Type I error vs Type II error

Background story:

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?

Review:

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.

Standard deviation:σ

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 H0Reject H0
H0 is trueCorrectType I error: alpha
H0 is false
(Ha is true)
Type II error: betaCorrect (power)

Note:

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.

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