NRA Survey

I just received a call from the National Rifle Association today. A recorded message from the NRA Executive Vice-President concerning the U.N. Small Arms Treaty was followed by the following single question survey:

Do you think it’s OK for the U.N. to be on our soil attacking our gun rights?

I was instructed to press “1” if I did not think was OK for the U.N. to be on our soil attacking our gun rights. That was followed by a repeat instruction to press “1” if I did not think it was OK. I was then instructed to press 2 if I did think was OK for the U.N. to attack our gun rights. (Note that I was only given that instruction once.)

I am not criticizing the NRA’s position on the U.N. Small Arms Treaty, primarily since I have no interest in making enemies of the most well-armed group in the country. NRA membership outnumbers the people serving the U.S. Armed Forces by over a million. Even if there are no problems with the policy position, there are several problems with the survey. First, it is obvious that the NRA is not concerned what people think about the treaty. The survey is a classic example of a push-poll. It’s designed simply to push a message out to the population. This is evident from the question. What useful information do we expect to gain from asking people if they think it’s OK for the U.N to attack our gun rights. Do we really not know how people will answer that question? It’s no different from my polling my students to find out if they would like to get out of class early. I expect to soon hear an announcement from the NRA proclaiming that the American people are nearly unanimous in their rejection of the Small Arms Treaty. As far as information gathering goes, it’s a complete waste of time and money. For propaganda pushing, on the other hand, it’s very effective.

I wonder what the response rate would have been had the question been “Do you think it’s OK that the U.N. negotiate a treaty designed to prevent guns from falling into the hands of terrorists?” Another group could report that the American people nearly unanimously support the Small Arms Treaty. This survey would be no better as a survey, but just as effective as a propaganda tool.

I will be curious to see what percentage of respondents the NRA reports as supporting their position. It should not be 100%, since I pressed “2” just out of spite.

Car Accidents and Conditional Probabilities

A problem we looked at in Critical Thinking today asked why most car accidents occur close to home. The answer is that most of our driving is close to home. The problem then asked us to explain that in terms of conditional probabilities. I don’t think that I explained it very well, so let me take another shot at it.

Remember the definition of conditional probability: Pr(A|B) = Pr(A&B)/Pr(B).

Let’s assume that 90% of driving is close to home and 10% is not. Let’s also assume that the probability of having a car accident is 0.1 (that’s high, but it will keep the math easy). Then, the probability of being near home given that you had an accident is equal to the probability of the conjunction of being near home and having an accident divided by the probability of having an accident, or Pr(H|A) = Pr(H&A)/Pr(A).

On the assumptions I made above concerning the relative frequencies of trips and accidents, out of 110 total trips, 11 are away from home and 99 are near home. Out of those 11 trips away from home, 1 is an accident. Out of the 99 near home, 10 are accidents. So, Pr(H|A) = .1/.11 = .90, but Pr(not-H|A) = .01/.11 = .09.

Another way to look at it is to use Bayes’ Theorem, but we’ll save that for another time.

Expectations and Grades

There’s an interesting piece in the New York Times today about student expectations and grade inflation. Apparently, there are students (at institutions other than Oklahoma Baptist, I’m sure) that believe that doing the minimal work that is required of everyone in the course should be sufficient to earn a B for the course. Either we have lowered the level of work that we are willing to consider average, or it really is true that in today’s society someone who manages to complete the minimum requirements really is above average. Either disjunct strikes me as disturbing. If you are in Critical Thinking, keep this story in mind. It is relevant to some of the topics that we will be discussing later.

The Monty Hall Problem

One of the assignments in Critical Thinking was to figure the probability of winning the prize in the traditional three-door Monty Hall problem. Remember that there are three doors for you, the contestant, to choose from, but only one has the prize. The host knows what door the prize is behind, and opens another door to show you that there is nothing there. He will open neither the one you pick nor the one that has the prize. Let’s say that you pick Door 1, and Monty opens Door 2. What’s the probability that the prize is behind Door 3? From class, you know the answer is 2/3.

What’s important is that the host knows where the prize is. If he doesn’t know, then the probability is 1/2. You can calculate this using Bayes’ Theorem. Try it out!

By the way, if you can remember “1/2” then you should be able to get some extra-credit points on tomorrow’s exam. Even more points if you can do the calculation…