It’s been about two years by now, but the argument I got in with the Toxic Tort prof. This guy was the leading attorney in the field. Since he represented big companies, I can only imagine he was pure evil. The fact that he couldn’t understand basic statistics is just mind boggling.

It all started when he made us participate in an exercise where we had to guestimate certain measurements. For all the questions, we had to give a range where we thought we were 95 percent sure the measurement would fall in. Example: How long is the Nile river in miles? We were supposed to give the low and high end of our interval. Another question was write the year in which Ghangis Khan pillaged and plundered (or whatever he did).

He thought he was so witty when our answers were “wrong”. He claimed this was a human condition where we intentionally create smaller intervals and we overestimate our ability to narrow. I raised my hand (a rarity in lawschool, but particularly in that boring class), and tried to explain that what he was asking for was an impossible task.

I told him that I had no frame of reference in terms of the length of the nile river and thus I couldn’t form any type of confidence interval. He made some jokes at my expense where he mistook knowledge for intelligence. I don’t think I lack intelligence just because I have no concept of distance. This went back and forth for a couple of minutes. He got me to admit that I knew the Nile river was probably longer than 5 miles and probably shorter than a billion miles. He thought he had won.

What he refused to grasp is that a 95% confidence interval is actually very specific. It means that you expect to be right 95% of the time and wrong 5% of the time. That means that if I answered 100 of his questions, I should get 95 of them right. But these questions were impossible. I could come up with an interval that was 100% accurate by picking absurd book ends or I could guess numbers that I THINK are reasonable. But, my knowledge is so limited that it’s very easy that I could be wrong.

But this professor saw 95% and thought “dang jethro, that’s a big number. It’s gotta be easy to make an interval like that”. But he’s WRONG. A 95% interval is no more or less specific than a 50% interval. Or a 99% interval. Confidence intervals are based on 2 things. The mean and the standard deviation. My mean was just a guess. Based on essentially nothing. And the standard deviation was equally random.

I can’t remember how you specifically calculate a confidence interval, but it goes something like this. Say I’m measuring the length a lightbulb lasts. I have a sample of 100 out of the 1000 that were manufactured. I measure the length of each one of those 100. I find out that the mean length is 10 hours (these are the ones that Gino installed in our apartment). I also notice that each lightbulb lasts either exactly 9 hours or exactly 11 hours. I would take the mean and the average standard deviation (which is 1 b/c each one is 1 off from the mean of 10), and then plug it into an equation that involves the formula for the normal curve. The 95% interval could be something like [9.5-10.5] while the 99% interval could be [9-10]. You could say that, with this data, there is only a 1 percent chance that the actual mean length of the lightbulb is either less than 9 hours, or greater than 10. If I had less lightbulbs to measure (35 instead of a 100), and the average standard deviations were higher (ligtbulbs had individual measurements of 2 hours, 40 hours, 10 minutes, etc), then the confidence interval would expand considerably. It’s logical. If you are getting data all over the place, you gotta step back and think “hmm, I’m not that confident that we really know anything about these lightbulbs. We could just be getting unlucky”

He was confusing “confidence intervals” with gut feelings. If asked me to pick an interval that I was “pretty sure” was right, MAYBE I could (I probably still couldn’t). I’d be frustrated that it was still a guess based on essentially no knowledge, but I could live with it. But, he was bastardizing the use of a stat. He doesn’t have the right to define what a confidence interval is. That’s a stat term. If he’s going to use it, he better use it right. Especially when he’s used confidence intervals in courtrooms on cases worth millions and millions of dollars. He wasn’t telling a jury that he was “pretty sure” that he was right. He was saying he was statistically certain of something.

I wish I had the argument on tape. Because he was so condescending, b/c he’s old and successful and I’m just a punk kid with a baseball cap and shorts. But, that didn’t make him right. And of course, his little lapdog student had to come to his rescue. He used one of the props (a clock like wheel that had an ever expanding red “wedge” that covered more and more of the clock). He said that if he picked a number on the back, and then started making the wedge, I’d know when I was 95% sure that the wedge covered the mystery number.

Yeah, no kidding. Anyone who has seen the price is right knows that. But, in THAT example, there is a limited number of solutions. Say there were 100 numbers. I’d have to cover 95 of them. If we did this experiment thousands of times, I should get it right about 95% of the time.

BUT, with the Nile example, the possible solutions were essentially infinite. I hope that he was just so blown away by my lack of intelligence (well, it was actually a lack of knowledge) that he couldn’t grasp this inability. Because otherwise, it means that he really didn’t know what a confidence interval was. And that’s scary. If he changed the assignment to a 50% interval, I guarantee you that the majority of people would still get the exact number wrong. This wasn’t a situation of “well, I remember aunt sue telling me that the nile was 700 miles long, but I’m going to say 500-1000 just to be safe.” I have NO CLUE how long the nile is. I don’t even know if it goes through countries other than Egypt. I think it does. But, I have no idea what the length of Egypt is. Heck, I don’t even know how wide our country is. If I had to guess, I’d say it’s probably an 8 hour flight, and planes go about 200 miles, so it’s probably 1600 miles. Would I say that with any confidence? NO.

This old man still makes my blood boil. People claim that I “have to be right”. That’s not true. Rather, when I’m right, I have to win. That’s a big difference. I KNOW he’s wrong. But he “won”. I don’t even care what the other people in the class think. I care what HE thinks. It kills me that he walked away from that conversation thinking that I didn’t know what I was talking about.

I’m 95% certain that I hate him for it.