Type I and Type II Errors (A)

Dear Students,

Some authors of statistics books, in trying to help their readers understand the meaning of Type I and Type II errors, draw a parallel between court trials and hypothesis testing. Here's a summary of what these authors say:

Suppose there's been a murder and someone's been charged with the crime. When the accused goes to trial, there's a presumption of innocence. (You've undoubted heard the oft-stated saying: "You're innocent until proven guilty.") Well, this presumption of innocence is like the null hypothesis in hypothesis testing.

The presumption of innocence will be discarded only if the prosecuting attorney can present convincing evidence that the accused is not innocent. This is like hypothesis testing, for a researcher will reject the null hypothesis only if the sample evidence is "convincing" in the sense that it does not conform to what we'd expect to see, in a sample, if the null hypothesis were true.

Now, at the end of the trial, the jury comes forth with its decision. They will say, in essence, either "guilty" or "innocent." The first of these decisions is analogous to rejecting the null; the second is analogous to failing-to-reject the null.

Regardless of what the jury says, its decision might be right or it might be wrong. If the jury says "guilty," that might be a mistake because the accused is actually innocent; or if the jury says "innocent," this too might be a mistake because the accused is actually guilty. The first of these two possible mistakes is analogous to a Type I error because it would constitute wrongly rejecting the presumption of innocence. The second of the two possible mistakes is like a Type II error because it would constitute wrongly staying with the presumption of innocence.

If juries were perfect, they would never reach a verdict that's wrong. But juries sometimes make a mistake. Hypothesis testing isn't perfect either. The decision reached by a researcher after he/she analyzes the sample data may be the right decision. That's what he/she/we hope will happen. But the researcher's decision to reject or to fail to reject the null hypothesis may be the wrong decision. If the null hypothesis is rejected when it's actually true, that's a Type I error. If the null hypothesis is not rejected when it's actually false, that's a Type II error.

One last parallel is worth noting. After a jury renders its verdict, we usually do not not know FOR CERTAIN whether its decision was correct. There are exceptions, of course, but normally the jury's verdict represents its "best guess" as to the likely truth of the charges lodged against the accused. Similarly, a researcher does not know FOR CERTAIN, after moving through the steps of the hypothesis testing procedure, whether his/her decision about the null hypothesis was correct. That decision represents only his/her "best guess" as to the state of affairs in the population(s) that was/were sampled.

Sky Huck

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Schuyler W. Huck
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