# Math Geek Mom: Nail Polish Statistics

Worries for now, and the future.

## By

September 11, 2014

In Statistics, we talk about different types of error that may arise when decisions are made. Thinking of the state of the world as being the “null hypothesis” (for example, a criminal defendant is innocent or the world is flat), if we reject that world view in favor of another (the defendant is guilty or the world is actually round), we can either be correct or incorrect. If we are incorrect in rejecting the way the world is assumed to be, we call this error “type one error”. Committing such error, we may have been led to change behavior in ways that we would not want, as when we incarcerate an innocent person. However, if we do not change our world view, but should have (such as when we should have convicted a guilty defendant, who is incorrectly found to be innocent,) we call that error “type two error.” I found myself thinking of this lately, as a conversation spread around my neighborhood about a new type of nail polish that is designed to detect “date rape” drugs in drinks.

At a neighborhood swim party a few weeks ago, I sat with my daughter, a neighbor, and her teenage daughter. After listening to adult conversation for quite a while, the two girls decided that it was time to jump in the pool. As they got up to go swimming, I pointed out to them that they should not leave their open drinks sitting there, with the intention of coming back to them. Of course, two adults were staying at the table, so the danger was minimal, but I wanted to make the point to my daughter when there was actually a chance that she would listen to what I was saying. Thanks to the support of my neighbor, the two girls were soon listening to what their (hopelessly out of touch) mothers had to say. I was sad that I even had to have such a conversation, but in light of what some people are saying about campus culture these days, I know that I need to talk about such things years before she plans to enroll in college.

This last week, that same neighbor told me that some college students have developed a way to perhaps help young women detect the presence of “date rape drugs” in their drinks. They are producing a special nail polish that will change color when exposed to certain drugs that enable date rape. It is information about this nail polish that led me to think about “type one” and “type two” error. What if there are drugs in a drink and the nail polish does not change color, an example of “type two” error? Indeed, could this lead to an “arms race” in which drugs are developed quickly that are not detectable by such nail polish? Such type two error could leave a woman hopelessly exposed to danger. Indeed, some have said that there are so many potential drugs that that is almost impossible to design such a nail polish, and that such a nail polish might leave young women with a false sense of security. And what if type one error occurs, and drugs are incorrectly indicated? What effect would that have on an innocent bystander who might be accused of adding drugs to a drink? Indeed, I wonder if young men would start to be insulted if a woman innocently begins to swirl her finger through a drink, without any intention of testing for drugs.

It will be years before I need to send my daughter off to college, but I truly hope that some sort of method for detecting drugs in drinks is found by then. Even better, I hope that the campus cultures change so that such a method is not needed. In the meantime, I will just keep reminding her not to leave open drinks sitting around, in hopes of coming back to them.

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