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

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

Review of one-way ANOVA Kristin Sainani Ph.D. http://www.stanford.edu/~kcobb Stanford University Department of Health Research and Policy

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

View Full Document
ANOVA for comparing means between  more than 2 groups
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 ~

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

View Full Document
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
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)

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

View Full Document
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
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
Ask a homework question - tutors are online