What is the difference between type I and type II errors?

 What is the difference between type I and type II errors?

 What is the difference between type I and type II errors?

In hypothesis testing, Type I and Type II errors are two types of mistakes that can occur when making a decision based on data. They relate to whether we reject or fail to reject the null hypothesis (which typically represents 'no effect' or 'no difference').

1. Type I Error (False Positive):

• A Type I error occurs when we reject the null hypothesis when it is actually true. In simple terms, it means we think we found an effect or difference when, in reality, there isn’t one.

• It is also called a false positive or a false alarm.

• The probability of making a Type I error is denoted by α (alpha), which is typically set at 0.05. This means there is a 5% chance of rejecting the null hypothesis when it is true.

Example: In a medical study, a Type I error would mean concluding that a drug is effective when, in reality, it is not.

2. Type II Error (False Negative):

• A Type II error occurs when we fail to reject the null hypothesis when it is actually false. In other words, we miss a real effect or difference that actually exists.

• It is also called a false negative or a miss.

• The probability of making a Type II error is denoted by β (beta). The complement of β (1 - β) is the power of the test, which measures the test’s ability to detect a true effect.

Example: In the same medical study, a Type II error would mean concluding that a drug does not work when, in reality, it is effective.

3. Summary:

• Type I error: Incorrectly rejecting the null hypothesis (a false positive).

• Type II error: Incorrectly failing to reject the null hypothesis (a false negative).

4. Balancing the Errors:

• There is typically a trade-off between Type I and Type II errors. Reducing the probability of a Type I error (by using a smaller α, such as 0.01 instead of 0.05) increases the likelihood of a Type II error, and vice versa. Therefore, it’s important to find a balance depending on the consequences of each type of error in the specific context.

Conclusion:

In summary, a Type I error is when you find a difference or effect that isn’t really there (a false alarm), while a Type II error is when you miss a real effect or difference (a missed detection). Both errors are important to consider in hypothesis testing, and the goal is to minimize them as much as possible."