Type I and Type II Errors and the Power of a Test Type I error: Also known as a false positive error. This means rejecting the null hypothesis when...
Type I error:
Also known as a false positive error.
This means rejecting the null hypothesis when it is actually true.
In other words, we wrongly conclude that there is a significant difference between groups when there is no real difference.
Often referred to as a type I error, and denoted by the symbol .
Type II error:
Also known as a false negative error.
This means accepting the null hypothesis when it is actually false.
In other words, we wrongly conclude that there is no significant difference between groups when there actually is a difference.
Often referred to as a type II error, and denoted by the symbol .
Power of a test:
The probability of rejecting the null hypothesis when it is false.
It tells us how confident we can be in rejecting the null hypothesis.
A high power means we are more confident of making the right decision when the null hypothesis is false.
It is expressed as a percentage and is denoted by the symbol .
Relationship between Type I and Type II errors:
If we want to decrease the risk of a type I error (false positive), we increase the risk of a type II error (false negative).
Conversely, if we want to decrease the risk of a type II error, we decrease the risk of a type I error.
Importance of knowing the power of a test:
It helps us determine the appropriate sample size needed to achieve a desired level of power.
Knowing the power allows us to choose the right level of significance for our test.
A high power is crucial when the outcome of a test is highly sensitive, as it allows us to make a correct decision even when the null hypothesis is false