HLSC 1F90 Lecture Notes - Lecture 45: Acne Vulgaris, Type I And Type Ii Errors, Randomized Experiment
27 Mar 2017
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In previous sections, we were able to do inferential procedures on the two population means. Analysis of variance is an inferential method used to test. Imagine you wanted to see the difference of average times for three different acne medications to cleanse out all the acne on a specific body part. Our null and hypothesis would look like this: (cid:2868):(cid:2869)=(cid:2870)=(cid:2871) (cid:2869):(cid:1872) (cid:1864)(cid:1857)(cid:1853)(cid:1871)(cid:1872) (cid:1867)(cid:1866)(cid:1857) (cid:1867)(cid:1858) (cid:1872) (cid:1857) (cid:1853)(cid:1855)(cid:1866)(cid:1857) (cid:1865)(cid:1857)(cid:1856)(cid:1855)(cid:1853)(cid:1872)(cid:1867)(cid:1866)(cid:1871) (cid:1853)(cid:1874)(cid:1857)(cid:1870)(cid:1853)(cid:1859)(cid:1857) (cid:1872)(cid:1865)(cid:1857) (cid:1858)(cid:1867)(cid:1870) (cid:1855)(cid:1864)(cid:1857)(cid:1853)(cid:1866)(cid:1871)(cid:1866)(cid:1859) (cid:1853)(cid:1855)(cid:1866)(cid:1857) (cid:1871) (cid:1856)(cid:1858)(cid:1858)(cid:1857)(cid:1870)(cid:1857)(cid:1866)(cid:1872) (cid:1872) (cid:1853)(cid:1866) (cid:1872) (cid:1857) (cid:1867)(cid:1872) (cid:1857)(cid:1870)(cid:1871) Your null and alternative hypothesis, in theory, could be separated into three separate tests. In this example, since there are 3 means, we could separate the hypotheses as: (cid:2868):(cid:2869)=(cid:2870) (cid:2869):(cid:2869) (cid:2870, (cid:2868):(cid:2869)=(cid:2871) (cid:2869):(cid:2869) (cid:2871, (cid:2868):(cid:2870)=(cid:2871) (cid:2869):(cid:2870) (cid:2871) However, separating it in this way, would increase the probability of type i errors. This is why we use the anova procedure instead. Why is it called (cid:370)analysis of variance(cid:371) if we are looking at.
