What are the chances? - USM Forum -- Message Board

Date: Jun 4, 2004

What are the chances?

Date: Jun 4, 2004

This is very interesting; thanks for posting it! I've sent it on to the IHL.

Date: Jun 4, 2004

Interesting.

However, you might want to consider the percentage of Mississippians who simply don't care one way or the other about higher education. They would come out of your denominator. Since I don't know the population figures that you used as the base for your probabilities, I can't recalculate with this factor in the mix. But if 60% of the folks who care are pro-Thames, then you'd really be taking 60% of probably something like 10% of the general population. This makes the odds not so incredibly small that the 1st 75 letters were all pro-Thames. The odds are still incredibly small that this would happen by "random chance."

The other thing to remember with probabilities is something that Ralph Bisland taught me in a business stats class at USM almost 30 years ago: never underestimate the effects of intent & practice. You can bet that SFT's folks had 75 letter writers with their letters in the mail the day that Robinson was announced. In other words, it was not a probabilistic situation.

Finally, don't forget the old "experimenter bias effect." Robinson expected the letters to be overwhelmingly pro-Thames, so that's what she observed. Same thing happens in science: if someone in polymer science found something that would kill mesothelioma cells on contact, they would throw it away unless it made good paint.

Date: Jun 4, 2004

Invictus, I appreciate your thoughts on my post. You may well be right in betting that maneuvers were undertaken to insure that Mrs. Robinson could correctly assert that each of the first 75 letters she received voiced support for Thames. I am convinced that the only likely alternative is that she fabricated her data. In either event, it seems that Mrs. Robinson wanted the Hattiesburg American readers to believe that the letters arrived in “random” order and that support for Thames is essentially unanimous in the community.

The model I used in generating the probabilities presented above is very simple. It is based on a binomial distribution with n=75 Bernoulli trials. If we force ourselves to think of “success” as a vote of confidence for Thames, and if we assume that (100p)% of the interested public voices confidence in Thames, then the probability of all letters being “successful” is p^75. That is, p raised to the 75th power. Above I consider the cases that 60%, 70%, 80%, and even 90% of the interested public support Thames. The cases correspond to taking the values p=.6, p=.7, p=.8, and p=.9, respectively. You are quite correct in pointing out that I am ignoring the disinterested public, and a better model should take into account the size of the interested public. Using a hypergeometric distribution might be preferable here, but this model would require us to choose values for the population of the interested public. Until a statistician steps in and sets me straight, I’ll stick with my simplistic model. My guess is that the binomial distribution model actually overestimates the probability of all 75 letters being pro-Thames.

Finally, your point about the “experimenter bias effect” is well taken.