Type I and Type II Errors (B)
Some of you have wondered whether a researcher, in testing a single null hypothesis, can make, simultaneously, both a Type I error AND a Type II error. There quick answer is "No," and here's an explanation why:
Think of a man who's on trial for murder. He is, of course, innocent until proven guilty. So let's agree that the NULL HYPOTHESIS is that the man did not commit the murder.
After the jury deliberates, it will announce its verdict. Now if the jury says "guilty" when the man really did commit the murder, the jury has made the right decision. Likewise, if the jury says "innocent" when the man did not commit the murder, the jury has made the correct decision.
There are however, two other possibilities. The jury might say "guilty" when the man didn't commit the murder. Let's call that a TYPE I ERROR. Or, the jury might say "innocent" when the man really is the murderer. Let's call that a TYPE II ERROR.
Now, imagine that the only things you know for sure about this trial are (1) the man is accused of murder and (2) the jury brings forth a "guilty" verdict. You won't know whether this is the correct decision or not. One of the two kinds of error mentioned above might have been made...but only ONE of those errors. The jury (in saying "guilty") either is right or its wrong...and if it's wrong, which of the two kinds of error is the ONLY kind of error the jury could make?
Now, change the second of the two things you know for sure, this time imagining that you know for sure that the accused murderer has been found "innocent" by the jury. This verdict might be right or it might be wrong; and it its the wrong verdict, then the mistake could be described as being one of the two kinds of error mentioned above...but only ONE of those errors. The possible error cannot be "either a Type I error or a Type II error" but instead could only be a Type __ error. (I've left a blank for you to fill in.)
In talking about the accused man on trial and the two kinds of mistakes that the jury can make, I've tried to help you see that when a researcher rejects a null hypothesis, there's only one kind of mistake he/she could make. Likewise, if the null is not rejected, there's only one kind of mistake the researcher could have made. Of course, we don't know in a research study whether the decision to reject (or to fail-to-reject) the null is right or wrong. But if we know what decision the researcher has made, THEN WE CAN SAY WITH CERTAINTY THAT HE/SHE DID NOT MAKE ONE OF THE TWO KINDS OF ERROR. (In my jury story, is it possible for the jury to make a Type I error if it comes forth with an "innocent" verdict . . . or to make a Type II error if its verdict is "guilty"?)
Copyright © 2012
Schuyler W. Huck