COMPSCI C8 Lecture Notes - Lecture 21: Null Hypothesis, Test Statistic

• School: Berkeley
• Department: Computer Science
• Course: COMPSCI C8
• Professor: John Denero

Document Summary

Define 2 mutually exclusive descriptions: either this or that. One of them can be evaluated using probability (the null) You (cid:272)a(cid:374) (cid:862)(cid:396)eje(cid:272)t the (cid:374)ull,(cid:863) so the(cid:374) (cid:455)ou a(cid:272)(cid:272)ept the alte(cid:396)(cid:374)ati(cid:448)e. Othe(cid:396)(cid:449)ise: (cid:455)ou"(cid:396)e still not sure, but null looks reasonable. Step 1: two descriptions of the world: null: data come from a well-defined random process, alternative: something else is going on, we evaluate how unusual the data would be under the null. Step 2: choose a test statistic to summarize the data. Step 3: compute the following probability (p-value: p(the test statistic would be equal to or more extreme than the observed test statistic under the null hypothesis) Inconsistent: the test statisti(cid:272) is (cid:862)i(cid:374) the tail(cid:863) of the (cid:374)ull dist(cid:396)i(cid:271)utio(cid:374) In the tail, first convention: the area in the tail (p-value) is less than 5, the result is statistically significant. In the tail, second convention: the area in the tail (p-value) is less than 1, the result is highly statistically significant.