Last time, when we used R to calculate the sample size, we specified Type I error α and Type II error β, but what does the meaning behind α and β?
We define the “best” sample size that has less variation of the sample mean from sample to sample.
Sample Size Factors:
Type I error: α
Type II error:β
Null and Alternative hypotheses: Difference trying to detect.
Difference between Type I error and Type II error:
Type I error: Reject the Null when Null is true.
α = P(reject H0| H0 is true)
Type II error: Fail to reject null when Ha is true
β= P(fail to reject the H0 | Ha is true)
Power: the probability reject the Null give alternative is true
Power= 1- β
|Fail to reject H0||Reject H0|
|H0 is true||Correct||Type I error: alpha|
|H0 is false|
(Ha is true)
|Type II error: beta||Correct (power)|
standard deviation σ : measure spread of the individual observation
standard error σ/√n: standard deviation of the sample mean.
as the sample size gets larger, the standard error will decrease, but the standard deviation won’t.