Decisions

# How to understand the different ways you might be wrong

In statistical hypothesis testing, a type I error occurs when a null hypothesis is rejected when it is actually true. This is also known as a false positive. The probability of a type I error is typically set at a level of 0.05, meaning that there is a 5% chance of falsely rejecting the null hypothesis.

On the other hand, a type II error occurs when a null hypothesis is not rejected when it is actually false. This is also known as a false negative. The probability of a type II error is typically set at a level of 0.20, meaning that there is a 20% chance of falsely failing to reject the null hypothesis.

It is important to note that there is a trade-off between the two types of errors. The smaller the chance of a type I error, the larger the chance of a type II error or visa versa.

In statistical tests, alpha and beta are two important parameters used to evaluate the performance of a statistical hypothesis test.

Alpha (α) is the level of significance for a hypothesis test, and it represents the probability of making a type I error. A type I error occurs when the null hypothesis is rejected when it is actually true. Alpha is often set at 0.05, meaning that there is a 5% chance of making a type I error.

Beta (β) is the probability of making a type II error in a hypothesis test. A type II error occurs when the null hypothesis is not rejected when it is actually false. Beta represents the power of the test, which is the probability of detecting an effect when it actually exists. A low beta value means that the test has low power and is unlikely to detect an effect if one exists.

For example, in a medical trial to test a new drug, a type I error would occur if the drug is rejected as ineffective when it is actually effective. This could lead to patients not receiving the treatment they need. A type II error would occur if the drug is not rejected as ineffective when it is actually ineffective. This could lead to patients receiving a treatment that is not effective.

To minimize these errors, it is important to have a large sample size, as well as to set a stringent significance level (e.g. 0.01) and to use appropriate statistical tests. Additionally, it is important to interpret the results in the context of the research question, and to consider other factors that may have influenced the results.

Type I and Type II errors are two types of errors that can occur during the process of statistical hypothesis testing. Type I error is a false positive, and it occurs when the null hypothesis is rejected when it is actually true. Type II error is a false negative, and it occurs when the null hypothesis is not rejected when it is actually false. Both errors can lead to incorrect conclusions. To minimize these errors, it is important to have a large sample size, to set a stringent significance level, to use appropriate statistical tests, and to interpret the results in the context of the analysis question.