MATH 203 Lecture Notes - Lecture 23: Binomial Test, Probability Distribution, Test Statistic

• School: McGill University
• Department: Mathematics & Statistics (Sci)
• Course: MATH 203
• Professor: Michael Wallace

Document Summary

Non parametric tests 6 one sample sign test. Single populaion tests with the normality assumpion: these test are formulated in terms of ranks. Sort the data into the ascending order, and assign ranks in order. Median instead of mean: pr[observaion <= xmed] = , the sample median is the halfway point of the sorted sample, pop median eta . H0: = 0: conduct the test my comparing how many obs are above or below 0. One-sample sign test: we deine a test staisic s depending on our ha, e. g. ) one-sided tests. In either case, h0|t then s ~ binomial (n, ) If null|t; there should be an equal chance each obs is greater/less than 0. E. g. ) c(0. 24, 3. 16, 1. 97, 2. 10, 0. 92: h0: = 0. 5, ha: > 0. 5, 4 values are larger than 0. 5 -> s =4. P-value -> p[x>=4] w/ x ~ binomial (5, ) Comparing two populaion: independent samples: non-parametric equivalent of the two-sample t-test, instead of.