Type 1 and Type 2 Errors

Be honest… If you got your test back and the teacher marked a question right you knew was wrong, would you bring it to his/her attention? If you got your test back and the teacher marked a question wrong and you knew it was right, would you bring it to his/her attention?

Why the difference???

What about something possibly more critical??? Which is worse: an innocent man going to jail, or a guilty man being set free?

Why the difference???

Here’s what’s happening… There is an event, called a “Null Hypothesis, Ho” This is what you will be making all your decisions with: Is it true or false? Should you reject it or fail to reject it? So, there are going to be 4 scenarios for each situation just mentioned. Two of them turn out right, and two of them have errors in them…

Decision Ho is True Ho is False Do not reject Ho Correct Decision Type 1 Error Reject Ho Type 2 Error Type 1 Error: When you say something is true, but it turns out to be false. This is called alpha 𝛼. Type 2 Error: When you say something is false, but it turns out to be true. This is called beta 𝛽.

So, back to the examples… The test mis-scoring: If the teacher made the error in your favor, is that a Type 1 or Type 2 error? If the teacher made the error not in your favor, is that a Type 1 or Type 2 error? The trial outcome: If the defendant was set free, although guilty, which type of error was that? If the defendant was sent to jail, although not guilty, which type of error was that?

The Answers: The scoring: The defendant: Type 1 Error…When the teacher marked the answer right, even though it was wrong. Type 2 Error…When the teacher marked the answer wrong, even though it was right. The defendant: Type 1 Error…When the defendant was set free, even though he was guilty. Type 2 Error…When the defendant was put in jail, even though he was not guilty.

Now, in your groups… Discuss and write your feelings about the scenario of a guilty man being set free / innocent man going to jail.