A professor presented this question: "If a cancer screen comes back positive in 68 of 75 cases of actual cancer and in 5 of 191 cases of no cancer, when the actual cancer rate in the total sample is 1/3, what is the probability of a false negative test result (patient has cancer but test comes back negative)?"
I was thinking the simplest calculation is as follows: the cancer screen identifies 68/75 = 91% of cases where the patient has cancer. It fails to identify 7/75 = 9% of cases that it should identify. The probability of a false negative is 9%.
One person tells me that it is necessary to use Bayes' Theorem to arrive at a correct answer. I don't know how to do that. He says the correct answer is 4.57%. But when I use the Bayesian calculator at http://www.vassarstats.net/clin1.html, I don't get that number.
Possibly I am using the calculator wrong. Even so, I don't know why the 9% figure wouldn't be right. I am wondering whether this is a situation where Bayesian and non-Bayesian statisticians diverge.
In case anyone is wondering, this is not a homework question. It used to be a quiz question, but right now it's just spilt milk.
Thanks for any insights.
I was thinking the simplest calculation is as follows: the cancer screen identifies 68/75 = 91% of cases where the patient has cancer. It fails to identify 7/75 = 9% of cases that it should identify. The probability of a false negative is 9%.
One person tells me that it is necessary to use Bayes' Theorem to arrive at a correct answer. I don't know how to do that. He says the correct answer is 4.57%. But when I use the Bayesian calculator at http://www.vassarstats.net/clin1.html, I don't get that number.
Possibly I am using the calculator wrong. Even so, I don't know why the 9% figure wouldn't be right. I am wondering whether this is a situation where Bayesian and non-Bayesian statisticians diverge.
In case anyone is wondering, this is not a homework question. It used to be a quiz question, but right now it's just spilt milk.
Thanks for any insights.
