33121 - Review of oneway ANOVA Kristin Sainani Ph.D.

Info iconThis preview shows pages 1–7. Sign up to view the full content.

View Full Document Right Arrow Icon
Review of one-way ANOVA Kristin Sainani Ph.D. http://www.stanford.edu/~kcobb Stanford University Department of Health Research and Policy
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
ANOVA for comparing means between  more than 2 groups
Background image of page 2
The F-distribution A ratio of variances follows an F-distribution: 2 2 2 2 0 : : within between a within between H H σ = The F-test tests the hypothesis that two variances are equal. F will be close to 1 if sample variances are equal. m n within between F , 2 2 ~
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
How to calculate ANOVA’s by  hand… Treatment 1 Treatment 2 Treatment 3 Treatment 4 y 11 y 21 y 31 y 41 y 12 y 22 y 32 y 42 y 13 y 23 y 33 y 43 y 14 y 24 y 34 y 44 y 15 y 25 y 35 y 45 y 16 y 26 y 36 y 46 y 17 y 27 y 37 y 47 y 18 y 28 y 38 y 48 y 19 y 29 y 39 y 49 y 110 y 210 y 310 y 410 n =10 obs./group k =4 groups The group means 10 10 1 1 1 = = j j y y 10 10 1 2 2 = = j j y y 10 10 1 3 3 = = j j y y 10 10 1 4 4 = = j j y y The (within) group variances 1 10 ) ( 10 1 2 1 1 - - = j j y y 1 10 ) ( 10 1 2 2 2 - - = j j y y 1 10 ) ( 10 1 2 3 3 - - = j j y y 1 10 ) ( 10 1 2 4 4 - - = j j y y
Background image of page 4
Sum of Squares Within  (SSW), or Sum of Squares  Error (SSE) The (within) group variances 1 10 ) ( 10 1 2 1 1 - - = j j y y 1 10 ) ( 10 1 2 2 2 - - = j j y y 1 10 ) ( 10 1 2 3 3 - - = j j y y 1 10 ) ( 10 1 2 4 4 - - = j j y y ∑∑ = = - = 4 1 10 1 2 ) ( i j i ij y y + = - 10 1 2 1 1 ) ( j j y y = - 10 1 2 2 2 ) ( j j y y = - 10 3 2 3 3 ) ( j j y y = - 10 1 2 4 4 ) ( j j y y + + Sum of Squares Within (SSW) (or SSE , for chance e rror)
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Sum of Squares Regression (SSR) Sum of Squares Between (SSB). Variability of the group means compared to the grand mean (the variability due to the treatment). Overall mean
Background image of page 6
Image of page 7
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 24

33121 - Review of oneway ANOVA Kristin Sainani Ph.D.

This preview shows document pages 1 - 7. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online