10 - excellent, one of the next best 500 songs of all time
8/10 - great, I'd put it on my MP3 player
7/10 - good, like to hear it on the radio
6/10 - OK, don't mind hearing it
5/10 - would probably switch channels
4/10 - would definitely switch channels
3/10 - aargh, quick, get rid of it
2/10 - dear god, why
1/10 - the smurf song

Converting this into a 5 point scale, I'd say
5/5 excellent, one of the best 700 songs of all time (9-10/10)
4/5 great, I'd put it on my MP3 player (8/10)
3/5 OK, like to hear it occasionally (6-7/10)
2/5 would switch channels (4-5/10)
1/5 awful (1-3/10)
_________________
My photography:
http://www.flickr.com/photos/artrock2006/

[MatthewV]

I agree with DP for the most part. And fort that reason, I would map

1 --> 1 or 2 (does it really matter?)
2 --> 4
3 --> 5 (I would do a 5.5 but that is essentially a 20 point scale)
4 --> 7 (or a 7.5)
5 --> 9

I feel that is better to downrate than to overrate.

Also, after converting the ratings, weight them so that after a few (a relative term) new people could influence the score by about 1 point.

[Samadhi]

I castle that reason.
_________________
And he lived happily ever after. Except for the dieing at the end and the heartbreak in between.