Type I and Type II Errors
ASSIGMENT
Truth about the population
true / trueDecision based / Reject / Type I error / Correct Decision
on sample / Accept / Correct Decision / Type II error
Ramifications: A Type I error is made when the null hypothesis is actually true but the alternative hypothesis is chosen.
A Type II error is made when the alternative hypothesis is actually true but the conservative step of accepting the null hypothesis is actually made.
Example 1: Conjecture: I believe that this student cheated in an exam.
: the student did not cheat
: the student cheated
Truth about the student
true (student did not cheat / true (student cheated)Decision based / Reject / Type I error – come to the conclusion that the student cheated when he did not / Correct Decision
on evidence / Accept / Correct Decision / Type II error – come to the conclusion that the student did not cheat when he really did.
Which is worse?
If you want to reduce the possibility of a type I error, you must lower your alpha value - you want to be as sure as possible that a person did it. Circumstantial evidence is not enough. We don't have an innocent person punished. But if we do that, there are certainly going to be more people who get away with the cheating because in that process of being crystal sure of the person's guilt, we will be letting more people go for whom we have strong suspicion but not positive proof. That means we are increasing the possibility of a type II error.
If we want to reduce the possibility of a type II error, (we don't want cheaters getting away with it), we need to take anyone we strongly have suspicions about cheating and punish them. But if we do that, there are bound to be students who get caught by the circumstantial evidence against them and possibility get punished for cheating when they didn't do it. Hence more type I errors.
Ramifications:
Type I error – punishing a person who is truly innocent and perhaps mistrusting them for a long time
Type II error – student gets away with cheating and perhaps thinks he always can. Later in life, this can lead to larger crimes.
Example 2: Conjecture: The Eagles are really good this year and I am willing to bet money that they will get to the Super Bowl.
: the Eagles will not get to the Super Bowl.
: the Eagles will get to the Super Bowl.
Truth about the Eagles
true (Eagles do not go to Super Bowl) / true (Eagles go to Super Bowl)Decision based / Reject / Type I error – Come to the conclusion that the Eagles will go to the Super Bowl when they really will not / Correct Decision
on history / Accept / Correct Decision / Type II error – come to the conclusion that the Eagles will not go to the Super Bowl when they really will
Ramifications:
Type I Error: I may bet on them and lose a lot of money. I also may make reservations in the Super Bowl city long beforehand and may lose my down payment. Also, plain disappointment when I find out I am wrong.
Type II error: I may not be able to go and watch them play because it will be impossible to get tickets and reservations at the last minute. There is no living and dying with every play because I have decided that they will ultimately lose.
The Type I error is clearly the worst error. We get ourselves so excited when we think they have a chance and actually end up believing that they will get in. When they don’t the error is devastating. Many of us actually look forward to the Type II error – being pleasantly surprised when they get to the Super Bowl when we assume they won’t.
Assignment: For each conjecture below, you are to describe in words what and are. Consider the decision that you have to make based upon your conjectures. Then make a chart similar to the ones I created and fill in words what the Type I and Type II errors mean. Finally, describe the ramifications of making these errors within the context of the problem and describe which of the 2 errors are worse (in your opinion).
Do any 4 you wish. Problems are to be written neatly on notebook paper or word processed.
1. It is believed that a new drug can cure a cold.
2. The teacher will never check homework today.
3. In a big store like Wal-Mart, they will never catch me if I shoplift.
4. If I try to learn to ski, I will end up hurting myself.
5. I’ll apply to the University of Pennsylvania because I am sure I’ll get in.
6. There might be a bomb in the school because someone called in a threat. We should evacuate.
7. Heaven and Hell exist.