#### 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 H0 | Reject H0 | |
---|---|---|

H0 is true | Correct | Type I error: alpha |

H0 is false (Ha is true) | Type II error: beta | Correct (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.*