Monday, November 15, 2004
In which I write an essay on Statistics so as to avoid learning about it.
“This is your first statistics lesson: They’re all a bunch of lies. Don’t trust ‘em.”
--Blaine Hollingsworth, my Statistics professor
I’ve long felt a vague, unsettling sort of doubt that suspected this to be true, which is partly why I’ve put off taking the class for so long. Of course, Blaine was only referring to the “2 out of 3 dentists agree” kind of propaganda that is hurled at us in advertisements everyday, but I automatically distrust all forms of probability. It bothers me that our culture seems to make its decisions not out of faith but possibility, manipulating the facts into two or three discrete envelopes of outcome: support or rejection; success or failure; yes, no, undecided. But does it ever happen so categorically?
I understand that the sort of calculations we’ve been doing in STAT 2510 aren't like that (“Let’s see...stage four metastasized ovarian cancer: four months to live, 10% chance of survival...” like it’s a crapshoot or something), but are actually pretty legitimate and even helpful within the proper context. Bell curves and standardizations shine perspective on those silly Scantrons we fill in just before our next matriculation, and any form of research is meaningless without a mean and standard deviation. We’re learning how to manipulate the raw data into something that we can work with, to form and support the hypotheses that create theories. It’s all well and good. But it still gets me to thinking about some greater issues.
I guess my problem is that, in the non-science world, when we use probability it’s because we’re focusing on the negative. We only make a percentage of likely success when we don’t believe we’re going to get what we want, as if we’re trying to trick our dying hope into hanging on for just a few more minutes.
My main problem deals with these ‘likelihoods of survival’ you always hear when someone gets sick. I suppose when I get to medical school I’ll understand this concept better, and I imagine I’ll even end up using it myself. But from my current stance (which, I admit, might best be termed "ignorance"), it doesn’t seem right. What do these numbers mean? That 90% of women with stage four metastasized ovarian cancer have died within four months of diagnosis? What does that matter? Every person’s different.
It’s true that the universe is kept in line by rigid natural laws. We think ourselves very clever for having come up with complicated formulas to help us understand the basic laws of physics and human behavior, at least in theory. But since a large sample size is required before one can confidently calculate a probability, can we ever apply that number to the individual? All it tells us is how likely we are to succeed at achieving some desired outcome. But it's just a likelihood. A chance. There’s always a chance for either outcome--even if it’s what we’d have to call a miracle--or even a result entirely different from the two we had defined.
The guy who designed the Epcott Center hated probability. He said it’s an artificial construct created to help us deal with the fact that we don’t understand all the laws that govern the universe. The outcome of every event could, theoretically, be predicted precisely, if only we could comprehend all of the outside forces acting upon it.
We can certainly calculate how fast a ball will hit the ground when it is dropped from a balcony. We’ve tested that one, determined the forces acting upon it, and developed a formula to tell us, without fail, so long as no unforeseen forces should disrupt the defined system, how long its trip will take. But a human life isn’t as simple as a body free-falling through a constant gravitational field. There’s something intangible there that defies the laws of the universe, something connected to the higher Power who designed those laws and is free to manipulate them as He sees fit. Since we don’t understand such forces, we spend years concocting formulas to help us feel better about our actions. These ratios of success allow us to make informed decisions, let us act "cautiously".
Maybe we should try not to be so cautious about everything.
Blaine tried to get us to understand the benefits of probability with this illustration:
On the old game show Let’s Make a Deal, Monty Hall would present an audience member with three closed doors. Behind one of these doors was a fashionable new car, and behind each of the other two doors stood a wild goat. If you were so fortunate as to be afforded this opportunity to acquire a new vehicle, you would stand up in your outlandish costume and chat briefly with Monty before he asked you to select the door you believed to be hiding the new car. You would have a one-in-three chance of picking the right door, agreed? Pretty good odds. Without opening the door you selected, Monty, who knew the positions of the car and goats, would offer to open a different door, one that was certain to be hiding a goat. You would then be left with two doors to choose from, and Monty would give you the option to change your mind, if you had begun to doubt your initial instincts.
So, Blaine’s question to the class was this: should you change your mind and pick the other closed door, or should you trust your gut instinct and stick with the first door you picked?
I’m a firm believer in the legitimacy of the sixth sense, so I was slightly offended when he declared that only a fool would choose to stay with his first decision.
Mathematically, though, he’s right:
When you make your first choice, you’re working with a 1/3 likelihood of choosing the correct door. Say Door #2 holds the car. Whether you pick Door #1, #2, or #3, Monty will be able to show you a door with a goat, because he knows where each one is. If you pick #2, he can show you #1 or #3. If you pick #1 he’ll show you #3, and if you pick #3 he’ll show you #1.
So. Say you pick #1. Monty shows you the goat behind #3. Now you’re given the chance to change your mind and pick #2.
When there are two doors left—one which hides the car and one which hides a goat—you will only have a 1/2 chance of choosing the car IF YOU CHANGE YOUR MIND. This is because, even though you now have new information that increases your likelihood of choosing the right door, your first pick was made under the old information about the location of the car (that is, no information whatsoever) when your chances of success were 1/3, and the only way to utilize your new knowledge of the situation is to change your mind. You are then picking from Door #1 and Door #2. If you stick with #1, more confident of your decision now that #3 is out of the picture, you’re STILL picking from 1, 2, and 3, because you picked #1 from the three of them. It seems illogical, but really it’s true!
In this case, you changed from #1 to #2 and won the car. You were just as likely to have chosen #3, seen #1, and changed to #2, winning again. And just as likely to have chosen #2, seen #1, and changed to #3, losing.
So see, as long as you change your mind after Monty opens the door, you have a 2/3 chance of getting it right. If you stick doggedly with your gut feelings, you have a 1/3 chance of winning. Compare 33% with 66% and the difference is significant.
Congratulations! You have learned to manipulate the laws of probability to your advantage. It’s time to graduate to the crapshoot.
If you still don't get it, maybe a demonstration would help.
Blaine puts his faith in probability. He doesn’t understand the greater forces at work in the universe. But this is a petty example. What about the woman with stage four metastasized ovarian cancer? Should she resign herself to death, tacitly including herself in the overwhelmingly large bracket of failure?
And anyway, who says that the outcome of an illness is divided so cleanly into success (life) and failure (death)? To the doctor, I suppose the death of the patient would be a failure to defeat the cancer, and the survival of the patient would mean he was successful in clearing it from her body. But for the human being that is most powerfully effected (we call her the patient) it’s far less cut-and-dry than win or lose, live or die. She’s had a long life full of all sorts of events with various sorts of outcomes, and a failed attempt isn’t always losing.
Maybe it’s arrogant of me, but I don’t like being shoved into a large random sample like that: it only holds true when it’s repeated hundreds of times. If you’re only gonna be on Let’s Make a Deal once in your whole life, do you have the luxury of hoping in a mathematical concept?
To wrap it up, if I must boil this down to a single thesis, I think it's this: Statistical estimates are all well and good when dealing with objects and fixed outcomes, but we shouldn’t be too quick to put our own lives into the same number-crunching machine. There’re too many variables.
Who are the people who perform all these calculations, anyway? Are they real people, even? Sitting in sterile laboratories testing every possible event for every possible outcome, cooking up statistics to be put in some arcane database so that insurance companies can blackmail us with the fear of possibility? Why don’t they find something more helpful to do with their time?
Plant trees. Say prayers. LIVE LIFE!
Okay, Blaine, I’ll take your silly tests, if I must. I’ll learn to crunch the numbers. I’ll even change my mind when Monty shows me the first goat. But I won’t tell my patients how likely they are to die. I’ll tell them how much I want them to live...and not just keep their hearts beating, but offer them lives of abundance and joy.
--Blaine Hollingsworth, my Statistics professor
I’ve long felt a vague, unsettling sort of doubt that suspected this to be true, which is partly why I’ve put off taking the class for so long. Of course, Blaine was only referring to the “2 out of 3 dentists agree” kind of propaganda that is hurled at us in advertisements everyday, but I automatically distrust all forms of probability. It bothers me that our culture seems to make its decisions not out of faith but possibility, manipulating the facts into two or three discrete envelopes of outcome: support or rejection; success or failure; yes, no, undecided. But does it ever happen so categorically?
I understand that the sort of calculations we’ve been doing in STAT 2510 aren't like that (“Let’s see...stage four metastasized ovarian cancer: four months to live, 10% chance of survival...” like it’s a crapshoot or something), but are actually pretty legitimate and even helpful within the proper context. Bell curves and standardizations shine perspective on those silly Scantrons we fill in just before our next matriculation, and any form of research is meaningless without a mean and standard deviation. We’re learning how to manipulate the raw data into something that we can work with, to form and support the hypotheses that create theories. It’s all well and good. But it still gets me to thinking about some greater issues.
I guess my problem is that, in the non-science world, when we use probability it’s because we’re focusing on the negative. We only make a percentage of likely success when we don’t believe we’re going to get what we want, as if we’re trying to trick our dying hope into hanging on for just a few more minutes.
My main problem deals with these ‘likelihoods of survival’ you always hear when someone gets sick. I suppose when I get to medical school I’ll understand this concept better, and I imagine I’ll even end up using it myself. But from my current stance (which, I admit, might best be termed "ignorance"), it doesn’t seem right. What do these numbers mean? That 90% of women with stage four metastasized ovarian cancer have died within four months of diagnosis? What does that matter? Every person’s different.
It’s true that the universe is kept in line by rigid natural laws. We think ourselves very clever for having come up with complicated formulas to help us understand the basic laws of physics and human behavior, at least in theory. But since a large sample size is required before one can confidently calculate a probability, can we ever apply that number to the individual? All it tells us is how likely we are to succeed at achieving some desired outcome. But it's just a likelihood. A chance. There’s always a chance for either outcome--even if it’s what we’d have to call a miracle--or even a result entirely different from the two we had defined.
The guy who designed the Epcott Center hated probability. He said it’s an artificial construct created to help us deal with the fact that we don’t understand all the laws that govern the universe. The outcome of every event could, theoretically, be predicted precisely, if only we could comprehend all of the outside forces acting upon it.
We can certainly calculate how fast a ball will hit the ground when it is dropped from a balcony. We’ve tested that one, determined the forces acting upon it, and developed a formula to tell us, without fail, so long as no unforeseen forces should disrupt the defined system, how long its trip will take. But a human life isn’t as simple as a body free-falling through a constant gravitational field. There’s something intangible there that defies the laws of the universe, something connected to the higher Power who designed those laws and is free to manipulate them as He sees fit. Since we don’t understand such forces, we spend years concocting formulas to help us feel better about our actions. These ratios of success allow us to make informed decisions, let us act "cautiously".
Maybe we should try not to be so cautious about everything.
Blaine tried to get us to understand the benefits of probability with this illustration:
On the old game show Let’s Make a Deal, Monty Hall would present an audience member with three closed doors. Behind one of these doors was a fashionable new car, and behind each of the other two doors stood a wild goat. If you were so fortunate as to be afforded this opportunity to acquire a new vehicle, you would stand up in your outlandish costume and chat briefly with Monty before he asked you to select the door you believed to be hiding the new car. You would have a one-in-three chance of picking the right door, agreed? Pretty good odds. Without opening the door you selected, Monty, who knew the positions of the car and goats, would offer to open a different door, one that was certain to be hiding a goat. You would then be left with two doors to choose from, and Monty would give you the option to change your mind, if you had begun to doubt your initial instincts.
So, Blaine’s question to the class was this: should you change your mind and pick the other closed door, or should you trust your gut instinct and stick with the first door you picked?
I’m a firm believer in the legitimacy of the sixth sense, so I was slightly offended when he declared that only a fool would choose to stay with his first decision.
Mathematically, though, he’s right:
When you make your first choice, you’re working with a 1/3 likelihood of choosing the correct door. Say Door #2 holds the car. Whether you pick Door #1, #2, or #3, Monty will be able to show you a door with a goat, because he knows where each one is. If you pick #2, he can show you #1 or #3. If you pick #1 he’ll show you #3, and if you pick #3 he’ll show you #1.
So. Say you pick #1. Monty shows you the goat behind #3. Now you’re given the chance to change your mind and pick #2.
When there are two doors left—one which hides the car and one which hides a goat—you will only have a 1/2 chance of choosing the car IF YOU CHANGE YOUR MIND. This is because, even though you now have new information that increases your likelihood of choosing the right door, your first pick was made under the old information about the location of the car (that is, no information whatsoever) when your chances of success were 1/3, and the only way to utilize your new knowledge of the situation is to change your mind. You are then picking from Door #1 and Door #2. If you stick with #1, more confident of your decision now that #3 is out of the picture, you’re STILL picking from 1, 2, and 3, because you picked #1 from the three of them. It seems illogical, but really it’s true!
In this case, you changed from #1 to #2 and won the car. You were just as likely to have chosen #3, seen #1, and changed to #2, winning again. And just as likely to have chosen #2, seen #1, and changed to #3, losing.
So see, as long as you change your mind after Monty opens the door, you have a 2/3 chance of getting it right. If you stick doggedly with your gut feelings, you have a 1/3 chance of winning. Compare 33% with 66% and the difference is significant.
Congratulations! You have learned to manipulate the laws of probability to your advantage. It’s time to graduate to the crapshoot.
If you still don't get it, maybe a demonstration would help.
Blaine puts his faith in probability. He doesn’t understand the greater forces at work in the universe. But this is a petty example. What about the woman with stage four metastasized ovarian cancer? Should she resign herself to death, tacitly including herself in the overwhelmingly large bracket of failure?
And anyway, who says that the outcome of an illness is divided so cleanly into success (life) and failure (death)? To the doctor, I suppose the death of the patient would be a failure to defeat the cancer, and the survival of the patient would mean he was successful in clearing it from her body. But for the human being that is most powerfully effected (we call her the patient) it’s far less cut-and-dry than win or lose, live or die. She’s had a long life full of all sorts of events with various sorts of outcomes, and a failed attempt isn’t always losing.
Maybe it’s arrogant of me, but I don’t like being shoved into a large random sample like that: it only holds true when it’s repeated hundreds of times. If you’re only gonna be on Let’s Make a Deal once in your whole life, do you have the luxury of hoping in a mathematical concept?
To wrap it up, if I must boil this down to a single thesis, I think it's this: Statistical estimates are all well and good when dealing with objects and fixed outcomes, but we shouldn’t be too quick to put our own lives into the same number-crunching machine. There’re too many variables.
Who are the people who perform all these calculations, anyway? Are they real people, even? Sitting in sterile laboratories testing every possible event for every possible outcome, cooking up statistics to be put in some arcane database so that insurance companies can blackmail us with the fear of possibility? Why don’t they find something more helpful to do with their time?
Plant trees. Say prayers. LIVE LIFE!
Okay, Blaine, I’ll take your silly tests, if I must. I’ll learn to crunch the numbers. I’ll even change my mind when Monty shows me the first goat. But I won’t tell my patients how likely they are to die. I’ll tell them how much I want them to live...and not just keep their hearts beating, but offer them lives of abundance and joy.
