Jun

10

Errors in statistics are usefully classified as type 1 and type 2. A type 1 is a false positive or undue credulity and a type 2 error is a false negative or false skepticism. The greater you try to reduce the level of error in one the greater the likelihood of error in the other.

                                          Don't reject             reject

no effect hypothesis true       correct                type 1 error              

no effect hypothesis false      type 2 error          correct

A useful way of considering the decision making is above. Consider for example the no effect hypothesis that a pill is not healthy. if it's not healthy and you say it's healthy you make a type 1. If it's healthy and you don't say it is healthy you make a type 2.

A certain agency that regulates drugs is famous for only considering the type 1 errors, making sure with endless and ruinous double blinds that type 1 errors are minimized to the excessive making of type 2 errors and keeping off magic bullets that would extend life span and health enormously.

There are many areas where these trade-offs between errors occur. For example in spam filters. You can reject good things, that's type 1. You can accept bad things– that's type 2.

Our own field often has trade-offs like this. The hypothesis that a system or set point for a trade is random is a good null hypothesis. If you accept the system, you're just incurring churning for a worthless randomness. If you don't accept the system, and it's good, why then you've lost some good money.

The decision to expand your business or trading is another area that crops up frequently. If you expand it you might get in over the head. If you dont expand it, you might miss the gold. The movement into a new field, or the engagement of an employee or employer is another frequent trade off of type 1 and type 2, gullible reaching versus excessive caution that frequently arises.

The usual way to trade off between the two types of errors is to consider the cost of both errors, and to balance your decisions based on the relative costs. Considerations relative to randomness, and variability must also be considered. Also, the myriad psychological biases that lead us to place too much reliance on avoiding the two types of errors that the cognitives have contrived with their silly experiments on college students et al.

What other trade-offs of type 1 versus type 2 do you see that mite be of use to market people or others and what better way to consider gullibility versus skepticism do you see?

Alan Millhone writes:

This weekend I will travel to Grove City, Pa for a yearly Checker Tournament. While playing I will have choices to make. Sometimes there's only one way to move. Often times there's more than one way to move or jump. Checker players and Market players need to evaluate all moves or trades before executing. In Checkers if you touch a piece you have to move that piece– often with disastrous results. If you trade on line you need to consider your trade carefully before hitting "send". Tom said, "Move in haste— repent in leisure". 

Victor Niederhoffer adds:

Sharif KhanThe trade-off in errors in games like checkers and chess would be someone offers you a seeming advantage. Your null hypothesis is that it's not worth accepting. If you take the gambit or seeming opportunity when it's really no good you're making a type 1 error.

In checkers I've found that no opportunity that looks good, no opportunity to set a trap for example, is worthwhile against a good player, as good players never make mistakes. You were too gullible. If you don't take the opportunity when it would have been good, you're making a type 2 error. You were too skeptical. I find that in checkers the type 1 errors are much more costly than the type 2 errors, but in chess I don't know enough to say. But among the good players, I think they often are too cautious or too skeptical if they wish to win a world championships. They are too likely to go for the draws. In general, I would say if you want to be the best you have to be ready to make the type 2 errors to a greater extent. But then you always risk going belly up.

The situations are not without personal applicability to myself. It's easier in squash. I played an errorless game. Never made a type 1 error of going for broke with very risky shots. Well, it wasn't that bad. i went for about 5 years without losing a game in a match or so. But it wasn't good enough to beat the infernal Sharif Khan as much as I should. I should have played a much more errorful game, being willing to accept the risky shots and confrontations and hitting it on the rise and changing my infernal errorless slice backhand to a top spin so I could belt the ball through the Khans the way the Cubans who played Jai Lai could. In other words, I didn't make as many type 2 errors as I should have. 

Anatoly Veltman comments:

I remember grandpa coaching me at 5 or so: "always believe a man." If it turns out to be a lie, you'll find ways to extricate. But if you distrusted without good reason to begin with, you risk losing a friend– and that's an ultimate loss.

Jim Sogi adds:

Why do smart people make either type 1 or 2 mistakes? Presumably, and by definition, it is not because of stupidity, so some heuristic must be at play. In type 1, the fear and result is that you look and feel stupid. In type 2, there is less risk of looking and feeling stupid, but you end up being frustrated by the loss of opportunity. The joke around here is "which is worse" –you present a bad and a ridiculously bad alternative. Weighing the cost benefit is faulty because of proven heuristics are lopsided towards avoidance rather than gain. Add in marginal utility considerations and the difficulty is even harder. 

Bill Egan comments:

I will add a twist to the type 1 error problem. I have seen certain extremely intelligent people simply be unable to conceive they might be wrong. This is a problem that gradually gets worse. They have been right 99% of the time because they are so smart, and as time passes, they make bigger and bigger bets because, 'hey, I've been right.' This isn't quite hubris or arrogance because they really are that good. Finally the odds catch up with them.

Roger Longman writes:

Roger LongmanVic,

Love this.

So seems to me the real challenge is figuring the cost of a type 1 or 2 decision.

In the case of the FDA, the costs of a type 2 error are dramatically higher than the cost of a type 1. Those costs aren't financial, or not primarily financial. There's the substantial humiliation cost, for example, of approving a drug that turns out to have some important side-effect (or a side-effect more important to a group of influential people than its benefit to a group of less influential people) and being dragged in front of a congressional committee (Charles Grassley of Iowa has been the grandmaster of this, but he's got plenty of competition). There's the bureaucratic cost of being passed over for a more visible job, or an interesting review opportunity, if your name is associated with a controversial decision.

All of which is to say: of course the FDA errs more on type 2's. And the growing pharmacopeia (much of which is generic and therefore low- cost) only encourages this bias towards type 2 errors, particularly in regard to follow-on drugs (i.e., new molecular entities in the same class as approved drugs). If — the FDA figures, albeit not publicly
– by instinct, as it were — there is already a good drug that helps a majority of people why take the chance that a second drug in the same class will provide more incremental benefit than incremental risk, which — as I note above — comes with disproportionate institutional costs?

There's also an inherent problem with drug development divorced from serious comparative effectiveness (the current system of purchasing drugs, based as much on rebates retained by payers as medical and economic value provided to patients and employers, actually discourages the kind of comparisons common in most sectors of the consumer economy).

Victor Niederhoffer comments:

Longman was editor of Windhover Information Ventures Biomed and is very knowledgeable about the FDA. I wish he had been at Prof Tabarrok 's talk at junta where the positive case for the FDA going out of business was limned with statistics and current studies on deaths caused by lack of approval.
 


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