"There are three kinds of lies: lies, damned lies, and statistics."
- Benjamin Disraeli, Prime Minister of England (1868, 1874-1880)
As Disraeli knew, statistics can be used to deceive. Statistics also can be misleading, even when there is no intent to deceive. Yet statistical analysis is just too powerful a tool to ignore. I have taught statistics at the graduate level, but there is much I still have to learn, not only about how to use statistics properly, but also about how to communicate statistical information accurately and effectively.
In comments on just another vet's excellent diary, One man's perspective on abortion, plymouth and I had a brief exchange about statistics for contraceptive failure. I am repeating most of that exchange below the fold both to provide some information that might be of general interest, and also to invite further comments on my use of statistics.
The exchange with plymouth was triggered by a
comment, in which I
made the following assertion:
The actual rate of unintended pregnancy for those using the pill is about 8% per year. That translates into an 80% chance of pregnancy over a 10 year period.
In a response, plymouth pointed out:
Actually it's a 56.6% chance:
1-(0.92^10)=.5656
(approximately)
I posted the following
reply to explain the difference between my calculations and plymouth's, and to further clarify the intent of my original comment.
I was describing population probabilities rather than individual probabilities. Medical data of this type typically describes population probabilities. In reading my post, I realize that it could be taken as a statement concerning individual probabilities. It is not. In writing the post, my goal was to convey the reality that the contraceptive methods currently available to most women are not going to eliminate unwanted pregnancy. I realize now that my post could be interpreted as saying that each woman taking birth control pills has an 80% chance of getting pregnant over the course of 10 years. That is not true. It is true, however, that a large population of women taking birth control pills will produce approximately 80 pregnancies per 100 women over a 10 year period. (Note: This is based on the assumption that each year constitutes what statisticians call an "independent event." Clearly this is not true at the individual level, but the assumption provides a good approximation at the population level.) However, I think it is misleading to characterize this as "an 80% chance." I apologize for my carelessness and thank you for bringing it to my attention.
For tThose wishing to understand the difference between population probability and individual probability may find it helpful to consider the following example: You have a large population of coins. You flip every coin in that population, and you end up with about 8% heads. You flip the coins again, and you end up with about 8% heads. You do this 8 more times, and each time you come up with about 8% heads. Over the course of your 10 flips, you have seen approximately 80 heads for every 100 coins in your population.
Now let's take out an individual coin. We don't know what the probability of heads is for this individual coin. In fact, for medical data of the type I've cited, the relationship between population probability and individual probability is not straightforward. For tort litigation, methods such as Bayesian analysis are sometimes used to get from population risk to individual risk. But suppose we make the simplifying assumptions that each coin in the population has an 8% probability of coming up heads and that each flip of the coin is an independent event. Now we take one of those coins and we flip it 10 times. Using the binomial formula, we can calculate the probability that heads will come up in one or more of our 10 flips to be .05656 (approximately).
So if you are a woman taking birth control pills, should you assume that you have a 56% risk of unintended pregnancy over the next 10 years? If you have no other information, that's the way to bet. However, there is other information available. If you use birth control pills correctly and consistently, your risk will be much lower - unless, of course, you are one of those women for whom birth control pills do not work. That's the thing about individual risk, we usually don't know what the odds really are. However, we do know what the odds are for populations. We also can do things to change the odds for populations. Through better education, we can reduce the incidence of contraceptive failure. But even with education and contraception, we are going to have unwanted pregnancy. So what do we do about it? Do we insist that anytime a woman has sex she must be willing to accept full-term pregnancy and motherhood as a possible consequence, or is she going to have other options?
Feel free to correct, criticize, improve, etc.
