This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.View Full Document
Unformatted text preview: STANDARD DEVIATIONS FOR GROUPS AND FOR ANOVA People are sometimes mixing two different important things. The first one is the standard deviation of the sample used in STA2023 (the notations used in STA2023 was S or s .) The notation I will be using in this course is to emphasize that is it the estimate of the population standard deviation ( is the unknown population parameter which is estimated by from the sample. ) The second one is the population standard deviation estimate from the ANOVA model, which unfortunately uses exactly the same notation . This ? MS E is also supposed to be the estimate of the population standard deviation . The first one. Let us consider an example. We have a sample that consists of four ele- ments p 3 , 4 , 1 , q then X 1 3 ,X 2 4 ,X 3 1 and X 4 . The sample mean is X 2 (please see Review 1 for details.) Then our sample standard deviation looks like. d 1 n 1 n i 1 p X i X q 2 For our sample we have g f f e 1 4 1 4 i 1 p X i X q 2 c 1 3 p 3 2 q 2 p 4...
View Full Document