• Quick note - the problem with Youtube videos not embedding on the forum appears to have been fixed, thanks to ZiprHead. If you do still see problems let me know.

10/10 scale

talldave

New Blood
T
Joined
Mar 17, 2004
Messages
24
I've made up a (not totally original) scale for use in my Science and Nonsense class. I call it the 10/10 scale, pronounced "ten, ten".

On the 10/10 scale,
-10 means definitely not true
-5 means probably not true
0 means hard to tell
+5 means probably true
+10 means definitely true

Most scales go from 1 to 5 or 1 to 10. I think a negative to positive scale is important because it gives a nice symmetry to the situation and it has a definite place for 0.

I'm not proposing this as an Earth-shattering improvement, but as a nice incremental improvement over the previous scales.

It also clarifies that "probably true" is not the same as "hard to tell" is not the same as "probably not true", something we might imagine a t.v. lawyer in a trial badgering a witness towards.

I have students come up with claims that fall in different parts of the scale and ask them to come up with a claim that they put at +10 and think up what sort of evidence would change their mind.

For instance, "the Earth is round" is a claim that most people would place at +10. The evidence needed for most people to change their mind would be, say, being brought to the edge of the world (as seen is Eric the Viking) and looking over that edge.

The idea is, is that we can at the same time be sure of something and still imagine extraordinary evidence that could change our minds. I think this captures the tentative nature of science pretty well. It's not that we religate everything to live between probably-not-true to probably-true for fear of being wrong, it's that the more certain we are of something the better the evidence needs to be to change our minds.

I would like to hear what my fellow skeptics think of the scale, if they've seen it elsewhere and if they have any questions.

-David
 
I never used a numerical scale, but did have a 'confidence' level. I would ask my students how confident they were about something. A lot of them got into a habit of giving a percentage, which other kids picked up.

The good thing about having an arbitrary 'confidence' level is that students now had language they could use to describe when they either couldn't quite grasp something or had trouble believing it. There was no stigma about admitting you were confused, as kids could just say 'Sir, I'm really not confident in understanding what you mean by that', or 'I'm not confident that you're right about that'.

The language plays a large role in helping people to express skepticism without seeming negative. Lack of 'confidence' does not lay blame on either the individual or the information; it's another way of saying 'I'm not yet convinced about what you're saying', and leaves it open to be swayed.

Good luck.

Athon
 
talldave said:
I would like to hear what my fellow skeptics think of the scale, if they've seen it elsewhere and if they have any questions.
Click to expand...
Are the numbers you mentioned the only options? If so, it's not different from the 1 to 5 scale. If not, I would find it very difficult to discern between, say, probability 7 and 8. Do *you* have 20 probability levels?
 
My cosmology professor liked to place bets. I.e.,

"I would bet my life that the universe is old and has expanded from a hotter, denser state.

I would bet my yearly salary that inflation theory is essentially correct (at least the universe went through a phase of rapid expansion).

I would bet my boss's monthly salary that dark energy is real."

Etc etc.
 
NO! NO! NO!

It ought to start from 0.

Mathematically, introducing negative numbers makes for nonsense.

Either have it go from 0 to 1, or from 0% to 100%, which means the same thing --- like a probability measure.

Then actual maths will apply.

I think a negative to positive scale is important because it gives a nice symmetry to the situation ...
Click to expand...
Thank you for your insight. I'll tell the people who dish out the Fields Medal.

In the meantime, there are reasons why we do it this way and they are good.
 
I like scales that go from 1 - 5. Then there is a definite difference between one number and another. In this scale 3 would be neutral; 4 would be probable; 5 is almost certain.

In your scale what is the difference between 6 and 7?
 
Thank you all for your responses.

There's not much difference between 6 and 7 or 7 and 8, true, but people like nice round numbers (like 10). And just because you could be more precise, doesn't mean you have to be. The choice of 19 shades of grey (21 choices -2 endpoints) between the opposite ends is pretty arbitrary, but I don't think it's agregiously so. If the student's want to be more precise with their shades of grey, they can, but I certainly don't require it.

If you wanted to enforce a lower level of precision, a -2 to +2 scale might make more sense than my 10/10 scale. You could call it the 2/2 scale.

I originally used my 10/10 scale (at the time I called it the "Dave scale", but I thought naming something after myself for class materials could be funny, but in then end would be a bit pretentious) for movies, so that there was a definite position for average and positive went with good and negative, bad. 10 was the best movie I'd currently seen (no 11's allowed, only recalibrations of 10) and -10 the worst.

-David
 
* bangs head against desk until it BLEEDS *

Here's a quick question. If you assign -3 to proposition X and -5 to proposition Y, and X and Y are independent, what value should you assign to the proposition that X and Y are both true?

Can you show me any way of answering questions like this without first converting into a SENSIBLE scale, doing the maths, and then converting back?

PEOPLE ARE DUMB ENOUGH ABOUT PROBABILITY WITHOUT YOU MAKING IT WORSE.

Why make it hard for them?

Sheesh, why don't you just teach creationism while you're at it?
 
Please Dr Adequate do not self harm. If X and Y are independent variables then you need two numbers to represent them. Not one number. So on a 2/2 scale (see above)
x=2;y=2
Where 2 = highly probably true.

Or on a 1 - 5 scale
x=5
y=5
Where 5 = highly probably true.

I thought the above was obvious.

Also what has creationism got to do with anything? Do not make it any harder than it need be.
 
Dr A., he's not approaching this with mathematics in mind. That is a slight cause for concern, I agree, if it is insinuated to be quantitative.

There is a different connotation in place. As I said earlier, kids in classes tended to respond to the question in percentages, when I asked how confident they were. I never presented it as an option, but the trend started and I never corrected it.

If I were to treat the percentages as hard figures and operate on them mathematically, no doubt it would have confused matters to no end. They didn't say '99% happy' because 1% had an empirical value. They said it because the connotation was that it demonstrated obligatory doubt while still conveying strong certainty. It was simply a means of expression.

I understand your apprehension, however I don't think you really need to make yourself bleed.

Athon
 
athon said:
Dr A., he's not approaching this with mathematics in mind. That is a slight cause for concern, I agree, if it is insinuated to be quantitative.

There is a different connotation in place. As I said earlier, kids in classes tended to respond to the question in percentages, when I asked how confident they were. I never presented it as an option, but the trend started and I never corrected it.

If I were to treat the percentages as hard figures and operate on them mathematically, no doubt it would have confused matters to no end. They didn't say '99% happy' because 1% had an empirical value. They said it because the connotation was that it demonstrated obligatory doubt while still conveying strong certainty. It was simply a means of expression.

I understand your apprehension, however I don't think you really need to make yourself bleed.
Click to expand...

I think Dr A has a very good point. The Dave Scale is worse than useless, compared to simple percentages or fractions. Making probabilities under 0.5 into negative numbers just causes confusion, because they aren't negative probabilities.

Everything Dave suggested as a use or an advantage of the Dave Scale can be done as well or better with percentages.

It's not the worst idea ever in the history of education, but it's still a bad idea.
 
Dr Adequate said:
* bangs head against desk until it BLEEDS *

Here's a quick question. If you assign -3 to proposition X and -5 to proposition Y, and X and Y are independent, what value should you assign to the proposition that X and Y are both true?

Can you show me any way of answering questions like this without first converting into a SENSIBLE scale, doing the maths, and then converting back?

PEOPLE ARE DUMB ENOUGH ABOUT PROBABILITY WITHOUT YOU MAKING IT WORSE.

Why make it hard for them?

Sheesh, why don't you just teach creationism while you're at it?
Click to expand...

=MIN(X,Y)

X or Y
=MAX(X,Y)
 
Kevin_Lowe said:
I think Dr A has a very good point. The Dave Scale is worse than useless, compared to simple percentages or fractions. Making probabilities under 0.5 into negative numbers just causes confusion, because they aren't negative probabilities.

Everything Dave suggested as a use or an advantage of the Dave Scale can be done as well or better with percentages.

It's not the worst idea ever in the history of education, but it's still a bad idea.
Click to expand...

But they aren't probabilities. It isn't mathematical at all, or quantitatively empirical. I don't think Dave's treating it as scalar as much as orderly. And for the most part, if the scale is established, I don't see kids applying empirical values to them anyway.

Neutrality is '0', having strong doubts is negative, and having few doubts is positive. Personally, I think it is needlessly complicated, however I don't think the mathematical notion of negative value is at fault as much as it being plain unnecessary.

Athon
 
sphenisc said:
=MIN(X,Y)

X or Y
=MAX(X,Y)
Click to expand...

That would imply that the odds of a roulette wheel coming up black twice in a row are the same as the odds of a roulette wheel coming up black a billion times in a row.

The correct way to set such things out is to express the odds as a number between 0 and 1 inclusive, and then the answer is XY.
 
talldave said:
I've made up a (not totally original) scale for use in my Science and Nonsense class. I call it the 10/10 scale, pronounced "ten, ten".

On the 10/10 scale,
-10 means definitely not true
-5 means probably not true
0 means hard to tell
+5 means probably true
+10 means definitely true

Most scales go from 1 to 5 or 1 to 10. I think a negative to positive scale is important because it gives a nice symmetry to the situation and it has a definite place for 0.

I'm not proposing this as an Earth-shattering improvement, but as a nice incremental improvement over the previous scales.

-David
Click to expand...

You can get pretty far using three scales,

open ended on both sides: example: pH
closed on one end: Temperature
bounded on both ends: probabilities, best using 0 to 1

Who are you teaching?

KISS-keep it simple sir
 
There is a lot that already relates numbers in that range to probability. Logistic regression is a popular alternative to regression used when the variable that one is trying to estimate is either 0 or 1. The dot product of the independent variables and the coefficients will be in the logit scale. To transform to the probability scale, apply
estProb = 1 / (1 + exp(-estLogit))

-10 and 10 are essentially negative and positive infinity in the logit scale and map to 0 and 1 in probability scale.

Believe it or not, there are people who prefer to work with the logit.
 
The class I teach is a general education class, typically, but not always, taken by college Freshman.

Most of the kids I get for my class have are very hip. And most can do good work if I just give them half a chance. One of my instructor friends warned me that they might not appreciate the irony of the Colbert Report (I use his bit about Truthiness as part of an intro for 'wishful thinking'), but it turned out that his concerns where unfounded. It would be hard to not know Stephen Colbert is being ironic when a class full of college kids are laughing.

Not all of them appreciate my sense of humor, but then I'm a physics guy, so my sense of humor is pretty nerdy, for instance:

"It's really bad luck to be superstitious."
"All generalizations are bad."
"Value judgements are wrong; morally and ethically wrong."

When my students thought I had said "bitch" when I thought I said "bit" (I sometimes put "ch" after closing t's, something I need to work on) I told them that I don't use the word "bitch" to describe mean girls.... because it's not fair to dogs.

Anyway, I used my 10/10 scale in the Spring 2006 semester and they had very little trouble with it. I think if you asked them, they would say that it was pretty intuitive, which is what I was going for.

In addition to what I mentioned before, I would ask the students to tell me what they thought about a topic, rate it on the 10/10 scale go online and do some easy research and then tell me what they thought of it then, rerate it and tell me why, what changed their minds. The point of the exercise is that evidence can change your mind.

The only trouble I had was a couple students thought I was tricking them and they thought that the correct answer for something they'd never heard of before was always 0. I told them if that was truly what they thought, that that was fine, but I usually get a feel for how valid a story is regardless of how detatched I think I am.

Oh, and one of my girls that barely ever showed up to class seemed a little confused about how to use it.

I have no intention of using these numbers in calculations, maybe on the outside chance, I might take an average, but probably not. The use of the word 'probably' in the "+5 means probably true" is not meant to be an indication of a probablity calculation, but rather meant in the the everday use of the word.

To be clear, the 10/10 scale is an indication of an intuitive confidence level rather than anything as precise as probability.

I also emphasize logical and rhetorical fallacies (which I collectively call 'crazy talk').

For instance the sentence:

"In the meantime, there are reasons why we do it this way and they are good."

Would, I think, be a good example of an appeal to authority. If this was given on an exam, I would also accept 'appeal to tradition' or 'appeal to the masses'.

So, Dr. A, I think that is great nerd humor to use fallacies in a skeptic's discussion board. Unless you are not trying to be funny, in which case (at the risk of being pretentious) I would refer you to Nietzsche:

"He who fights with monsters might take care lest he thereby become a monster."

Then again, I tend to think that people are doing bits, when they (in fact) are not. When I was a student, taking a logic class, we had spent the entire month working on logical operations. (True and True equals True, that sort of thing.) On the day of the exam, the instructor asked if there were any questions before we started the exam. A guy sitting behind me ask "can you explain that T and F stuff". That is exactly the kind of bit I would do, so I laughed. But he was serious and more than a little pissed at my reaction. Oh well, if you don't come to class for a month and a half, you might miss a few things.

-David
 
Last edited:
What's wrong with allocating probability in alphabetical order, so the nearer the start of the alphabet, the less believable?
We could then use such metaphors as "Easy as poo" and pretend they were meaningful. Also anything quantum would have a high credibility factor.
Do I know what I'm drivelling about?
No.
But I know I know.

Now wot's you lot's excuse?
 
You must log in or register to reply here.

Back
Top Bottom