[RAILhead]

I don't even know if I'm using the right terminology, but here's what I'm trying to do...

Say I have the ratios "4.5 : 286" and "4.3 : 188".

How could I "normalize" them so that they were representing equal proportions? Kind of like a reverse common denominator thing...? I'm wanting to be able to determine if 4.5 out of 286 is really better than 4.3 out of 188, etc.

Anyone?

[BRussell]

You could just divide. 4.5 divided by 286 = .016, and 4.3 divided by 188 = .023. So that means that 4.3 : 188 is more (better?) than 4.5 : 286.

[hyteckit]

Would normalizing mean getting rid of decimal places?

Like TV ratios. 16:9 and 4:3

So with 4.5:286, I would just times it by 2, so I normalize it to 9:572

[RAILhead]

Originally Posted by BRussell 

You could just divide. 4.5 divided by 286 = .016, and 4.3 divided by 188 = .023. So that means that 4.3 : 188 is more (better?) than 4.5 : 286.

This was my original method -- I was just wondering if there was another method. I using this with TripAdvisor's hotel reviews to find the truly highest rated.

[f1000]

Originally Posted by RAILhead 

This was my original method -- I was just wondering if there was another method. I using this with TripAdvisor's hotel reviews to find the truly highest rated.

If you don't have a calculator handy, just cross-multiply.

Example: Since 4.5 x 188 < 4.3 x 286, the first ratio is smaller.

[turtle777]

Huh ?

I gotta come back when I'm sober. LULZ.

-t

[Doofy]

I'm drunk, so unsure as to the ease of this, but...

"4.5 : 286"
"4.3 : 188"

Multiply both figures of one by the second figure of the other...

4.5 * 188 = 846
286 * 188 = 53768

4.3 * 286 = 1229.8
188 * 286 = 53768.

"846 : 53768" vs "1229.8 : 53768"

Thus, the second one is "better".

[turtle777]

Originally Posted by Doofy 

I'm drunk, so unsure as to the ease of this, but...

WTF ?

You are obviously not as drunk as I am

-t

[Doofy]

Originally Posted by turtle777 

WTF ?

You are obviously not as drunk as I am

If I was sober, I'd be able to figure out if the solution I wrote was complete crap or not. As it stands, I have no idea.

[mduell]

Normalizing can be through of as making the biggest value 1.

So divide the bigger value and smaller value in each set by the bigger value in each set. Then it becomes easier to see which smaller value is a larger proportion of the bigger values. Exactly what BRussell said in the first reply.

Finding ratios of really big numbers is a round about way of getting there.

[ghporter]

What mduell said. What you want to do is make things easy to manipulate, and by changing the scaling of the values so that one (almost always the higher number) is of unit value makes things MUCH easier to manipulate. Just looking at it gives you a much better grasp of proportions.

Note that almost all mathematics can be simplified by scaling (multiplying all values by a common factor) to put the values that must be worked with into the easiest form possible. That's what you do with finding lowest common denominators.

[d4nth3m4n]

can't you just think of them as fractions and find the common denominator?

[RAILhead]

Now that I have more time, here's what started all of this. We're going on vacation soon, and we're looking at hotels on Trip Adviser. One hotel gets 4.5 after 286 reviews, and another gets 4 stars out of 188. So, it pops into my head to wonder if they both had the same number of reviews, how would the second hotel stand up against the first, statistically?

At first blush, I'd say the 4.5 star hotel was higher rated -- but I wondered if the sheer quantity of votes could raise the average when compared to the 188 votes of the second hotel. Thus, I wanted to try and normalize the number, just for the kicks of it.

The first method (dividing stars by reviews) simply gives me Hotel A = .016 start/review, and Hotel B = .02 stars/review. This shows the "concentration" of stars in the total reviews -- but that's a flawed method, because if you have 2 stars and 10 reviews, you get .2 stars/review. Obviously, the latter is not a better-rated hotel than the previous two.

So, even after all the help you guys have given, I'm still not sure if what I'm wanting to do is possible.

[Eriamjh]

Normallizing is comparing something to a value of 1.

4.5 : 256 would be 1 : 56.9 and 4.3 : 188 is 1 : 43.7

Now you can see how they compare. The second value is 13.2 "points" less than the first.

If you had a sting of data, normallizing it would be setting the first point equal to one (by dividing it by itself) then dividing all the other points by the first number.

So the string of data 50, 75, 100, 200, 150, 25 would become 1, 1.5, 2, 4, 3, 0.5. It makes it easier to see relationships if values are compared to the number one.

Let's take the TV example: 4:3 and 16:9 are 1.33:1 and 1.77:1. Therefore, if someone made a TV that was as wide as a Panavision movie (like Star Wars), which is 2.35:1, it would be 21.15:9 which would be much wider than a 16:9 screen.

Class dismissed.

[BRussell]

Railhead in that case what youn want is really a confidence interval. I bet excel could give that to you, bit you'd have to enter in all the numbers. The best estimate of the 'true' means would still be the sample means you have though.

[Doofy]

Originally Posted by RAILhead 

Now that I have more time, here's what started all of this. We're going on vacation soon, and we're looking at hotels on Trip Adviser. One hotel gets 4.5 after 286 reviews, and another gets 4 stars out of 188. So, it pops into my head to wonder if they both had the same number of reviews, how would the second hotel stand up against the first, statistically?

At first blush, I'd say the 4.5 star hotel was higher rated -- but I wondered if the sheer quantity of votes could raise the average when compared to the 188 votes of the second hotel.

Hmmm. In my hangovered state, it appears that what you have to do is accept the star ratings given online.

Could the sheer number of votes raise the average? Probably only if they're high votes - otherwise they'd lower the average, surely?

[RAILhead]

Originally Posted by Eriamjh 

Normallizing is comparing something to a value of 1.

4.5 : 256 would be 1 : 56.9 and 4.3 : 188 is 1 : 43.7

Now you can see how they compare. The second value is 13.2 "points" less than the first.

So does that mean the first hotel would really be better than the second?

[BRussell]

Originally Posted by RAILhead 

So does that mean the first hotel would really be better than the second?

No, I think he posted that before reading your clarification.

[RAILhead]

Yeah, I didn't think so -- that's the same thing I was doing, basically: getting stars per review. I'm looking into the confidence interval thingies, but I don't know what numbers to put where. =/

[Eriamjh]

Originally Posted by RAILhead 

So does that mean the first hotel would really be better than the second?

Are these numbers "Star Ratings" versus number of ratings? I just noticed the hotel comment (missed it earlier).

In any case, the higher rating number is the "better rated".

4.5 star average out of 256 reviews is still higher rated than a 4.3 star average out of 188 reviews. It has nothing to do with normalizing. Both total review numbers are high enough to be significant. If one had only 10 reviews, you couldn't really trust the data.

If you really want to get technical, you need a histogram of the rating by distribution. A hotel with a TON of high ratings and a few of the lowest rating might have a lower average compared to a hotel with a bunch of ratings in the middle to high range. If someone gives a 1 or a zero, it may be because they got screwed or there was a massive misunderstanding that was never resolved. I would prefer to trust a hotel with the reviews all lumped together showing consistency.