Would this meet your requirement for “beyond reasonable doubt”? At 20% we stand a 1 in 5 chance of committing an error. What if I said the probability of committing a Type I error was 20%? A more common way to express this would be that we stand a 20% chance of putting an innocent man in jail. Without slipping too far into the world of theoretical statistics and Greek letters, let’s simplify this a bit. The probability of a Type I Error is α (Greek letter “alpha”) and the probability of a Type II error is β (Greek letter “beta”). In statistics, we want to quantify the probability of a Type I and Type II error. In fact, in the United States our burden of proof in criminal cases is established as “Beyond reasonable doubt”. Which error is worse? The generally accepted position of society is that a Type I Error or putting an innocent person in jail is far worse than a Type II error or letting a guilty person go free. When we commit a Type II error we let a guilty person go free. When we commit a Type I error, we put an innocent person in jail. However, the distinction between the two types is extremely important. Many people find the distinction between the types of errors as unnecessary at first perhaps we should just label them both as errors and get on with it. A Type II (read “Type two”) error is when a person is truly guilty but the jury finds him/her innocent. However, the other two possibilities result in an error.Ī Type I (read “Type one”) error is when the person is truly innocent but the jury finds them guilty. If the truth is they are guilty and we conclude they are guilty, again no error.
If the truth is they are innocent and the conclusion drawn is innocent, then no error has been made. Two of the four possible outcomes are correct.
The rows represent the conclusion drawn by the judge or jury. Note that the columns represent the “True State of Nature” and reflect if the person is truly innocent or guilty. The table below has all four possibilities. The conclusion drawn can be different from the truth, and in these cases we have made an error.
#Type 1 error free#
At times, we let the guilty go free and put the innocent in jail. Unfortunately, our justice systems are not perfect. H 1: Defendant is Guilty ← Alternate Hypothesis In this classic case, the two possibilities are the defendant is not guilty (innocent of the crime) or the defendant is guilty.
#Type 1 error trial#
Here’s an example: when someone is accused of a crime, we put them on trial to determine their innocence or guilt. To perform a hypothesis test, we start with two mutually exclusive hypotheses. If you are familiar with Hypothesis testing, then you can skip the next section and go straight to t-Test hypothesis.
#Type 1 error software#
The math is usually handled by software packages, but in the interest of completeness I will explain the calculation in more detail.Ī t-Test provides the probability of making a Type I error (getting it wrong). I have had many requests to explain the math behind the statistics in the article Roger Clemens and a Hypothesis Test. Healthcare, Medical Devices, and Pharmaceutical Statistics Training.
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