STAT 104 Section 7 Daniel Moon

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

Type I and Type II Error

Type I and Type II Error Applet 1. Statistical Errors http://intuitor.com/statistics/T1T2Errors.html http://newton.stat.ubc.ca/~rollin/stats/ssize/n1.html Relationship with Type I error and Type II error 3c) Average is taken over 4 days Chance of misdiagnosis: 0.13%  6.68%

Power

Power

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

Deciding between t and z

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

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

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.

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