Probability vs Statistics

I'll start off by saying that I'm pretty sure I'm the only person who gets annoyed by what I'm about to talk about, and so the rest of you can feel free to make fun of me as you see fit. :)

I understand that probability and statistics are used interchangeably in society, and I guess this is what really bothers me. My most recent bout of annoyance came because of two separate events: one, a trip to the veterinarian, and two, a trip to a Lasik eye doctor.

My cat has been not well lately, and I took her to the vet. He ran some tests, prescribed some pills and a special diet. He then told me that, of course, cancer was always a possibility. But, the chances are 1 in 100 that it's cancer, and so we won't worry about that unless nothing else is working.

To me, this is a probability. It's like saying, there's a 1% chance that your cat has cancer. And this, I'm very much fine with.

I'm thinking about getting Lasik surgery on my eyes (and probably will). I have gone to several doctors to interview them for this procedure, and they all pretty much say the same thing: That about 1 in 10,000 people have "complications" after the surgery.

Now, to me, this is a statistic. The problem I have with this, is my next question is: How many people have you performed this surgery on? They answer, 40,000, or 50,000, or 100,000, and never had any problems. If that's so, then aren't they overdue for a complication? I mean, if they've done 9,999 surgeries with no complications, but they know they will have 1 in 10,000 complications, then the next surgery should be a complication.

Now, I understand that what they really mean is that the PROBABILITY of there being a complication is 1 in 10,000. But to me, that's a different statement than the statistic that 1 in 10,000 people will have a complication. Tell me that my sugery has a 1 in 10,000 chance of having a complication, and I'm fine. Tell me that 1 in 10,000 people have a complication and the doctor has done 9,999 surgeries without complications, and I'm not fine.

And yes, I get that the probabilities are based upon the statistics, and I understand how that all works. It's just the way they use the information, and the way they say things that bothers me. My vet telling me there's a 1% chance my cat has cancer is great way of telling me.

Perhaps I'm just innumerate. I know that most people have a hard time with very small or very large numbers. But I just think that doctors should use more of a probability wording that a statistical wording.

(As an interesting side note, I find it awesome that all of these doctors I interviewed didn't have any serious complications, even though, statistically, it should happen in 1 out of 10,000 patients. I just imagine there's some eye clinic somewhere in the world where everybody walking out of there is blind to balance out the statistics.)

This does relate somewhat to gambling, I suppose. I mean, just check out the "Hoax that is blah blah blah" thread for more on that. Sometimes the probabilities and statistics don't match up. I know that on my next trip to Las Vegas, there's a greater than 50% probability that I will lose money. But yet, statistically, the last 3 of 4 trips I've made to Las Vegas resulted in me winning money.

Quote: konceptum

Now, to me, this is a statistic. The problem I have with this, is my next question is: How many people have you performed this surgery on? They answer, 40,000, or 50,000, or 100,000, and never had any problems. If that's so, then aren't they overdue for a complication? I mean, if they've done 9,999 surgeries with no complications, but they know they will have 1 in 10,000 complications, then the next surgery should be a complication.

First, sorry to hear about your cat. My beloved cat Simon died last year. Before he died he lost a lot of weight, and acted like he was ready to go, as pets often do. The doctor said he probably had cancer, but whatever it was, there was probably nothing she could do, so why go through the expense and suffering of diagnosing him?

Second, I think the 1 in 10,000 statistic probably is based on actual results. If a specific doctor has done 9,999 Lasik surgeries correctly, it does not mean he is overdue to fail. I don't think your specific doctor's personal record matters much. My wife had Lasik done about five years ago. You just lay down and the machine does its thing. She was fine by the way. They warned her that some patients have a temporary case of dry/itchy eyes. In her case, several hours after the surgery she was fine, saying it was one of the best decisions she ever made.

Here's the problem I have:

When a doc says he's done 100,000 procedures. OK, say that's an average of 2 procedures per patient :)

50,000 patients?

20 a day x 5 days a week x 50 weeks a year for 10 years?

About your probability: if your were playing roulette,0 and 00 wheel, and a number,say 31, has not been a winner for 37 spins, would you be certain that 31 would hit on the 38th spin? If this were true we all would be rich. Isn't this the same problem as the 9999 and 10000 surgeries.

Quote: matilda

About your probability: if your were playing roulette,0 and 00 wheel, and a number,say 31, has not been a winner for 37 spins, would you be certain that 31 would hit on the 38th spin? If this were true we all would be rich. Isn't this the same problem as the 9999 and 10000 surgeries.

I agree that it makes literally no sense to worry that a doctor is due for a complication.

Probability is the theory of prediction of outcomes. Statistics is the formal science of making effective use of numerical data relating to groups of individuals or experiments. It deals with all aspects of this, including not only the collection, analysis and interpretation of such data, but also the planning of the collection of data.

Quote: Wizard

First, sorry to hear about your cat. My beloved cat Simon died last year. Before he died he lost a lot of weight, and acted like he was ready to go, as pets often do. The doctor said he probably had cancer, but whatever it was, there was probably nothing she could do, so why go through the expense and suffering of diagnosing him?

I'm in the same boat with that. My main thing is that I don't want my pet to be in any pain and/or extreme discomfort. Once that is a factor, I will definitely have her put down. But if it's something as simple as medication and a change of diet, then I'm ok with dealing with that.

Quote: Wizard

Second, I think the 1 in 10,000 statistic probably is based on actual results. If a specific doctor has done 9,999 Lasik surgeries correctly, it does not mean he is overdue to fail. I don't think your specific doctor's personal record matters much. My wife had Lasik done about five years ago. You just lay down and the machine does its thing. She was fine by the way. They warned her that some patients have a temporary case of dry/itchy eyes. In her case, several hours after the surgery she was fine, saying it was one of the best decisions she ever made.

I know it doesn't mean he's overdue to fail. I just don't like the way in which the numbers are presented to me. As far as Lasik, I'm still looking into it. My regular eye doctor gave me the name of a Lasik eye surgeon. When I called that person to make an appointment, I was told that he no longer recommends Lasik eye surgery for people! He still does it for people with cataracts, severe astigmatism, or diabetic patients, but not for people just looking to correct their faulty eyes. I find it interesting that a Lasik eye surgeon doesn't recommend it. Makes me want to look into it.

I have also known several people that have gotten the surgery done, including my regular eye doctor, so I'm not too worried about the procedure or the risks on it. I suppose even if I go blind, I can still get someone to help me make bets at the crap/s table. :)

Quote: matilda

About your probability: if your were playing roulette,0 and 00 wheel, and a number,say 31, has not been a winner for 37 spins, would you be certain that 31 would hit on the 38th spin? If this were true we all would be rich. Isn't this the same problem as the 9999 and 10000 surgeries.

Yes, I know that the 31 won't hit on the 38th spin. I know that the chance of me having a problem with the surgery is 1 in 10,000. I just want doctors to phrase it that way instead of saying that statistically speaking, 1 in 10,000 will have a problem. Again, it's a symantic difference in the way things are stated.

Perhaps it is the gambler spirit in me. When I'm told that the chance of number 31 being on the next spin of the wheel is 1 in 38, then I know what that probability is, what the payout is, and I can determine whether or not I want to take the chance on it. Same with the eye surgery. Tell me there's a 99.99% chance of nothing going wrong, and I'm fine with that, and the 0.01% chance of risk. But tell me that if the doctor lines up 10,000 people and 1 of those will have a problem, and he has 9,999 previous patients with no problems, then I don't like hearing that part.

Again, I know that the probabilities are based on the statistics. It's the wording of things I don't like, I suppose. Maybe it's not so much an innumeracy problem as it is an English language problem. I think if the doctor said, "The odds on you becoming blind is worse than the odds of hitting the number 31 twice on a roulette wheel.", then I'd say sign me up.

If the doctor said "of the 1,000,000 cases that I know about, 100 have had problems", would you sign up? Keep in mind that while I might let a doctor mess with my eyes, I would not let him/her calculate my probabilities. Just give me the data and I will calculate my own probabilities.

Quote: konceptum

... I suppose even if I go blind, I can still get someone to help me make bets at the crap/s table. :) ...

My brother isn't much of a gambler, but we've played craps together a couple of times. His favorite game is roulette.

Quote: konceptum

I'm thinking about getting Lasik surgery on my eyes (and probably will). I have gone to several doctors to interview them for this procedure, and they all pretty much say the same thing: That about 1 in 10,000 people have "complications" after the surgery.

question: because you can't quantify the probability of a surgery having complications (ie, you can with craps because we know how many sides there are and the value to each side) why wouldn't you be nervous about being around the 10,000th person getting the surgery done (say no prior complication) if the odds are that 1 in 10,000 mess up? because if it wasn't happening that often wouldn't they say 1 in 50,000 or 1 in 100,000?

Scenario: Suppose that there is a procedure I am considering and that it is commonly recognized that on average 1 out of 10,000 patients for this procedure has complications. Suppose also that the practitioner I am considering has already conducted 15,000 of these procedures without any problems at all. Some people might think he/she is "overdue" for a patient to have complications. Personally, I tend to think this practitioner might just be performing the procedure just a mite better than average, which leads me to think that with him/her I would have a lower than 1 in 10,000 chance of complications. Any body else think the way I do?

Note: I have no idea how/whether this scenario relates at all to the original rant of statistics vs. probability.

Quote: konceptum

Yes, I know that the 31 won't hit on the 38th spin. I know that the chance of me having a problem with the surgery is 1 in 10,000. I just want doctors to phrase it that way instead of saying that statistically speaking, 1 in 10,000 will have a problem. Again, it's a symantic difference in the way things are stated.

Perhaps it is the gambler spirit in me. When I'm told that the chance of number 31 being on the next spin of the wheel is 1 in 38, then I know what that probability is, what the payout is, and I can determine whether or not I want to take the chance on it. Same with the eye surgery. Tell me there's a 99.99% chance of nothing going wrong, and I'm fine with that, and the 0.01% chance of risk. But tell me that if the doctor lines up 10,000 people and 1 of those will have a problem, and he has 9,999 previous patients with no problems, then I don't like hearing that part.

Again, I know that the probabilities are based on the statistics. It's the wording of things I don't like, I suppose. Maybe it's not so much an innumeracy problem as it is an English language problem. I think if the doctor said, "The odds on you becoming blind is worse than the odds of hitting the number 31 twice on a roulette wheel.", then I'd say sign me up.

First, look at definition #4 from this page:

http://dictionary.reference.com/browse/Probability

I think you're getting confused by the semantics. You seem to feel like they are referring to two different concepts and thus have different rulesets, when it's just two different ways to refer to Probability.

It's like the concept of "A square is a rectangle, but a rectangle is not a square". Probability is statistics, but statistics contains probability + other shapes.

As a result, these two sentences can be used interchangeably:

1.) "The probability of something happening to you is 1 in 10,000"
2.) "Statistically speaking, 1 in 10,000 patients has something happen to them"

In the first one, you're referring to the specific name of the part of statistics that came up with this stat. In the second example, you're referring to the overall study's name, and not really drilling down into the certain part of statistics that applies. That doesn't mean that it WASN'T probability that determined it, just that you're not referring to it that specifically.

Quote: Doc

Scenario: Suppose that there is a procedure I am considering and that it is commonly recognized that on average 1 out of 10,000 patients for this procedure has complications. Suppose also that the practitioner I am considering has already conducted 15,000 of these procedures without any problems at all. Some people might think he/she is "overdue" for a patient to have complications. Personally, I tend to think this practitioner might just be performing the procedure just a mite better than average, which leads me to think that with him/her I would have a lower than 1 in 10,000 chance of complications. Any body else think the way I do?

Note: I have no idea how/whether this scenario relates at all to the original rant of statistics vs. probability.

It's a possibility, but it's hard to get a good guesstimate on it without knowing the applicable variance. It could be that 15,000 falls within the normal deviation.