The Unauthorized Investigator's Guide to
The Church of JESUS CHRIST of Latter-day Saints

Lesson 3

Faith Through the Eyes of a Statistician

Say that I have a hat that contains 5 dice. One die has 4 sides numbered 1-4, one has 6 sides numbered 1-6, one has 8 sides numbered 1-8, one has 12 sides numbered 1-12 and one has 20 sides numbered 1-20. I pick a die out of the hat without showing it to you and role it 4 times. The results of the 4 roles are 1, 6, 4, and 7. Based upon that information, you need to guess which of the 5 dice I picked out of the hat. Letís say 2 students, Albert and Brian, answer that question. Albert guesses that it was the 8-sided die that I was rolling. Brian guesses that it was the 12-sided die.

We ask Albert why he guessed 8-sides. He explains that since there was a 7 rolled, it couldnít have been the 4-sided or the 6-sided die that I choseóneither of those has a 7. So it had to be the 8, 12, or 20. Of those three, the 8-sided die is the most likely one to show a 1, 6, 4, and 7. If it was the 12-sided die, there probably would have been a role greater than 8. More so with the 20-sided die. Using this reasoning, the 8-sided die is most likely die.

We then ask Brian why he chose 12. He said that he chose it because 12 is his lucky number.

Now, which student had the better answer to the question, Albert or Brian? My contention is that Albert had the better answer. Albertís answer is based upon a valid statistical argument. Brianís is based upon a haphazard guess. Answers based upon valid statistical arguments are always better than answers based upon haphazard guessesóvalid statistical reasoning is a superior problem solving method than the method of haphazard guessing.

Letís say that after both people make their guesses I show the die. It turns out that Brian was rightóthe die has 12 sides. Even though Brian turned out to be right, Albertís method was still superior. It is better to arrive at the wrong answer through a better method than arrive at the right answer through an inferior method.

This is the point of the text book Loss Models when it said:

An important point is that quality is a property of the estimator and not of the estimate. We are interested in the quality of the method, not the quality of any particular outcome from using the method. Use of a high-quality estimator does not ensure that realized outcomes will be consistent with estimated outcomes. (Loss Models: From Data to Decisions by Klugman, Panjer, & Willmot. page 26)

What is the point of this you ask? The point is this: the church tells you that you should "firmly believe" something, with little regard to how you arrive at that belief. In contrast, I contend that it isnít the ultimate belief that matters, but rather the method used to derive it. Even if it turns out that the die has 12 sides, an outcome that is certainly possible, Iíd still rather be Albert, knowing that I made the best decision with the information I had available at the time.


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