1. Discussion 4 1/27/2015

2. Outline Orthogonal Contrast – How are the sums of squares partitioned? – How to check if they are truly contrast and orthogonal – Scheffe’s test for contrast Multiple Comparisons – How are the minimum significant differences calculated? Fixed Ranged Test Multiple – Range Test

3. Questions?

4. Orthogonal Contrast How are the sums of squares partitioned? The experiment we are analyzing – Lecture reading example: Rice seed was treated with different acids to test if the rice seedlings have different shoot dry weight (mg) (Table 4.1)

5. Orthogonal Contrast How are the sums of squares partitioned? The ANOVA

6. What group comparisons are being made? Orthogonal Contrast How are the sums of squares partitioned? ControlHClPropionicButric 3-1-1-1 0 2-1-1 0 0 1-1 1) 2) 3)

7. How are the sums of square partitioned? Examples: Orthogonal Contrast How are the sums of squares partitioned? Control Butric Propionic HCl Butric Propionic HCl Butric Propionic

8. Orthogonal Contrast How to check if they are truly contrast and orthogonal ControlHClPropionicButric 3-1-1-1 0 2-1-1 0 0 1-1 1) 2) 3) 000000 If truly a contrast then the sum of the coefficients equals 0 Sum of products 1*2 0-211 1*3 0 0-11 2*3 0 0-11 000000 If truly orthogonal then the sum of the products are equal to 0

9. Orthogonal Contrast Scheffe’s Test for contrast Reject null hypothesis if |Q| > F s To calculate Q: To calculate F s : Control HCl Propionic Butric df Trtmt F-value (α = 0.05, df trt = 3, df MSE = 16) MSE

10. Multiple Comparisons How are the minimum significant differences calculated? Least significant difference (LSD) Dunnetts test (Compare all treatments to one control) t * not the same as t Fixed Range Tests

11. Multiple Comparisons How are the minimum significant differences calculated? TukeyScheffe’s test Fixed Range Tests

12. Multiple Comparisons How are the minimum significant differences calculated? Multiple Range Tests Multiple ranged test use different minimum significant differences. The minimum significant difference depends on how far apart the means are.

13. Multiple Comparisons How are the minimum significant differences calculated? Multiple Range Tests Multiple ranged test use different minimum significant differences. The minimum significant difference depends on how far apart the means are. Duncan’s multiple range test SNK

14. Multiple Comparisons How are the minimum significant differences calculated? Multiple Range Tests Multiple ranged test use different minimum significant differences. The minimum significant difference depends on how far apart the means are. REGWQ