Listener Mail! (Part One)

In our latest Recess, we open up the mail bag and answer questions, tell stories, and defend ourselves from scurrilous attacks!  Listen to see if we answered YOUR question!

Here is the full text of Joe's complaint against our logic. Enjoy!

 

"P.S. This email wouldn't be complete without a criticism, so I would like to formally take issue with the notion that choosing the same letter on a multiple choice test every time a student must guess will increase their probability of hitting their target.  I believe this proposal only holds true if the student is in no way able to narrow the field or estimate that one or more of the options is probabilistically less likely to be correct than the remaining answers.  In other words, fixing the letter you choose for all of your guesses ahead of time introduces bias free randomness only if you perceive all answers to be equally likely to be correct.  We know from experience that this is virtually never the case (provided you aren't in the wrong classroom taking a test on a subject of which you know literally nothing about).  For example, one of the available choices is often a "gimme" or an obvious toss out... what happens if that choice happens to be adorned with the letter you previously decided was going to be your "guess" letter?  Bear in mind that fixing the letter is a strategy that can never actually improve the probabilistic success rate above 25% (if there are 4 choices).  This is an important consideration when paired with my suggestion that there are times that it will actually reduce your likelihood  of selecting a correct answer, as in the example where one choice is obviously 0%, each of the remaining 3 are 1/3 likely to be correct, so it's better to simply randomly choose one of the three.  That means that fixing the letter choice ahead of time can actually only decrease a student's success, similar to any other bias they may introduce. "

"Ideally, I think you could assign an estimated probability of each choice being correct (with the sum of the probabilities equal to 1) and then use a simple excel model with a random number generator to introduce the critical element of randomness to wash away any bias attached to a tendency to choose one letter over another, anchor to one answer irrationally, etc but that is obviously not possible during a test.  There are a lot of ways to introduce randomness that allow to account for scenarios when a student is able to give themselves an edge by reducing the list of choices (like flipping a coin between two available answers, or flipping two coins to decide between three or four answers by assigning each letter one of the 4 Heads/Tails combinations). "