1. STAT 104 Section 7
Daniel Moon

2. Agenda
Type I, II error, and power
Applet
Sign Test
T and F Test

3. Type I and Type II Error

4. Type I and Type II Error Applet 1. Statistical Errors
Relationship with Type I error and Type II error
3c) Average is taken over 4 days
Chance of misdiagnosis: 0.13%  6.68%

5. Power

6. Power

7. Paired Sign Test t - Test Sign Test Nonparametric Method
Cope with non-normal data
Concern the center of a distribution
Less powerful than t-test
P-value = 2 * P( X <= obs value) or
= 2 * P( X >= obs value)
t - Test
Sign Test

8. Deciding between t and z

9. T distribution (Unpooled)
Degree of Freedom
Data Desk
We use min(v1, v2)
V1 = n1 – 1 , v2 = n2 - 1

10. T distribution (Pooled)
Degree of Freedom
n1+n2-2
The smaller degree of freedom is, the more conservative. Why? (Shape of t-dist’n)

11. F distribution Test statistics F = larger s^2 / smaller s^2
When you calculate p-value,
Don’t forget to multiply by 2 if it’s two-tail.

12. Problems D Type I error Type II error 1 0.000 0.998 2 0.980 3 0.917 4
0.775 5
0.562 6
0.335 7
0.001
0.158 8
0.004
0.057 9
0.026
0.015 10
0.111
0.003 11
0.341 12
0.718