This is when you incorrectly reject the null hypothesis even though it is true
What is a type 2 error?
This is when you incorrectly fail to reject the null hypothesis event though H1 is true
What is the statistical significance of a type 1 error?
1-a, meaning how confident we are that we are not making a type 1 error
A common choice is 0.05, meaning we are accepting a 5% chance of incorrectly rejecting H0
What is the statistical significance of a type 2 error?
The statistical power of a test is 1−β, which is the probability of correctly detecting a true effect. Higher power means our test is better at detecting real differences.
α is the threshold for rejecting H0H0. If we make α smaller (e.g., from 0.05 to 0.01), we are being stricter about rejecting H0H0, reducing the chance of a Type I error.
However, a smaller α also makes it harder to reject H0H0, which means we might increase the chance of a Type II error (β) and decrease power.
A larger sample size reduces standard errors (i.e., how much sample means vary).
This leads to narrower confidence intervals, meaning we estimate the true effect more precisely.
Smaller standard errors also reduce β, meaning we are less likely to make a Type II error, which increases statistical power.
