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Degree of belief or frequency of occurence November 22, 2006

Posted by Sharath Rao in science, statistics.

Going by the last two posts, looks like I am staying on the doctors topic for a while !! Anyway, this single article contains several themes that interest me as a student and a curious observer of daily life.

Firstly this :

For example, a depressed patient told me she had read that the chances were 60 percent that she would respond to the antidepressant I had prescribed for her.

“That means that 60 percent of the time I will feel better on this, right?” she asked.

Well, not exactly. I explained that if 10 people with a depression just like hers walked into my office, about 6 would be expected to respond to that antidepressant.

I hope you see that there is a difference between the two.

Consdier this example – “If there is a war between the US and China, there is a 50% chance it being a nuclear war.” Does it mean that if they fight 100 wars, 50 of them will be nuclear !! Or is it a degree of belief or strength of your conviction ?

How about this example – “There is a 0.7 probability that my classmates are male”. Does it mean that each person in class has 70% chance of being male ? Or is it that 7 out of every 10 are male.

The above infact is an example of frequentist and Bayesian interpretations of probability. Very simply, is probability something like a degree of belief or is it frequency of something happening ? Its quite an involved ( and unresolved ) debate ( like almost every other debate ! ).

Later in the article is something about how we intepret chance.

In a classic 1966 study, a group of subjects was told that a man had parked his car on a hill and that the car had rolled back into a hydrant after the man had left. The subjects were sympathetic to the man.

But a second group of subjects, told that the car had rolled into another person after the man walked away, held him responsible, even though the cause was the same.

People might chalk up a minor mishap to chance, but they are reluctant to blame a serious event on bad luck. Someone or something has to be held responsible.

And finally the conclusion.

The truth is that random events can make or break us. It is more comforting to believe in the power of hard work and merit than to think that probability reigns not only in the casino but in daily life.

I think its more serious than that. My next post suggests why.



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